Table of Contents

Basic Properties of Fluids

1.1 Introduction 3

1.2 Basic fluid properties 4

1.3 Non-Newtonian fluids 6

1.3.1 The ideal plastic 7

1.3.2 Pseudoplastic 7

1.3.3 Dilatant 7

1.4 Velocity profiles 7

1.4.1 Ideal profile 7

1.4.2 Laminar flow 8

1.4.3 Turbulent flow 9

1.4.4 Swirl 9

1.5 Reynolds number 10

1.6 Flow measurement 11

1.6.1 Volumetric flow rate 11

1.6.2 Velocity 11

1.6.3 Point velocity 11

1.6.4 Mean flow velocity 11

1.7 Mass flow rate 13

1.8 Multi-phase flows 13

1.8.1 Rangeability 13

Objectives

When you have completed this chapter you should be able to:

• Describe the basic concept of viscosity
• Define the differences between Newtonian and non-Newtonian fluids including plastic, pseudoplastic and dilatant
• Describe the differences between ideal, laminar and turbulent flow profiles and how the Reynolds number may be used to describe their behaviour
• Examine the problems of swirl
• List the various parameters used to define flow measurement

1.1 Introduction

Over the last fifty years, the importance of flow measurement has grown, not only because of its widespread use for accounting purposes, such as the custody transfer of fluid from supplier to consumer, but also because of its application in manufacturing processes. Throughout this period, performance requirements have become more stringent — with unrelenting pressure for improved reliability, accuracy, linearity, repeatability and rangeability.

These pressures have been caused not only by major changes in manufacturing processes, but also because of several dramatic circumstantial changes, such as the increase in the cost of fuel and raw materials and the need to minimise pollution. Industries involved in flow measurement and control include:

• food and beverage;
• medical;
• mining and metallurgical;
• oil and gas transport;
• petrochemical;
• pneumatic and hydraulic transport of solids;
• power generation;
• pulp and paper; and
• water distribution.

Fluid properties can vary enormously from industry to industry. The fluid may be toxic, flammable, abrasive, radio-active, explosive or corrosive; it may be single-phase (clean gas, water or oil) or multi-phase (e.g. slurries, wet steam, unrefined petroleum, or dust laden gases). The pipe carrying the fluid may vary from less than 1 mm to many metres in diameter. The fluid temperature may vary from close to absolute zero to several hundred degrees centigrade, and the pressure may vary from high vacuum to many atmospheres.

Because of this large variation in fluid properties and flow applications, many flowmeter techniques have been developed with each suited to a particular area. However, of the numerous flow metering techniques that have been proposed in the past, only a few have found widespread application and no one single flowmeter can be used for all applications.

1.2 Basic fluid properties

One of the most important primary properties of a fluid (liquid or gas) is its viscosity — its resistance to flow or to objects passing through it.

In essence viscosity is an internal frictional force between the different layers of the fluid as they move past one another. In a liquid, this is due to the cohesive forces between the molecules whilst in a gas it arises from collisions between the molecules.

Different fluids possess different viscosities: treacle is more viscous than water; and gearbox oil (SAE 90) is more viscous than light machine oil (e.g. 3-in-1).

If the fluid is regarded as a collection of moving plates, one on top of the other, then the viscosity is a measure of the resistance offered by a layer between adjacent plates.

Figure 1.1 shows a thin layer of fluid sandwiched between two flat metal plates — the lower plate being stationary and the upper plate moving with velocity V. The fluid directly in contact with each plate is held to the surface by the adhesive force between the molecules of the fluid and those of the plate. Thus the upper surface of the fluid moves at the same speed V as the upper plate whilst the fluid in contact with the stationary plate remains stationary. Since the stationary layer of fluid retards the flow of the layer just above it and this layer, in turn, retards the flow of the next layer, the velocity varies linearly from 0 to V, as shown.

In this manner, the fluid flows under the action of a shear stress due to the motion of the upper plate. It is also clear that the lower plate exerts an equal and opposite shear stress in order to satisfy a ‘no-slip’ condition at the lower stationary surface. It follows, therefore, that the shear stress at any point in the flow, is directly proportional to the velocity gradient or ‘shear rate’. Thus:

            Shear stress ∝ Shear gradient

or:        Shear stress = K. Shear gradient

where: K is the dynamic viscosity (μ) measured in Pascal-Seconds (Pa.s).

In the cgs system, dynamic viscosity was formerly measured in poise, centipoise or (in the case of gases) micropoise where:

1 Pa.s = 10 poise

The viscosity of a fluid varies with changes in both pressure and temperature. To this effect, Table 1.1 lists the viscosity of various fluids at specified temperatures — the viscosity of liquids such as motor oil, for example, decreasing rapidly as temperature increases.

Surprisingly, pressure has less effect on the viscosity of gases than on liquids.

A pressure increase from 0 to 70 bar (in air) results in only an approximate 5% increase in viscosity. However, with methanol, for example, a 0 to 15 bar increase results in a 10-fold increase in viscosity. Some liquids are more sensitive to changes in pressure and some less.

The term dynamic viscosity is used to distinguish it from kinematic viscosity. Kinematic viscosity is density related viscosity and is given by:

v = μ / ρ

where:

v = kinematic viscosity measured in m²/s;

μ = dynamic viscosity measured in Pa.s; and

ρ = density of the liquid (kg/m³).

Kinematic viscosity was formerly measured in stokes or centistokes where:

1 stoke = 1/10⁴ m²/s

1.3 Non-Newtonian fluids

The majority of fluids used in engineering systems exhibit Newtonian behaviour in that, for a given value of pressure and temperature, the shear stress is directly proportional to the shear rate. Thus, if the shear stress is plotted against shear rate the result is a straight line passing through the origin (Figure 1.2).

There are, however, certain fluids that do not exhibit this behaviour. Examples include: tar, grease, printers’ ink, colloidal suspensions, hydrocarbon compounds having long-chain molecules, and polymer solutions.

1.4 Velocity profiles

One of the most important fluid characteristics affecting flow measurement is the shape of the velocity profile in the direction of flow.

1.4.1 Ideal profile

In a frictionless pipe in which there is no retardation at the pipe walls, a flat ‘ideal’ velocity profile would result (Figure 1.3) in which all the fluid particles move at the same velocity.

However, we have already seen that real fluids do not ‘slip’ at a solid boundary but are held to the surface by the adhesive force between the fluid molecules and those of the pipe. Consequently, at the fluid/pipe boundary, there is no relative motion between the fluid and the solid.

At low flow rates the fluid particles will move in straight lines in a laminar manner — with each fluid layer flowing smoothly past adjacent layers with no mixing between the fluid particles in the various layers. As a result the flow velocity increases from zero, at the pipe walls, to a maximum value at the centre of the pipe and a velocity gradient exists across the pipe.

1.4.2 Laminar flow

The shape of a fully developed velocity profile for such a laminar flow is parabolic, as shown in Figure 1.4, with the velocity at the centre being equal to twice the mean flow velocity. Clearly, this concentration of velocity at the centre of the pipe can compromise the flow computation if not corrected for.

1.4.3 Turbulent flow

For a given pipe and liquid, as the flow rate increases, the paths of the individual particles of fluid are no longer straight but intertwine and cross each other in a disorderly manner so that thorough mixing of the fluid takes place. This is termed turbulent flow.

As shown in Figure 1.5, the velocity profile for turbulent flow is flatter than for laminar flow and thus closer approximates to the ‘ideal’ or ‘one dimensional’ flow.

1.4.4 Swirl

Turbulent flow should not be confused with swirl or disturbed flow that can cause an asymmetric flow profile (Figure 1.6). Obstructions in the pipe, such as elbows, steps, control valves, and T-pieces, can produce vortices or swirls in the fluid flow that can severely affect measurement accuracy. Indeed, such disturbances can have an important bearing on accuracy for as much as 40 pipe diameters ahead of the measuring device.

The effects of swirls can be minimised by the use of a flow conditioner, or straightener in the upstream line.

1.5 Reynolds number

The onset of turbulence is often abrupt and in order to be able to predict the type of flow present in a pipe, for any application, use is made of the Reynolds number, Re — a dimensionless number given by:

Re = ρvD/μ

where:

ρ = density of fluid (kg/m³)

μ = viscosity of fluid (Pa.s)

v = mean flow velocity (m/s)

D = diameter of pipe (m).

Osborne Reynolds (1842-1912) showed that irrespective of the pipe diameter, type of fluid, or velocity, then the flow is:

Laminar:                 Re < 2000

Transitional: Re 2000 – 4000

Turbulent:                 Re > 4000

From the foregoing it is seen that, in addition to viscosity, Re is also dependent on density.

Since most liquids are pretty well incompressible, the density varies only slightly with temperature. However, for gases, the density is strongly dependent on the temperature and pressure in which (for ideal gas):

PV = mRT

where:

P = pressure (Pa);

V = volume of the gas (m³);

T = temperature (K)

m = number of moles; and

R = universal gas constant (8,315 J/(mol.K))

Since:

ρ = m/V = P/RT

Most gases may be considered ideal at room temperatures and low pressures.

Both laminar and turbulent flow profiles require time and space to develop. At an entrance to a pipe, the profile may be very flat — even at low Re. And it may stay laminar, for a short time, even at high Re.

1.6 Flow measurement

In flow measurement a number of parameters can be used to describe the rate at which a fluid is flowing:

1.6.4 Mean flow velocity

The mean flow velocity,v̄, can be obtained by measuring the volumetric flowrate, Q, and dividing it by the cross-sectional area of the pipe, A:

v̄ = Q/A (m/s)

Alternatively, if the velocity profile is known the mean flow velocity v̄ can be obtained by averaging the velocity over the velocity profile, giving equal weighing to equal annular regions.

An example of the calculation of the mean velocity of the flow conduit by area-weighting point-velocity measurements is illustrated in Figure 1.7, in which a number of velocity bands are scaled across the cross-sectional area of a 320 mm diameter conduit.

The mean velocity can be determined using standard averaging techniques in which the velocities of each band are summed and then divided by the number of bands:

V_AV = (V_A + V_B + V_C + V_D)/4 = 108.25 cm/s.

In the area-weighted technique, the scaled areas, velocities and the products of each area, times its local velocity, are tabulated for each velocity band (Table 5). The area-weighted mean velocity is calculated by summing the velocity-area products, and dividing the sum of the cross-sectional area of the flow conduit.

Band	Radius (cm)	Velocity (cm/s)	Area (cm2)	Vn . An
A	4.0	130	50.26	6533
B	8.0	120	150.80	18096
C	12.0	107	251.33	26892
D	16.0	76	351.86	26741
Total			804.25	78262

The error thus obtained using the standard averaging technique is:

1.7 Mass flow rate

Most chemical reactions are largely based on their mass relationship and, consequently, in order to control the process more accurately, it is often desirable to measure the mass flow of the product. The mass flow rate, W, gives the total mass of fluid flowing at any instant in time. A knowledge of volume flow rate, Q and the fluid density, ρ, determines the mass flow rate from:

W = Q. ρ (kg/s)

Some flowmeters, such as Coriolis meters, measure the mass flow directly. However, in many cases, mass flow is determined by measuring the volumetric flow and the density and then calculating the mass flow as shown above. Sometimes the density is inferred from the measurement of the pressure and temperature of the fluid. This type of measurement is referred to as the inferred method of measuring mass flow.

1.8 Multi-phase flows

For multi-phase flows, the mass or volume flow rate of one of the constituents is often of interest. For example, in the case of a slurry, the mass flow rate of the solid phase is usually the required variable.

1.8.1 Rangeability

Rangeability is the ratio of maximum to minimum flow. Rangeability is used to give a relative measure of the range of flows that can be controlled.

Table of Contents

Positive Displacement Meters

2.1 Introduction 3

2.2 Sliding vane 3

2.2.1 Typical Applications 4

2.2.2 Advantages 4

2.2.3 Disadvantages 4

2.3 Oval gear meters 5

2.3.1 Advantages 6

2.3.2 Disadvantages 6

2.4 Lobed impeller 6

2.4.1 Typical applications 7

2.4.2 Advantages 7

2.4.3 Disadvantages 7

2.5 Oscillating piston 7

2.5.1 Typical applications 8

2.5.2 Advantages 8

2.5.3 Disadvantages 9

2.6 Nutating disc 9

2.7 General summary 9

Chapter 2

Positive Displacement Meters

Objectives

When you have completed this chapter you should be able to:

• Describe the basic principle of direct volume totalizers
• Explain the working principle of the sliding vane, oval gear, lobed impeller, oscillating piston and nutating disc displacement meters, together with their advantages and disadvantages

2.1 Introduction

Positive displacement meters (sometimes referred to as direct volumetric totalizers) all operate on the general principle in which defined volumes of the medium are separated from the flow stream and moved from the inlet to the outlet in discrete packages.

totalising the number of packages provides the total volume passed and the total volume passed in a given time provides the flow rate, e.g. litres/min.

Because they pass a known quantity, they are ideal for certain fluid batch, blending and custody transfer applications. They give very accurate information and are generally used for production and accounting purposes.

Many different configurations of positive displacement meters are available and this chapter discusses some of the most popular types.

2.2 Sliding vane

The sliding vane meter is one of the highest performance liquid positive displacement meters. In its simplest form it comprises a rotor assembly fitted with four spring-loaded sliding vanes so that they make constant contact with the cylinder wall (Figure 2.1). The rotor is mounted on a shaft which is eccentric to the centre of the meter chamber.

As liquid enters the measuring chamber the pressure on the exposed portion of vane 1 causes the rotor to turn. While the rotor turns on its shaft, vane 2 moves to seal off the inlet port — rotating to occupy the position formerly occupied by vane 1.

This process is repeated, without pulsations, as the vanes move around the measuring chamber — with ‘packets’ of fluid trapped and passed to the outlet manifold as a discrete known quantities of fluid.

A mechanical counter register or electronic ;pulse counter is attached to the shaft of the rotor so that flow volume is directly proportional to shaft rotation.

Close tolerances and carefully machined profile of the casing ensures the blades are guided smoothly through the measuring crescent to give high performance.

2.3 Oval gear meters

The Oval gear flowmeter comprises two identical precision moulded oval rotors which mesh together by means of gear teeth around the gear perimeter. These oval rotors rotate on stationary shafts which are fixed within the measuring chamber.

The meshed gears seal the inlet from the outlet flow, developing a slight pressure differential across the meter that results in movement of the oval rotors.

When in the position shown in Figure 2. 2 (a) Gear A receives torque from the pressure difference while the net torque on Gear B is zero; (b) Gear A drives Gear B; (c) as Gear B continues to rotate it traps a defined quantity of fluid until in this position, the net torque on Gear A is zero and Gear B receives torque from the pressure difference; (d) Gear B drives Gear A and a defined quantity of fluid is passed to the outlet. This alternate driving action provides a smooth rotation of almost constant torque without dead spots.

With flow through the meter, the gears rotate and trap precise quantities of liquid in the crescent shaped measuring chambers. The total quantity of flow for one rotation of the pair of oval gears is four times that of the crescent shaped gap and the rate of flow is proportional to the rotational speed of the gears. Because the amount of slippage between the oval gears and the measuring chamber wall is minimal, the meter is essentially unaffected by changes in viscosity and lubricity of the liquids.

An output shaft is rotated in direct proportion to the oval gears by means of a powerful magnetic coupling. Oval gear meters find widespread use in the measurement of solvents with close tolerances ensuring that leakage is minimised.

The major disadvantage of this meter is that the alternate driving action is, in fact, not constant and, as a result, the meter introduces pulsations into the flow.

Further, the viscosity of the fluid can affect the leakage, or slip flow. If the meter is calibrated on a particular fluid, it will read marginally higher should the viscosity increase.

Newer designs of this type of meter use servomotors to drive the gears. This eliminates the pressure drop across the meter and also the force required to drive the gear. This mainly applies to smaller sized meters and significantly increases the accuracy at low flows.

2.4 Lobed impeller

Similar in manly respects to the Oval meter, the lobed impeller type meter (Figure 2.3) is mainly used for gases. The meter comprises two high precision lobed impellers, which are geared externally and which rotate in opposite directions within the enclosure. A known volume of gas is transferred for each revolution.

2.5 Oscillating piston

The oscillating or rotating piston meter consists of a stainless steel housing and a rotating piston as shown in Figure 2.4. The only moving part in the measuring chamber is the oscillation piston which moves in a circular motion.

In order to obtain an oscillating motion, movement of the piston is restricted in two ways. First, the piston is slotted vertically to accommodate a partition plate which is fixed to the chamber. This plate prevents the piston from spinning around its central axis and also acts as a seal between the inlet and outlet ports of the chamber.

Secondly, the piston has a centre vertical pin which confines the piston’s movement to a circular track which is part of the chamber.

Differential pressure across the meter causes the piston to sweep the chamber wall in the direction of flow — displacing liquid from the inlet to the outlet port in a continuous stream.

The openings for filling and discharging are located in its base and thus in Figure 2.5 (a), areas 1 and 3 are both receiving liquid from the inlet port (A) and area 2 is discharging through the outlet port (B).

In Figure 2.5 (b), the piston has advanced and area 1, which is connected to the inlet port, has enlarged; and area 2, which is connected to the outlet port, has decreased, while area 4, is about to move into position to discharge through the outlet port.

In Figure 2.5(c), area 1 is still admitting liquid from the inlet port, while areas 2 and 3 are discharging through the outlet port.

In this manner known discrete quantities of the medium have been swept from the inlet port to the outlet port.

2.6 Nutating disc

The term nutation is derived from the action of a spinning top whose axis starts to wobble and describe a circular path as the top slows down.

In a nutating disc type meter the displacement element is a disc that is pivoted in the centre of a circular measuring chamber (Figure 2.6). The lower face of the disc is always in contact with the bottom of the chamber on one side, and the upper face of the disc is always in contact with the top of the chamber on the opposite side. . The chamber is thus divided into separate compartments of known volume.

Liquid enters through the inlet connection on one side of the meter and leaves through an outlet on the other side — successively filling and emptying the compartments and moving the disc in a nutating motion around a centre pivot.

A pin attached tot the disc’s pivot point drives the counter gear train.

Although there are inherently more leakage paths in this design, the nutating disk meter is also characterised by its simplicity and low-cost. It tends to be used where longer meter life is required rather than high performance, e.g. domestic water service. The meter is also suitable for use under high temperatures and pressures.

2.7 General Summary

Because of their high accuracy, positive displacement meters are used extensively in liquid custody transfer applications where duty is applicable on such commodities as petrol, wines, and spirits.

In use, some of the following application limitations should be noted:

— Owing to the mechanical contact between the component parts, wear and tear is a problem. In general, therefore, positive displacement meters are primarily suited for clean, lubricating and non-abrasive applications.
— In some cases, filters (down to 10 µm) may be required to filter debris and clean the fluid before the meter. Such filters require regular maintenance. If regular maintenance is not carried out, the added pressure drop may also need to be considered.
— Their working life also depends on the nature of the fluid being measured, especially in regard to solids build-up and the media temperature.
— Positive displacement meters are an obstruction to the flow path and consequently produce an unrecoverable pressure loss.
— Because many positive displacement meters have the same operating mechanisms as pumps, they may be driven by a motor and used as dosing or metering pumps.
— One of the drawbacks of the positive displacement meter is its high differential pressure loss. This, however may be reduced by measuring the differential pressure across the meter and then driving it with a motor that is controlled by a feedback system.
— Positive displacement meters are limited at both high and low viscosities. Errors can occur due to leakage (slippage) around the gears or pistons. Slippage may be reduced by using viscous fluids which have the ability to seal the small clearances. However if the fluid is too viscous then it can coat the inner chambers of the meter and reduce the volume passed — causing reading errors. Thus, whilst low viscosities limit the use at low flows (due to increased slippage), high viscosities limit the use at high flows due to the high pressure loss.
— If slippage does occur, and is calibrated for, it can change with temperature as the viscosity varies.
— Positive displacement meters can be damaged by over-speeding.
— In certain cases (e.g. the oval gear meter) positive displacement meters give rise to pulsations. This may inhibit the use of this type of meter in certain applications.
— Positive displacement meters are primarily used for low volume applications and are limited when high volume measurement is required.

Table of contents

Inferential Meters

3.1 Introduction 3

3.2 Turbine meter 3

3.2.1 K-factor 4

3.2.2 Selection and sizing 5

3.2.3 Application limitations 5

3.2.4 Advantages 6

3.2.5 Disadvantages 6

3.3 Woltman meter 7

3.4 Propeller type 8

3.5 Impeller meters 9

3.6 Installation recommendations 10

Chapter 3

Inferential Meters

Objectives

When you have completed this chapter you should be able to:

• Explain the working principle of a inferential meter
• Compare the advantages and disadvantages of the turbine meter, horizontal and vertical Woltman meters, propeller meters and impeller meters

3.1 Introduction

Inferential meters, loosely referred to as ‘turbine meters’, are indirect volumetric totalizers, in which packages of the flowing media are separated from the flow stream and moved from the input to the output. However, unlike the positive displacement meter, the enclosed volume is not geometrically defined.

Inferential meters have rotor-mounted blades in the form of a vaned rotor or turbine which is driven by the medium at a speed proportional to the flowrate. The number of rotor revolutions is proportional to the total flow and is monitored by either a gear train or by a magnetic or optical pick-up.

Competing with the positive displacement meter for both accuracy and repeatability, the turbine flowmeter is used extensively in custody transfer applications on such products as crude oil or petroleum.

3.2 Turbine meter

Available in sizes from 5 to 600 mm, the turbine meter usually comprises an axially mounted bladed rotor assembly (the turbine) running on bearings and mounted concentrically within the flow stream by means of upstream and downstream support struts (Figure 3.1). The support assembly also often incorporates upstream and downstream straightening sections to condition the flow stream.

The rotor is driven by the medium (gas or liquid) impinging on the blades.

The simplest method of measuring the rotor speed is by means of a magnet, fitted within the rotor assembly, that induces a single pulse per revolution, in an externally mounted pick-up coil. In order to improve the resolution, the externally mounted pick-up coil is integrated with a permanent magnet and the rotor blades are made of a magnetically permeable ferrous material. As each blade passes the pick-up coil, it cuts the magnetic field produced by the magnet and induces a voltage pulse in the coil.

To improve the resolution even further, especially in large turbine meters (200 mm and above) where the rotor operates at much lower angular velocities, small magnetic bars are inserted in a non-magnetic rim that is fitted around the blades. This modification can improve the pulse resolution by as much as ten times.

3.2.1 K-factor

The number of pulses produced per unit volume is termed the K-factor.

Ideally, the meter would exhibit a linear relationship between the meter output and the flow rate — a constant K-factor. In reality, however, the driving torque of the fluid on the rotor is balanced by the influence of viscous, frictional and magnetic drag effects.

Since these vary with the flowrate, the shape of the K-factor curve (Figure 3.2) depends on viscosity, flowrate, bearing design, blade edge sharpness, blade roughness and the nature of the flow profile at the rotor leading edge. In practice, all these influences have differing effects on the meter linearity and thus all turbine meters, even from the same manufacturing batch, should be individually calibrated.

The linear relationship of the K-factor is confined to a flow range of about 10:1 — sometimes extending up to 20:1.

At low flows, the poor response of the meter is due to bearing friction, the effect of fluid viscosity and magnetic drag on the rotor due to the use of a magnetic pick-off. It is possible to extend the lower limit of the meter’s response by using, for example, a radio pick-off coupled with the use of high quality rotor bearings. The humping section of the curve flattens as the viscosity decreases — with resultant increase in accuracy.

3.3 Woltman meter

The Woltman meter, used primarily as a water meter, is very similar in basic design to the turbine meter. The essential difference is that the measurement of rotation is carried out mechanically using a low friction gear train connecting the axle to the totalizer.

The Woltman meter is available in two basic designs — one with a horizontal turbine (Figure 3.3) and one with a vertical turbine (Figure 3.4). The vertical design offers the advantage of minimal bearing friction and therefore a higher sensitivity resulting in a larger flow range. Whilst the pressure drop of the vertical turbine meter is appreciably higher, because of the shape of the flow passage, it is widely used as a domestic water consumption meter.

In may designs, an adjustable regulating vane is used to control the amount of deflection and thus adjust the meter linearity.

3.4 Propeller type

In the propeller type flowmeter (Figure 3.5) the body of the meter is positioned above the flow path and only the propeller is in the flow line.

With the bearings thus outside of the main flow, the effects of contamination from dirty liquids is eliminated or reduced to a minimum. Further, the use of a three-bladed propeller with large clearances between each blade, enables particles in suspension to pass with ease.

Another advantage of this type of meter is that manufacturing costs are significantly reduced. In addition, the transmitter and all working parts can be removed and replaced in a few minutes, without breaking the pipeline.

On the negative side performance is correspondingly lower with the linearity typically ±2% and repeatability typically ±1% of full scale.

3.5 Impeller meters

The impeller type meter, typified by the Pelton wheel turbine (Figure 3.6) is able to measure extremely low flow rates down to 0,02 litres/min, coupled with a turn-down ratio of up to 50:1.

The incoming low velocity fluid is concentrated into a jet that is directed onto a lightweight rotor suspended on jewel bearings. The rotational speed is linear to flow rate and is detected by means of ferrite magnets located in the rotor tips that induces voltage pulses in a sensing coil. One drawback is that the nozzle can cause a rather large pressure drop.

A variation of this design, shown in Figure 3.7, is the insertion type impeller meter in which the main bearing is again located out of the main flow stream and thus provides only a minimal pressure drop. One of the main advantages of this type of sensor is that the same meter can be used on pipe sizes ranging from 75 mm to 1 m diameter. This technique also allows its use in a ‘hot tap’ mode whereby it may be removed and replaced on high pressure lines without the necessity for a shutdown.

3.6 Installation recommendations

In order to reap the benefits of high accuracy the following installation practices should be observed:

— At least 10 pipe diameters of straight approach and 5 pipe diameters of straight outlet piping are required.
— Turbines should never be subjected to a swirling flow
— Flow must not contain any solids — especially fibre.
— Do not exceed the measuring range.
— A turbine for liquids should never be subjected to gas flow (danger of over-speeding)
— Never clean with compressed air.

TABLE OF CONTENTS

4.1 Introduction 3

4.2 Primary devices 3

4.2.1 Vortex flowmeters 3

4.2.1.1 Formation of vortices 4

4.2.1.2 Strouhal factor 5

4.2.1.3 Shedder design 6

4.2.2 Vortex precession 7

4.2.3 Fluidic flowmeter 8

4.3 Sensors 9

4.3.1 Thermal sensing 9

4.3.2 Mechanical sensors 10

4.3.3 Piezoelectric sensor 11

4.3.4 Capacitive sensor 12

4.3.5 Strain gauge sensor 12

4.3.6 Ultrasonic sensing 12

4.4 Application guidelines for vortex flowmetering 13

4.4.1 Viscosity 13

4.4.2 Low flow 13

4.4.3 Batching operations 14

4.4.4 Rangeability 14

4.4.5 Process noise 15

4.4.6 Accuracy 15

4.4.7 Effects of erosion 16

4.4.8 Low density gases 16

4.4.9 Orientation 16

4.4.10 Pressure drop 16

4.4.11 Multiphase flow 16

4.4.12 Wet steam 17

4.4.13 Material build-up 18

4.4.14 Piping effects 18

4.4.15 Mass measurement 19

4.5 Avoiding problems 19

Chapter 4

Oscillatory Flow Meters

Objectives

When you have completed this chapter you should be able to:

• Explain the principle of vortex shedding
• Describe the relationship between Reynolds number and Strouhal factor
• Compare the differences between various bluff bodies used in vortex meters
• List the different technologies used to detect vortex oscillations
• Describe the Swirlmeter
• Outline the principle used in the fluidic meter
• Apply the various guidelines related to oscillatory technology including the effects of viscosity, low flow, batching, rangeability, process noise, erosion, low density gases, orientation, wet steam, and piping effects.

4.1 Introduction

Oscillatory flow measurement systems involve three primary metering principles: vortex, vortex swirl (precession) and Coanda effect.

In all three, the primary device generates an oscillatory motion of the fluid whose frequency is detected by a secondary measuring device to produce an output signal that is proportional to fluid velocity.

4.2 Primary devices

4.2.1 Vortex flowmeters

Vortex flowmeters have been used for industrial flow measurement since the late 1960s. However, only in recent years have the original limitations been overcome — allowing this method to come of age.

Vortex meters are based on the phenomenon known as vortex shedding that takes place when a fluid (gas, steam or liquid) meets a non-streamlined obstacle — termed a bluff body. Because the flow is unable to follow the defined contours of the obstacle, the peripheral layers of the fluid separate from its surfaces to form vortices in the low pressure area behind the body (Figure 4.1). These vortices are swept downstream to form a so-called Karman Vortex Street. Vortices are shed alternately from either side of the bluff body at a frequency that, within a given Reynolds number range, is proportional to the mean flow velocity in the pipe.

In vortex meters, the differential pressure changes that occur as the vortices are formed and shed, are used to actuate the sealed sensor at a frequency proportional to the vortex shedding.

4.2.1.1 Formation of vortices

At very low velocities — the laminar flow region (Figure 4.2(a)) — the fluid flows evenly around the body without producing turbulence. As the fluid velocity increases the fluid tends to shoot past the body, leaving a low pressure region behind it (Figure 4.2(b)). As the fluid velocity is increased even further this low pressure region begins to create a flow pattern as shown in Figure 4.2(c) — the beginning of the turbulent flow region. This action momentarily relieves the pressure void on one side of the low pressure region and the fluid forms into a vortex. The interaction of the vortex with the main stream fluid releases it from the surface of the body and it travels on downstream. Once released, the low pressure region shifts towards the other rear side of the body to form another vortex. This process is repeated, resulting in the release of vortices from alternate sides of the bluff body as was illustrated in Figure 4.1.

Vortex shedding occurs naturally throughout nature and can be observed in the whistling tone that the wind produces through telephone wires or in a flag waving from a flagpole. Because the flagpole acts as a bluff body, vortex shedding occurs. As the wind speed increases the rate of vortex shedding increases and causes the flag to wave faster.

4.2.1.2 Strouhal factor

In 1878 Strouhal observed that the frequency of oscillation of a wire, set in motion by a stream of air, is proportional to the flow velocity.
Strouhal showed that:

f= St.V/d

where:

f = vortex frequency (Hz)
d = diameter of the bluff body (m)
V = velocity of liquid(m/s); and
St = Strouhal factor (dimensionless).

Unlike other flow sensing systems, because the vortex shedding frequency is directly proportional to flow velocity, drift is not a problem as long as the system does not leave its operating range. Further, the frequency is unaffected by changes in pressure, temperature and fluid density, as long as Re stays within certain limits. Consequently, the same vortex meter may be used for steam, gas and liquids — although not necessarily over the same volumetric flow velocity ranges.

In reality, the Strouhal factor is not a constant but, as illustrated in Figure 4.3, varies according to the shape of the bluff body and the Reynolds number. The ideal vortex flowmeter would, therefore, have a bluff body shape that features a constant Strouhal number over as wide a measuring range as possible.

Meters differ only in the shape of the bluff body and in the sensing methods used — with each manufacturer claiming specific advantages. Some of the body shapes are shown in Figure 4.4.

4.2.1.3 Shedder design

Cylindrical bodies
Early bluff bodies were cylindrical. However, because the vortex release point fluctuated backwards and forwards, depending on flow velocity, the frequency was not exactly proportional to velocity.

Delta-shaped bodies
The delta-shaped shedder has a clearly defined vortex shedding edge and tests (including those carried out by NASA) indicate that the delta shape provides excellent linearity. Accuracy is not affected by pressure, viscosity or other fluid conditions. Many variations of the Delta shape exist and are in operation.

Rectangular bodies
Current research indicates that this body shape produces considerable fluctuation in linearity in varying process densities.

Two-part bodies
In this configuration, the first body is used to generate the vortices and the second body to measure them.

The two part body generates a strong vortex (hydraulic amplification) that requires the use of less complicated sensors and amplifiers. On the negative side, the pressure loss is almost doubled.

4.2.2 Vortex precession

The ‘Swirlmeter’, a patented technology with manufacturing rights ceded to Bailey-Fischer & Porter, is based on the principle known as vortex precession.

The inlet of the Swirlmeter (Figure 4.5) uses guide vanes, whose shape is similar to a turbine rotor, to force the fluid entering the meter to spin about the centreline. This swirling flow then passes through a venturi, where it is accelerated, and then expanded in an expansion chamber.

The expansion changes the direction of the axis about which the swirl is spinning — moving the axis from a straight to helical path. This spiralling vortex is called vortex precession. A flow straightener is used at the outlet from the meter. This isolates the meter from any downstream piping effects that may affect the development of the vortex.

Above a given Reynolds number, the vortex precession frequency, which lies between 10 and 1500 Hz and is measured with a piezoelectric sensor, is directly proportional to the flow rate.

Although the Swirlmeter can be used with both gases or liquids, it finds its main application as a gas flowmeter.

The major advantage of the vortex precession technique over that of vortex shedding is that it has a very much lower susceptibility to the flow profile and hence only three diameters of straight line are required upstream of the meter. In addition, the Swirlmeter features: linear flow measurement; rangeability between 1:10 and 1:30; no moving parts; and installation at any angle in the pipeline.

Because of the higher tolerance in manufacture of this type of meter, it is more expensive then comparative meters.

4.2.3 Fluidic flowmeter

The fluidic flowmeter is based on the wall attachment or ‘Coanda’ effect. Wall attachment occurs when a boundary wall is placed in proximity to a fluid jet — causing the jet to bend and adhere to the wall.

This effect is caused by the differential pressure across the jet, deflecting it towards the boundary (Figure 4.6). Here it forms a stable attachment to the wall, which is little affected by any downstream disturbances.

In the fluidic meter (Figures 4.7 and 4.8), the flow stream attaches itself to one of the side walls — with a small portion of the flow fed back through a passage to a control port (Figure 4.7). This feedback, diverts the main flow to the opposite side wall where the same feedback action is repeated (Figure 4.8).

The result is a continuous oscillation of the flow between the sidewalls of the meter body whose frequency is linearly related to the fluid velocity.

The main benefit offered by the fluidic meter is that feedback occurs at much lower Reynolds numbers and thus it may be used with fairly viscous media. In addition, since fluidic oscillators have no moving parts to wear with time, there is no need for recalibration during its expected lifetime.

The main drawback of the fluidic oscillator is its relatively high pressure loss and its poor performance at low flowrates.

4.3 Sensors

In the vortex meter, the magnitude of each vortex is roughly proportional to the square of the flow velocity. Consequently, the dynamic sensitivity range of the vortex sensor needs to be quite large. Thus, for a turn down ratio of 1:50 in flow velocity, the magnitude of the vortex signal would vary by 1:2500. This leads to very small signal levels at the low end of the measuring range.

Whilst the vortex shedding frequency decreases as the size of the bluff body or meter increases, the signal strength falls off as the size decreases — thus, generally, limiting the meter size to within the range of 15 – 200 mm bore.

There are several methods available for measuring the vortex frequency. There is no sensor currently available that will suit all operating conditions.

4.3.1 Thermal sensing

Thermal sensors (Figure 4.9) make use of electrically heated thermistors (heat-sensitive semi-conductor resistors) having a high temperature coefficient and a rapid time response. As the vortices are shed, on alternate sides of the fluff body, heat is convected away from the preheated elements — resulting in a change in resistance that is in phase with the shedding frequency.

Disadvantages

• Depending on their location, thermistors are sensitive to dirt.
• Generally incapable of withstanding temperature shocks.
• Frequency limited to about 500 Hz.

Application
Mainly for clean gas — although may also be used for liquids.

4.3.2 Mechanical sensors

Sometimes called a shuttle ball sensor, a magnetic ball or disc moves from side to side, under the influence of the vortices, along a lateral bore that connects both sides of the bluff body (Figure 4.10). This movement is detected by a magnetic pick-up.

Problems

• Easily blocked by dirt
• In saturated steam the movement of the ball or disc may be slowed by condensation.
• Condensed water can cause the ball or disc to adhere to one side or other.

Application
Warm water, steam, or low temperature liquids.

4.3.3 Piezoelectric sensor

The alternating vortices, shed on each side of the shedder, act on two sealing diaphragms mounted on each side of the sensor (Figure 4.11). The space between the diaphragms is filled with a non-conductive fluid that transmits the alternating high and low pressures to a piezoelectric crystal.

The piezo elements produce a voltage output that is proportional to the applied pressure.

Whilst piezo-ceramic materials produce a high output for a given pressure (a high ‘coupling factor’) they have a limited operating temperature range (about 250 °C).

The piezoelectric material Lithium Niobate (LiNbO₃) offers only medium coupling factors but can be operated at temperatures above 300 °C.

Generally, piezoelectric materials are unsuitable for temperatures below -40 °C since below this point, the piezoelectric effect becomes too small.

Because the piezoelectric element produces an output that is affected by movement or acceleration, it is also sensitive to external pipe vibration. This problem can be overcome by using a second piezoelectric element to measure the vibration and use it in a compensating circuit to ensure that only the clean vortex shedding frequency is obtained.

Problems

• Possibility of diaphragm rupture.
• Generally insensitive in low measuring ranges.
• Sensitive to external pipe vibrations.
• Sensitive to pressure shocks.

Application
Mainly liquids but also for gas and low pressure steam.

4.3.6 Ultrasonic sensing

An ultrasonic detector system (Figure 4.12) makes use of an ultrasonic transmitter and receiver placed behind the bluff body. The vortices modulate the ultrasonic beam and the resultant output is the vortex signal.

This sensor system has a very good turn down ratio and, since there is no mass associated with the sensor that would experience a force under vibration, the sensor is virtually vibration insensitive.

Problems

• Extraneous sound sources can affect measurements.
• Different constructions required for different applications.

Application
Low cost system for gases or liquids.

4.4 Application guidelines for vortex flowmetering*

In general, a vortex shedding flowmeter works well on relatively clean low viscosity liquids, gases and steam. to obtain specified accuracy.

4.4.4 Rangeability

It is important to note that in vortex meters, rangeability is fixed for a given application and meter size. Although rangeability depends upon the specific application it is generally > 20:1 on gases and steam, and >10:1 on liquids.

A 50 mm vortex meter has, typically, a flow range over the range of 1 to 15 ℓ/s on water (15: 1 rangeability). If we need to measure over the range 0.5 to 3 ℓ/s there is nothing that can be done to the 50 DN meter to allow it to measure a lower range and it would be necessary to use a 25 DN meter. For this reason, vortex meters are sized to the desired flow range, rather than to the nominal pipe diameter. It is thus, often necessary, to use a smaller diameter meter than the nominal diameter of the pipe, to get the proper rangeability (Figure 4.13).

In many cases, when buying a flowmeter, the instrument engineer does not know the exact flow range but has to make an educated guess. Since vortex meter rangeability is fixed for a given line size by the process conditions, a meter sized on an educated guess may not meet the actual process conditions.

Consequently if the user does not have a good ‘ball park’ figure in regard to rangeability it is often better to opt for a more forgiving technology such a magnetic flowmeter.

4.4.9 Orientation

Vortex meters can be installed vertically, horizontally or at an angle. However, for liquid measurements the meter must be full at all times. The meter should also be installed to avoid formation of secondary phases (liquid, gas or solid) in the internal sensor chambers.

4.4.10 Pressure drop

If the inside meter diameter is the same as the nominal diameter of the process piping (i.e. a 50 DN meter is used in a 50 DN line), then the pressure drop will normally be less than 40 kPa on liquid flow at the URL (usually in the 14 to 20 kPa range at the user’s URV). However, when downsizing the vortex meter to achieve a desired rangeability, the unrecovered pressure loss through the meter is increased.

It must be ensured that this increased pressure loss is not enough to cause a liquid to flash or cavitate within the pipe. Flashing and cavitation have an adverse effect on meter accuracy, and can cause damage to the meter itself.

4.4.11 Multi-phase flow

Measurement of two- or three-phase flow (e.g. water with sand and air, or ‘wet’ steam with vapour and liquid) is difficult and if multi-phase flow is present the vortex meter will not be as accurate.

Because the vortex meter is a volumetric device, it cannot distinguish which portions of the flow are liquid and which portions of the flow are gas or vapour. Consequently, the meter will report all the flow as gas, or all the flow as liquid, depending on the original configuration of the device. Thus, for example, if the meter is configured to measure water in litres, and the actual water has some entrained air and sand mixed in, a litre registered by the meter will include the water, air and sand that is present. Therefore if the area of interest was the amount of water, the reading from the meter will be consistently high, based upon the proportions of air and sand present. A user would, consequently, need to separate the phases prior to metering or live with this inherent error.

4.4.12 Wet steam

The measurement of ‘wet’ low quality steam is possible with a vortex meter — depending on the distribution of the liquid phase within the steam. Ideally, the secondary phase should be homogeneously dispersed within the primary phase (Figure 4.14(a). This tends to be the case with low amounts of secondary phase due to the high velocities and turbulence produced by the meter. However, for very low quality steam the distribution of the liquid phase within the steam may not be homogeneous. In vertical pipes the trend is towards ‘slug’ flow (Figure 4.14(b), whilst in horizontal pipes the flow is stratified (Figure 4.15. If separation of the two phases does occur, the best installation for the vortex meter would be in a horizontal line with the shedder positioned in the horizontal plane.

Again, however the users should be aware that the meter will, at best, measure the total volume and performance will not be to standard specifications.

4.4.13 Material build-up

Fluids that tend to form coatings are bad applications for vortex meters. Coating build-up on the bluff body will change its dimensions, and therefore, the value of the K factor.

4.4.14 Piping effects

The specification for vortex meter accuracy is based upon a well-developed and symmetrical fluid velocity profile existing in the pipe, free from distortion or swirl. The most common way to prevent errors is to provide sufficient lengths of straight, unobstructed pipe, upstream and downstream of the meter, so as to create a stable profile at the meter site.

Generally, vortex meters require similar amounts of upstream and downstream pipe runs to orifice plates, turbine meters and ultrasonic meters. Vortex meters are not usually recommended for “tight” piping situations, with limited runs of straight pipe, unless repeatability is more important than accuracy.

Typically, manufacturers recommend a minimum of 30 diameters of straight pipe upstream of the vortex meter, and 3 diameters downstream, when flow conditioners are not being used.

Flow conditioners, such as tube bundles, can be used to condition the flow upstream of the meter. However, straight pipe will still be required, even when flow conditioners are used. For example, a Vortab Flow Conditioner is 3 diameters long, and requires 4 diameters of straight pipe between it and the meter. This reduces the total upstream pipe run (including the flow conditioner) to just 7 diameters for any upstream disturbance.

Most performance specifications are based on using schedule 40 process piping. This pipe should have an internal surface free from mill scale, pits, holes, reaming scores, bumps, or other irregularities for a distance of 4 diameters upstream, and 2 diameters downstream of the vortex meter. The bores of the adjacent piping, the meter, and the mating gaskets must be carefully aligned to prevent measurement errors.

For liquid control applications, it is recommended that the vortex meter be located upstream of the control valve for a minimum of 5 diameters. For gas or steam control applications, it is recommended that the vortex meter be located a minimum of 30 diameters downstream of the valve. The only exception to this rule is for butterfly valves. In this instance the recommended distances are increased to 10 diameters for liquids, and 40 to 60 diameters for gases and steam.

4.4.15 Mass measurement

Pressure and/or temperature measurements are generally used in conjunction with a vortex meter measurement when the user wants an output in mass.

• Pressure taps should be located 3.5 to 4.5 diameters downstream of the meter.
• The temperature tap should be located 5 to 6 diameters downstream of the meter, and the smallest possible probe is recommended to reduce the chances of flow disturbance.

4.5 Avoiding problems

The following guidelines will help prevent application and measurement problems with a vortex meter and ensure premium performance:

• Improper configuration
• Improper sizing
• Insufficient upstream/downstream relaxation piping
• Improper meter orientation
• Partially full piping
• Accumulation of secondary phase ( gas, liquid or solid) inside the meter
• Improper temperature/pressure taps
• Flows below Reynolds numbers of 30000
• Flows below the low flow cut-in
• Process noise (at low flows or zero flow)
• Presence of multiple phases

* These application guidelines have been compiled from a series of notes supplied by Krohne

Table of contents

Differential Pressure Meters

5.1 Introduction 3

5.2 Basic theory 4

5.2.1 Gas flow 6

5.3 Orifice plate 7

5.3.1 Orifice plate configurations 8

5.3.3 Tapping points 9

5.3.3 Orifice plates — general 12

5.3.3.1 Advantages 12

5.3.3.2 Disadvantages 12

5.3.3.3 Applications limitations 12

5.4 Venturi tube meter 13

5.4.1 Advantages 13

5.4.2 Disadvantages 13

5.5 Venturi and flow nozzles 14

5.5.1 Venturi nozzle 14

5.5.2 Flow nozzle 14

5.6 The Dall tube 15

5.7 Target meter 16

5.8 Pitot tube 17

5.9 Point averaging 19

5.10 Elbow 20

5.10.1 Advantages 22

5.10.2 Disadvantages 22

5.11 Troubleshooting 22

Chapter 5

Differential Pressure Meters

Objectives

When you have completed this chapter you should be able to:

• Explain Bernoulli’s theory
• Describe the term ‘head’ loss
• Outline the principle of the orifice plate
• List the various orifice plate configurations
• Determine the parameters required for the choice of suitable tapping points
• Describe the working principles of the venturi tube, the venturi nozzle and the flow nozzle and the advantages and disadvantages of each
• Outline the working principle of the Dall tube
• Describe how the target meter works
• Show the working principle of the pitot tube and how it has been adapted for point averaging

5.1 Introduction

Differential pressure flow meters encompass a wide variety of meter types that includes: orifice plates, venturi tubes, nozzles, Dall tubes, target meters, pitot tubes and variable area meters.

Indeed, the measurement of flow using differential pressure is still the most widely used technology. This chapter confines itself to the discussion of the orifice plate (the most accepted and most widely used flowmetering method) and directly related methods that include the venturi and pitot tubes. Variable area meters are discussed in a later section.

One of the unique features of the differential flow meter, sometime referred to as a ‘head’ meter, is that flow can be accurately determined from: the differential pressure; accurately measurable dimensions of the primary device; and properties of the fluid. Thus, an important advantage of differential type meters over other instruments is that they do not always require direct flow calibration. In addition they offer excellent reliability, reasonable performance and modest cost.

Another advantage of orifice plates in particular, is the that they can be used on liquid or gas applications with very little change.

5.2 Basic theory

Differential pressure flow rate meters are based on a physical phenomenon in which a restriction in the flow line creates a pressure drop that bears a relationship to the flow rate. This physical phenomenon is based on two well-known equations: the equation of continuity and Bernoulli’s equation.

Consider the pipe in Figure 5.1 that rapidly converges from its nominal size to a smaller size followed by a short parallel sided throat before slowly expanding to its full size again. Further, assume that a fluid of density ρ flowing in the pipe of area A₁, has a mean velocity v₁ at a line pressure P₁. It then flows through the restriction of area A₂, where the mean velocity increases to v₂ and the pressure falls to P₂.

The equation of continuity states that for an incompressible fluid the volume flow rate, Q, must be constant. Very simply, this indicates that when a liquid flows through a restriction, then in order to allow the same amount of liquid to pass (to achieve a constant flow rate) the velocity must increase.

Mathematically:

Q = v₁A₁ = v₂A₂

where: v₁ and v₂ and A₁ and A₂ are the velocities and cross-sectional areas of the pipe at points 1 and 2 respectively.

In its simplest form Bernoulli’s equation states that under steady flow conditions, the total energy (pressure + kinetic + gravitational) per unit mass of an ideal fluid (i.e. one having a constant density and zero viscosity) remains constant along a flow line.

P/ρ + v²/2 + gz = K

where:

P = the pressure at a point;
v = the velocity at that point;
ρ = the fluid density;
g = the acceleration due to gravity; and
z = the level of the point above some arbitrary horizontal reference plane.

Thus, in the restricted section of the flow stream, the kinetic energy (dynamic pressure) increases due to the increase in velocity and the potential energy (static pressure) decreases. The difference between the static pressures upstream and the pressure at or immediately downstream of the restriction can be related to flow by the following expression:

where:

Q = flow rate;
k = constant;
C_d = discharge coefficient;
ΔP = differential pressure (P₁ – P₂); and
ρ = density of fluid.

The discharge coefficient C_d is a function of the diameter ratio, the Reynolds number Re, the design of the restriction, the location of the pressure taps and the friction due to pipe roughness. Reference texts and standards are available that list typical values and tolerances for C_d under certain flows in standard installations.

The foregoing formula highlights two major limitations that are applicable to all differential pressure systems:

• the square root relationship between differential pressure (ΔP) and flow (Q) severely limits the rangeability of such techniques to a maximum of 5:1; and
• if density (ρ ) is not constant, it must be known or measured. In practice the effect of density changes is not significant in the majority of liquid flow applications and needs only to be taken into account in the measurement of gas flow.

A third limitation of meters based on differential pressure measurement is that, as shown in Figure 5.2, it creates a permanent pressure loss. This ‘head’ loss is dependent on the type of meter and on the square of the volume flow (Figure 5.3)

5.2.1 Gas flow

Vapour or gas flow through a restriction differs from liquid flow in that the pressure decrease in the throat is accompanied by a decrease in density. Thus, in order for the mass flow to remain constant, the velocity must increase to compensate for the lower density. The result is that the formula for gas flow is slightly modified by the addition of the term Y:

Here, Y is termed the upstream expansion factor that is based on the determination of density at the upstream of the restriction.

Tables and graphs are available for the expansion factor as a function of the pressure ratio across the restriction and the specific heat of the gas (BS 1042). Alternatively the expansion factor may be calculated by standard equations listed in BS 1042. The mass flow rate for both liquids and gases is found by multiplying the theoretical mass flow equation by the expansion factor and the appropriate discharge coefficient.

5.3 Orifice plate

The orifice plate is the simplest and most widely used differential pressure flow measuring element and generally comprises a metal plate with a concentric round hole (orifice) through which the liquid flows (Figure 5.4). An integral metal tab facilitates installation and carries details of the plate size, thickness, serial number, etc. The plate, usually manufactured from stainless steel, Monel, or phosphor bronze, should be of sufficient thickness to withstand buckling (3 – 6 mm). The orifice features a sharp square upstream edge and, unless a thin plate is used, a bevelled downstream edge.

A major advantage of the orifice plate is that it is easily fitted between adjacent flanges that allow it to be easily changed or inspected (Figure 5.5).

It is commonly assumed that, since the orifice is essentially fixed, its performance does not change with time. In reality the orifice dimensions are extremely critical and although the uncertainty may be as low as 0,6% for a new plate, this measurement accuracy is rapidly impaired should the edge of the orifice bore become worn, burred or corroded. Indeed, damaged, coated or worn plates that have not been examined for some time can lead to measurement uncertainties of 5 % or more.

Although a correctly installed new plate may have an uncertainty of 0,6%, the vast majority of orifice meters measure flow only to an accuracy of about ± 2 to 3%. This uncertainty is due mainly to errors in temperature and pressure measurement, variations in ambient and process conditions and the effects of upstream pipework.

An adaptation of the sharp, square edge is the quadrant edge orifice plate (also called quarter circle and round edge). As shown in Figure 5.6 this has a concentric opening with a rounded upstream edge that produces a coefficient of discharge that is practically constant for Reynolds numbers from 300 to 25 000, and is therefore useful for use with high viscosity fluids or at low flow rates.

The radius of the edge is a function of the diameters of both the pipe and the orifice. In a specific installation this radius may be so small as to be impractical to manufacture or it can be so large that it practically becomes a flow nozzle. As a result, on some installations it may be necessary to change maximum differentials or even pipe sizes to obtain a workable solution for the plate thickness and its radius.

5.3.1 Orifice plate configurations

Although the concentric orifice (Figure 5.7 (a)) is the most frequently used, other plate configurations are used:

Eccentric
In the eccentric bore orifice plate (Figure 5.7 (b)), the orifice is offset from the centre and is usually set at the bottom of the pipe bore. This configuration is mainly used in applications where the fluid contains heavy solids that might become trapped and accumulate on the back of the plate. With the orifice set at the bottom, these solids are allowed to pass. A small vent hole is usually drilled in the top of the plate to allow gas, which is often associated with liquid flow, to pass

Eccentric plates are also used to measure the flow of vapours or gases that carry small amounts of liquids (condensed vapours), since the liquids will carry through the opening at the bottom of the pipe.

The coefficients for eccentric plates are not as reproducible as those for concentric plates, and in general, the error can be 3 to 5 times greater than on concentric plates.

Segmental orifice plates
The opening in a segmental orifice plate (Figure 5.7 (c)) is a circular segment — comparable to a partially opened gate valve. This plate is generally employed for measuring liquids or gases that carry non-abrasive impurities, which are normally heavier than the flowing media such as light slurries, or exceptionally dirty gases.

5.3.2 Tapping points

The measurement of differential pressure requires that the pipe is ‘tapped’ at suitable upstream (high pressure) and downstream (low pressure) points. The exact positioning of these taps is largely determined by the application and desired accuracy.

Vena contracta tapping
Because of the fluid inertia, its cross-sectional area continues to decrease after the fluid has passed through the orifice. Thus its maximum velocity (and lowest pressure) is at some point downstream of the orifice — at the vena contracta. On standard concentric orifice plates these taps are designed to obtain the maximum differential pressure and are normally located one pipe diameter upstream and at the vena contracta — about ½-pipe diameter downstream (Figure 5.8).

The main disadvantage of using the vena contracta tapping point is that the exact location is dependent on the flow rate and on the orifice size — an expensive undertaking if the orifice plate size has to be changed.

Vena contracta taps should not be used for pipe sizes under 150 mm diameter because of interference between the flange and the downstream tap.

Pipe taps
Pipe taps (Figure 5.9) are a compromise solution and are located 2½ pipe diameters upstream and 8 pipe diameters downstream. Whilst not producing the maximum available differential pressure, pipe taps are far less dependent on flow rate and orifice size.

Pipe taps are used typically in existing installations, where radius and vena contracta taps cannot be used. They are also used in applications of greatly varying flow as the measurement is not affected by flowrate or orifice size.

Accuracy is reduced as they do not measure the maximum available pressure.

Flange taps
Flange taps are used when it is undesirable or inconvenient to drill and tap the pipe for pressure connections. Flange taps are quite common and are generally used for pipe sizes of 50mm and greater. They are, typically, located 25 mm either side of the orifice plate (Figure 5.10).

Flange taps are not used for pipe diameters less than 50mm, as the vena contracta starts to become close to and possible forward of the downstream tapping point.

Usually, the flanges, incorporating the drilled pressure tappings, are supplied by the manufacturer. With the taps thus accurately placed by the manufacturer the necessity to recalculate the tapping point, when the plate is changed, is eliminated.

Corner Taps
Suitable for pipe diameters less than 50 mm, corner taps are an adaptation of the flange tap (Figure 5.11) in which the tappings are made to each face of the orifice plate. The taps are located in the corner formed by the pipe wall and the orifice plate on both the upstream and downstream sides and require the use of special flanges or orifice holding rings.

5.4 Venturi tube meter

The venturi tube (Figure 5.12) has tapered inlet and outlet sections with a central parallel section, called the throat, where the low pressure tapping is located. Generally, the inlet section, which provides a smooth approach to the throat, has a steeper angle than the downstream section. The shallower angle of the downstream section reduces the overall permanent pressure loss by decelerating the flow smoothly and thus minimising turbulence. Consequently, one of the main advantages of the venturi tube meter over other differential pressure measuring methods is that its permanent pressure loss is only about 10 % of the differential pressure (Figure 5.3). At the same time, its relatively stream-lined form allows it to handle about 60 % more flow than, for example, that of an orifice plate.

The venturi tube also has a relatively high accuracy: better than ± 0,75 % over the orifice ratios (d/D) of 0,3 to 0,75. This order of accuracy, however, can only be obtained as long as the dimensional accuracy is maintained. Consequently, although the venturi tube can also be used with fluids carrying a relatively high percentage of entrained solids, it is not well suited for abrasive media.

Although generally regarded as the best choice of a differential type meter for bores over 1000 mm, the major disadvantage of the venturi type meter is its high cost — about 20 times more expensive than an orifice plate. In addition, its large and awkward size makes it difficult to install since a 1 m bore venturi is 4 – 5 m in length.

Although it is possible to shorten the length of the divergent outlet section by up to 35%, thus reducing the high manufacturing cost without greatly affecting the characteristics, this is at the expense of an increased pressure loss.

5.5 Venturi and flow nozzle meters

5.5.1 Venturi nozzle

The venturi nozzle is an adaptation of the standard venturi that makes use of a ‘nozzle’ shaped inlet (Figure 5.13), a short throat, and a flared downstream expansion section. Whilst increasing the permanent pressure loss to around 25 % of the measured differential pressure of the standard venturi, the venturi nozzle is cheaper, requires less space for installation, and yet still retains the benefits of high accuracy (± 0,75%) and high velocity flow.

5.5.2 Flow nozzle

The flow nozzle (Figure 5.14) is used mainly in high velocity applications or where fluids are being discharged into the atmosphere. It differs from the nozzle venturi in that it retains the ‘nozzle’ inlet but has no exit section.

The main disadvantage of the flow nozzle is that the permanent pressure loss is increased from between 30 to 80% of the measured differential pressure — depending on its design.

Offsetting this disadvantage, however, accuracy is only slightly less than for the venturi tube (± 1 to 1,5 %) and it is usually only half the cost of the standard venturi. In addition it requires far less space for installation and, because the nozzle can be mounted between flanges or in a carrier, installation and maintenance is much easier than for the venturi.

5.6 The Dall tube

Although many variations of low-loss meters have appeared on the market, the best known and most commercially successful is the Dall tube (Figure 5.15).

The Dall tube is virtually throatless and has a short steep converging cone that starts at a stepped buttress whose diameter is somewhat less than the pipe diameter. Following an annular space at the ‘throat’, there is a diverging cone that again finishes at a step.

A major feature of the Dall tube is the annular space between the ‘liner’ and tube into which the flowing media passes to provide an average ‘throat’ pressure.

With a conventional venturi, upstream and throat tappings are taken at points of parallel flow where the pressures across a cross section are constant. If the streamlines were curved the pressure would not be constant over the cross section but would be greater at the convex surface and less at the concave surface.

In the Dall tube the upstream tapping is taken immediately before the buttress formed by the start of the converging cone, where the convex curvature of the streamlines is at a maximum. At the ‘throat’, where there is an immediate change from the converging to diverging section, the ‘throat’ tapping is thus taken at the point of maximum concave curvature. This means that a streamlined curvature head is added to the upstream pressure and subtracted from the ‘throat’ pressure and the differential pressure is considerably increased. Thus, for a given differential head the throat can be larger — reducing the head loss.

Because of the annular gap, no breakaway of the liquid from the wall occurs at the throat and the flow leaves the ‘throat’ as a diverging jet. Since this jet follows the walls of the diverging cone, eddy losses are practically eliminated, while friction losses are small because of the short length of the inlet and outlet sections.

The main disadvantages are: high sensitivity to both Reynolds number and cavitation and manufacturing complexity.

5.7 Target meter

The target flowmeter is, in effect, an ‘inside out’ orifice plate used to sense fluid momentum.

Sometimes called a drag disc or drag plate, the target meter usually takes the form of a disc mounted within the line of flowing fluid (Figure 5.16). The flow creates a differential pressure force across the target and the resultant deflection is transmitted to a flexure tube — with strain gauge elements mounted external to the flowing medium indicating the degree of movement.

The major advantages of the target meter include: ability to cope with highly viscous fluids at high temperatures (hot tarry and sediment-bearing fluids); free passage of particles or bubbles; and no pressure tap or lead line problems.

Disadvantages include: limited size availability; limited flow range; and high head loss.

5.8 Pitot tube

The Pitot tube is one of the oldest devices for measuring velocity and is frequently used to determine the velocity profile in a pipe by measuring the velocity at various points.

In its simplest form the Pitot tube (Figure 5.17) comprises a small tube inserted into a pipe with the head bent so that the mouth of the tube faces into the flow. As a result, a small sample of the flowing medium impinges on the open end of the tube and is brought to rest. Thus, the kinetic energy of the fluid is transformed into potential energy in the form of a head pressure (also called stagnation pressure).

Mathematically this may be expressed by applying Bernoulli’s equation to a point in the small tube and a point in the free flow region. From Bernoulli’s general equation:

P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂

we can write:

P_h/ρ + 0 + gh₁ = P_s/ρ + v²/2 + gh₂

where:

P_s = static pressure;
P_h = stagnation pressure;
v = liquid velocity
g = acceleration due to gravity; and
h₁ and h₂ = heads of the liquid at the static and stagnation pressure measuring points respectively.

If h₁ = h₂ then:

Because the Pitot tube is an intrusive device and some of the flow is deflected around the mouth, a compensatory flow coefficient K_p is required. Thus:

For compressible fluids at high velocities (e.g. > 100 m/s in air) a modified equation should be used.

By measuring the static pressure with a convenient tapping, the flow velocity can be determined from the difference between the head pressure and the static pressure. This difference, measured by a differential pressure cell, provides a measurement of flow that, like a conventional differential pressure measurement, obeys a square root relationship to pressure. Low flow measurement at the bottom end of the scale is thus difficult to achieve accurately.

A problem with this basic configuration is that the flow coefficient K_p depends on the tube design and the location of the static tap. One means of overcoming this problem is to use a system as shown in Figure 5.18 that make use of a pair of concentric tubes — the inner tube measuring the full head pressure and the outer tube using static holes to measure the static pressure.

Both these designs of Pitot tube measure the point velocity. However it is possible to calculate the mean velocity by sampling the point velocity at several points within the pipe. Alternatively, provided a fully developed turbulent profile exists, a rough indication of the average velocity can be obtained by positioning the tube at a point three-quarters of the way between the centreline and the pipe wall.

5.9 Point averaging

Another method of determining the average velocity is with a point averaging Pitot tube system (Figure 5.19).

Essentially, this instrument comprises two back-to-back sensing bars, that span the pipe, in which the up- and down-stream pressures are sensed by a number of critically located holes. The holes in the upstream detection bar are arranged so that the average pressure is equal to the value corresponding to the average of the flow profile.

Because the point at which the fluid separates from the sensor varies according to the flow rate (Figure 5.20) extreme care must be taken in positioning the static pressure sensing holes. One solution is to locate the static pressure point just before the changing separation point. Alternatively, a ‘shaped’ sensor (Figure 5.21) is used that establishes a fixed point where the fluid separates from the sensor.

These multi-port averaging devices, commonly called ‘Annubars’ after the first design, are used mainly in metering flows in large bore pipes — particularly water and steam. Properly installed, ‘Annubar’ type instruments have a repeatability of 0,1% and an accuracy of 1% of actual value.

Although intrusive, pitot type instruments offer a very low pressure drop and application on a wide range of fluids.

On the negative side, the holes are easily fouled if used on ‘dirty’ fluids and they are sensitive to swirl and distorted profiles.

On a conventional integrated pitot tube, the alignment can be critical. Misalignment causes errors in static pressure since a port facing slightly upstream is subject to ‘part’ of the stagnation or total pressure. A static port facing slightly downstream is subjected to a slightly reduced pressure.

5.10 Elbow

A pipe elbow can be used as a primary device. Elbow taps have an advantage in that most piping systems have elbows that can be used. In applications where cost is a factor and additional pressure loss from an orifice plate is not permitted, the elbow meter is a viable differential pressure device.

If an existing elbow is used then no additional pressure drop occurs and the expense involved is minimal. They can also be produced in-situ from an existing bend, and are typically formed by two tappings drilled at an angle of 45^o through the bend. These tappings provide the high and low pressure tapping points respectively.

Whilst 45^o tappings are more suited to bi-directional flow measurement, tappings at 22.5^o have shown to provide more stable and reliable readings and are less affected by upstream piping.

A number of factors contribute to the differential pressure that is produced and, subsequently, it is difficult to accurately predict the exact flowrate. Some of these factors are:

— Force of the flow onto the outer tapping.
— Turbulence generated due to cross-axial flow due to the bend
— Differing velocities between outer and inner radius of flow
— Pipe texture
— Relationship between elbow radius and pipe diameter

Generally, the elbow meter is only suitable for higher velocities and cannot produce an accuracy of better than 5% . However, on-site calibration can produce more accurate results, with the added advantage that repeatability is good.

Although the elbow meter is not commonly used in industry, it is very much underrated since its low cost, together with its application after completion of pipework, can be a major benefit for low accuracy flow metering applications.

Suitable applications would include plant air conditioning, cooling water metering, site flow checkpoints possibly with local indicators, and check flow applications, where the cost of magnetic meters is prohibitive.

For installation, it is recommended that the elbow be installed with 25 pipe diameters of straight pipe upstream and at least 10 pipe diameters of straight pipe down stream.

5.11 Troubleshooting

One of the most common inaccuracies induced in differential pressure flowmeters is not allowing enough straight pipe. When the flow material approaches and passes some change in the pipe small eddies are formed in the flow stream. These eddies are localised regions of high velocity and low pressure and can start to form upstream of the change and dissipate further downstream.

Flowmeter sensors detect these changes in pressure and consequently produce erratic or inaccurate readings for flow rate.

Table of contents

Variable Area Meters

6.1 Introduction 3

6.2 Operating principle 3

6.3 Floats 5

6.3.1 Float centring methods 5

6.3.2 Float shapes 6

6.3.2.1 Ball float 7

6.3.2.2 Rotating float 8

6.3.2.3 Viscosity immune float 8

6.3.2.4 Low pressure loss float 8

6.4 Metering tube 8

6.5 Conclusion 9

Chapter 6

Variable Area Meters

Objectives

When you have completed this chapter you should be able to:

• Explain the basic operating principle of variable area flowmeters
• List the various float centring systems in use
• Describe the differences between the four basic float shapes
• Outline the application limitations of the variable area flowmeter

6.1 Introduction

The variable area flowmeter is an industrial meter reverse differential pressure meter used to measure the flow rate of liquids and gases.

6.2 Operating principle

The instrument generally comprises a vertical, tapered glass tube and a weighted float whose diameter is approximately the same as the tube base (Figure 6.1).

In operation, the fluid or gas flows through the inverted conical tube from the bottom to the top, carrying the float upwards. Since the diameter of the tube increases in the upward direction the float rises to a point where the upward force on the float created by differential pressure across the annular gap, between the float and the tube, equals the weight of the float.

As shown in Figure 6.1, the three forces acting on the float are:

• constant gravitational force W;
• buoyancy A that, according to Archimedes’ principle, is constant if the fluid density is constant; and
• force S, the upward force of the fluid flowing past the float.

For a given instrument, when the float is stationary, W and A are constant and S must also be constant. In a position of equilibrium (floating state) the sum of forces S + A is opposite and equal to W and the float position corresponds to a particular flow rate that can be read off a scale.

A major advantage of the variable area flowmeter is that the flow rate is directly proportional to the orifice area that, in turn, can be made to be linearly proportional to the vertical displacement of the float. Thus, unlike most differential pressure systems, it is unnecessary to carry out square root extraction.

The taper can be ground to give special desirable characteristics such as an offset of higher resolution at low flows.

In a typical variable area flowmeter, the flow q can be shown to be approximately given by:

where:

q = flow;
C = constant that depends mainly on the float;
A = cross-sectional area available for fluid flow past the float; and
ρ = density of the fluid.

Indicated flow, therefore, depends on the density of the fluid which, in the case of gases, varies strongly with the temperature, pressure and composition of the gas.

It is possible to extend the range of variable area flowmeters by combining an orifice plate in parallel with the flowmeter.

6.3 Floats

A wide variety of float materials, weights, and configurations are available to meet specific applications.

The float material is largely determined by the medium and the flow range and includes: stainless steel, titanium, aluminium, black glass, synthetic sapphire, polypropylene, Teflon, PVC, hard rubber, monel, nickel and Hastelloy C.

6.3.1 Float centring methods

An important requirement for accurate metering is that the float is exactly centred in the metering tube. One of three methods is usually applied:

1. Slots in the float head cause the float to rotate and centre itself and prevent it sticking to the walls of the tube (Figure 6.2(a)). This arrangement first led to the term ‘Rotameter’ being applied to variable area flowmeters (actually a registered trade mark of KDG Instruments Ltd). Slots cannot be applied to all float shapes and, further, can cause the indicated flow to become slightly viscosity dependent.

2. Three moulded ribs within the metering tube cone (Figure 6.2 (b)), parallel to the tube axis, guide the float and keep it centred. This principle allows a variety of float shapes to be used and the metering edge remains visible even when metering opaque fluids.

3. A fixed centre guide rod within the metering tube (Figure 6.3 (a)) is used to guide the float and keep it centred. Alternatively, the rod may be attached to the float and move within fixed guides (Figure 6.3 (b)). The use of guide rods is mainly confined to applications where the fluid stream is subject to pulsations likely to cause the float to ‘chatter’ and possibly, in extreme cases, break the tube. It is also used extensively in metal metering tubes.

6.3.2 Float shapes

The design of the floats is confined to four basic shapes (Figure 6.4):

• ball float
• rotating (viscosity non-immune) float
• viscosity immune float
• float for low pressure losses

6.3.2.1 Ball float

The ball float (Figure 6.4 (a)) is mainly used as a metering element for small flowmeters — with its weight determined by selecting from a variety of materials. Figure 6.5 shows the effect of viscosity on the flow rate indication. Since its shape cannot be changed, the flow coefficient is clearly defined (1) and, as shown, exhibits virtually no linear region. Thus, any change in viscosity, due often to even very small changes in temperature, results in changes in indication.

6.3.2.2 Rotating float

Rotating floats (Figure 6.4 (b)) are used in larger sized meters and are characterised by a relatively narrow linear (viscosity-immune) region as shown in Figure 6.5 (2).

6.3.2.3 Viscosity immune float

The viscosity immune float (Figure 6.4 (c)) is appreciably less sensitive to changes in viscosity and is characterised by a wider linear region as shown in Figure 6.5 (3). Although such an instrument is unaffected by relatively large changes in viscosity, the same size meter has a span 25% smaller than the previously described rotating float.

6.3.2.4 Low pressure loss float

For gas flow rate metering, very light floats (Figure 6.4 (d)) with relatively low pressure drops can be used.

The pressure drop across the instrument is due, primarily, to the float since the energy required to produce the metering effect is derived from the pressure drop of the flowing fluid. This pressure drop is independent of the float height and is constant.

Further pressure drop is due to the meter fittings (connection and mounting devices) and increases with the square of the flow rate. For this reason, This design requires a minimum upstream pressure.

6.4 Metering tube

The meter tube is normally manufactured from borosilicate glass that is suitable for metering process media temperatures up to 200 °C and pressures up to about 2 – 3 MPa.

Because the glass tube is vulnerable to damage from thermal shocks and pressure hammering, it is often necessary to provide a protective shield around the tube.

Variable area meters are inherently self-cleaning since the fluid flow between the tube wall and the float provides a scouring action that discourages the build-up of foreign matter. Nonetheless, if the fluid is dirty, the tube can become coated — affecting calibration and preventing the scale from being read. This effect can be minimised through the use of an in-line filter.

In some applications use can be made of an opaque tube used in conjunction with a float follower. Such tubes can be made from steel, stainless steel, or plastic.

By using a float with a built-in permanent magnet, externally mounted reed-relays can be used to detect upper and lower flow limits and initiate the appropriate action. The temperature and pressure range may be considerably extended (e.g. up to 400 °C and 70 MPa) through the use of a stainless steel metering tube. Again, the float can incorporate a built-in permanent magnet that is coupled to an external field sensor that provides a flow reading on a meter.

In cases where the fluid might contain ferromagnetic particles that could adhere to the magnetic float, a magnetic filter should be installed upstream of the flowmeter. Typically (Figure 6.6) such a filter contains bar magnets, coated with PTFE as protection against corrosion, arranged in a helical fashion.

6.5 Conclusion

Generally, variable area flowmeters have uncertainties ranging from 1 to 3% of full scale. Precision instruments are, however, available with uncertainties down to 0,4% of full scale

The variable area meter is an exceptionally practical flow measurement device.

Advantages
— Wide range of applications
— Linear float response to flow rate change
— 10 to 1 flow range or turn down ratio
— Easy sizing or conversion from one particular service to another
— Ease of installation and maintenance.
— Simplicity
— Low cost
— High low-flow accuracy (down to 5 cm³/ min
— Easy visualisation of flow.

Disadvantages
— Limited accuracy
— Susceptibility to changes in temperature, density and viscosity
— Fluid must be clean, no solids content
— Erosion of device (wear and tear)
— Can be expensive for large diameters
— Operate in vertical position only
— Accessories required for data transmission

Table of contents

Electromagnetic Flowmeters

7.1 Introduction 3

7.2 Measuring principle 3

7.3 Construction 5

7.4 Conductivity 7

7.5 Field characterisation 8

7.6 Measurement in partially filled pipes 10

7.7 Empty pipe detection 14

7.8 Field excitation 15

7.9 The pulsed d.c. field 16

7.10 Bipolar pulse operation 18

7.11 Meter sizing 20

7.12 Conclusion 21

Chapter 7

Electromagnetic Flowmeters

Objectives

When you have completed this chapter you should be able to:

• Explain Faraday’s Law and show how it can be applied to flow measurement
• Explain the basic construction of the magnetic flowmeter
• List the different liners available and describe the advantages and disadvantages of each
• Show the dependence of the electromagnetic flowmeter on the conductivity of the liquid being measured
• Demonstrate the importance of field characterisation
• Show how measurements can take place in partially filled pipes
• Explain the importance of empty pipe detection
• Discuss field excitation and the differences between an a.c. field and a d.c. pulsed field
• Apply meter sizing
• List the main advantages and disadvantages of the electromagnetic flowmeter

7.1 Introduction

Electromagnetic flowmeters, also known as ‘Magflows’ or ‘Magmeters’, have now been in widespread use throughout industry for more than 40 years and were the first of modern meters to exhibit no moving parts and zero pressure drop.

7.2 Measuring principle

The of the EM flowmeter is based on Faraday’s law of induction that states that if a conductor is moved through a magnetic field a voltage will be induced in it that is proportional to the velocity of the conductor.

Referring to Figure 7.1, if the conductor of length (l) is moved through the magnetic field having a magnetic flux density (B) at a velocity (v), then a voltage will be induced where:

e = B.l.v

and:

e = induced voltage (V);
B = magnetic flux density (Wb/m²);
l = length of conductor (m); and
v = velocity of conductor (m/s).

In the electromagnetic flowmeter (Figure 7.2) a magnetic field is produced across a cross section of the pipe — with the conductive liquid forming the conductor (Figure 7.3). Two sensing electrodes, set at right angles to the magnetic field, are used to detect the voltage that is generated across the flowing liquid and which is directly proportional to the flow rate of the media.

It can thus be seen that since v is the flow rate (the parameter to be measured) the generated voltage is limited by the length of the conductor (the diameter of the pipe) and the flux density. In turn, the flux density is given by:

B = μ. H

where:

μ = permeability; and
H = magnetising field strength (ampere turns/m).

Because the permeability of the magnetic circuit is largely determined by the physical constraints of the pipe (the iron liquid gap combination), the magnetic flux density B (and hence the induced voltage) can only be maximised by increasing H — a function of the coil (number of windings and its length) and the magnetising current.

7.3 Construction

Because the working principle of the electromagnetic flowmeter is based on the movement of the conductor (the flowing liquid) through the magnetic field, it is important that the pipe carrying the medium (the metering tube) should have no influence on the field. Consequently, in order to prevent short circuiting of the magnetic field, the metering tube must be manufactured from a non-ferromagnetic material such as stainless steel or Nickel-Chromium.

It is equally important that the signal voltage detected by the two sensing electrodes is not electrically short circuited through the tube wall. Consequently, the metering tube must be lined with an insulating material. Such materials have to be selected according to the application and their resistance to chemical corrosion, abrasion, pressure and temperature (Table 1).

Teflon PTFE
A warm deformable resin, Teflon PTFE is the most widely used liner material. Characteristics include:
— very high temperature capability (180°C)
— excellent anti-stick characteristics reduce build-up
— inert to a wide range of acids and bases
— approved in food and beverage applications.

Teflon PFA
Teflon PFA is a melt-processable resin that offers:
— a better shape accuracy than PTFE;
— better abrasion resistance, since there are no bulges or deformations;
— better vacuum strength because of the ability to incorporate stainless steel reinforcement.

Polyurethane
Generally, Teflon PTFE/PFA does not have adequate erosion resistance for some applications and, often, the best choice when extreme resistance to wear and erosion is required is polyurethane. Other characteristics include:
— cannot be used with strong acids or bases
— cannot be used at high temperatures since its maximum process temperature is 40 °C.

Neoprene
— resistant to chemical attack
— good degree of abrasion resistance
— temperature of 80 °C.

Hard rubber
— inexpensive general purpose liner
— wide range of corrosion resistance
— main application in the water and waste water industries

Soft rubber
— relatively inexpensive
— high resistance to abrasion
— main application in slurries.

Fused aluminium oxide
— highly recommended for very abrasive and/or corrosive applications
— high temperatures up to 180°C.
— used extensively in the chemical industry

7.4 Conductivity

The voltage developed across the electrodes is dependent on the impedance of the measuring amplifier and the source impedance that, in turn, is dependent on the fluid conductivity. Thus, in order to deliver the maximum voltage to the amplifier, its impedance should be as high as possible compared with that of the fluid.

The minimum conductivity of the fluid usually varies between 5 – 20 μS/cm for d.c. field instruments and obviously varies with the size of the metering tube.

Capacitively coupled meters have recently been introduced that can be used on liquids with conductivity levels down to 0,05 µS/cm.

Most refinery products, and some organic products, have insufficient conductivity to allow them to be metered using electromagnetic flowmeters (Table 5.2).

It should be noted that the conductivity of liquids can vary with temperature and care should be taken to ensure the performance of the liquid in marginal conductivity applications is not affected by the operating temperatures. Most liquids have a positive temperature coefficient of conductivity. However negative coefficients are possible in a few liquids.

7.5 Field characterisation

The purpose of a flowmeter is to measure the true average velocity across the section of pipe, so that this can be related directly to the total volumetric quantity in a unit of time. The voltage generated at the electrodes is the summation of the incremental voltages generated by each elemental volume of cross-section of the flowing fluid as it crosses the electrode plane with differing relative velocities.

Initially, designs assumed the magnetic field to be homogeneous over the measured cross-section and length of the pipe in order to achieve precise flow measurement. However, early investigators showed that, for a given velocity, the medium does not generate the same voltage signal in the electrodes at all points. Thus, for a given velocity (v) the medium flowing at position A₁ (Figure 7.4) does not generate the same voltage signal as that flowing in position A₂.

Rummel and Ketelsen plotted the medium flowing at various distances away from the measuring electrodes (Figure 7.5) and showed how these contribute in different ways towards the creation of the measuring signal. This shows that a flow profile that concentrates velocity in the area of one electrode will produce eight times the output of that at the pipe centre — leading to errors that cannot be overlooked.

One solution to this problem is to use a non- homogeneous field that compensates for these non-linear concentrations.

Subsequent to his research, Ketelsen designed a magnetic flowmeter making use of a ‘characterised field’. As distinct from the homogeneous field in which the magnetic flux density (B) is constant over the entire plane (Figure 7.6 (a)), the ‘characterised field’ is marked by an increase in B in the x-direction and a decrease in the y-direction (Figure 7.6 (b)).

Because commercial exploitation of this design is limited in terms of a patent in the name of B. Ketelsen, assigned to Fischer & Porter GmbH, a ‘modified field’ has been developed in which the lines of magnetic flux, at any place in the electrode-plane, are characterised by an increase in B in the x-direction, from the centre to the wall, but is constant in the y-direction (Figure 7.6 (c)). This ‘modified field’ is, therefore, a compromise between the ‘characterised field’ and the ‘homogeneous field’.

7.6 Measurement in partially filled pipes

A fundamental requirement for accurate volumetric flow measurement is that the pipe should be full. Given a constant velocity then, as the fill level decreases, the induced potential at the electrodes is still proportional to the media velocity. However, since the cross sectional area of the media is unknown it is impossible to calculate the volumetric flow rate.

In the water utility industry where large bore flowmeters are used and the hydraulic force is based on gravity, the occurrence of a partially filled pipe, due to low flow, is quite frequent.

Although installing the flowmeter at the lowest point of the pipeline in an invert or U-section (Figure 7.7) will combat this problem, there are still many situations where even the best engineering cannot guarantee a full pipe — thus giving rise to incorrect volume readings.

One answer to this problem would be to actually determine the cross-sectional area and thus calculate the volumetric flow.

In the solution offered by Bailey-Fischer & Porter in their Parti-MAG, two additional electrode pairs are located in the lower half of the meter to cater for partial flowrate measurements down to 10%. In addition, the magnetic field is switched successively from a series to a reverse coil excitation.

The series excitation mode (Figure 7. 8) corresponds to the excitation mode for a conventional meter. As a result of this field, a voltage is induced in the electrode pairs that is related to the media velocity.

In the reverse excitation mode (Figure 7. 9) the induced voltages in the upper and lower halves of the meter are of equal magnitude but opposite sign. Thus, in a full pipe the potential would be zero at the electrode pair E₁ and some definite value at the electrode pairs E₂ and E₃. As the level falls, the signal contribution from the upper half decreases while that from the lower half remains the same — resulting in a change in the potential at the various electrode pairs that can be related directly to the change in media level. Microprocessor technology is then used to compute the cross-sectional area and thus the volumetric flow.

A slightly different scheme is used in Krohne’s TIDALFLUX meter. This instrument combines an electromagnetic flowmeter with an independent capacitive level measuring system.

The electromagnetic flow measuring section functions like a conventional electromagnetic flowmeter, using a single set of electrodes that are placed near the bottom of the pipe as shown in Figure 7.10. In this manner, even when the filling level falls to less than 10% of the pipe diameter, the electrodes are still covered and capable of providing a flow velocity-related output.

The level measuring section makes use of a system of insulated transmission and detection plates embedded in the flowmeter liner (Figure 7.11) in which the change in capacitive coupling is proportional to the wetted cross-section.

Using these two measured values it is now possible to compute the actual volumetric flow (Figure 7.12) from:

Q = v.A

where:

Q = volumetric flow
v = velocity-related signal
A = wetted cross-sectional area.

7.7 Empty pipe detection

In many cases, measurement of partially filled pipes in not required. Nonetheless, in order to draw attention to this situation, many meters incorporate an `Empty Pipe Detection’ option.

In the most common system (Figure 7.13), a conductivity probe, mounted on top of the pipe, senses the presence of the conductive medium. If the medium clears the sensor, due to partial filling of the pipe, the conductivity falls and an alarm is generated.

An alternative scheme is to use a high frequency current generator across the flowmeter sensing probes. Because normal flow measurement uses relatively low frequencies, the high frequency signal used to measure the conductivity is ignored by the flow signal amplifier.

`Empty Pipe Detection’ is not only used to indicate that the volume reading is incorrect. For example, in a two-line standby system, one line handles the process and the other line is used for standby. Since the standby line does not contain any of the process medium, the flowmeter sensing electrodes are `open circuit’ and the amplifier output signal will be subject to random drifting. The resultant falsely generated inputs to any process controllers, recorders, etc, connected to the system will give rise to false status alarms. Here, the `Empty Pipe Detection’ system is used to ‘freeze’ the signal to reference zero.

Another application for `Empty Pipe Detection’ is to prevent damage to the field coils. Magnetic flowmeters based on a `pulsed d.c.’ magnetic field, generate relatively low power to the field coils —typically between 14 and 20 VA. This is usually of little concern regarding heat generation in the field coils. However, flow sensors based on an `a.c generated’ magnetic fields, consume power in excess of a few hundred VA. In order to absorb the heat generated in the field coils, a medium is required in the pipe to keep the temperature well within the capability of the field coil insulation. An empty pipe will cause overheating and permanent damage to the field coils and, consequently, this type of flowmeter requires an `Empty Pipe Detection’ system to shut down the power to the field coils.

7.8 Field excitation

The metallic electrodes in contact with the flowing liquid form a galvanic element that creates an interfering electrochemical d.c. voltage. This voltage is dependent on the temperature, the flow rate, the pressure and the chemical composition of the liquid as well as on the surface condition of the electrodes. In practice, the voltage between the liquid and each electrode will be different — giving rise to an unbalanced voltage between the two electrodes.

In order to separate the flow signal from this interfering d.c. voltage, an a.c. excitation field is used — allowing the interfering d.c. voltage to be easily separated from the a.c. signal voltage by capacitive or transformer coupling.

Whilst a.c. electromagnetic flowmeters have been used successfully for many years, the use of an alternating field excitation make them susceptible to both internal and external sources of errors.

7.9 The pulsed d.c. field

The pulsed d.c. field is designed to overcome the problems associated with both a.c. and d.c. interference. In the pulsed d.c. meter, the d.c. field is periodically switched on and off at specific intervals. The electrochemical d.c. interference voltage is stored when the magnetic field is switched off and then subtracted from the signal representing the sum of the signal voltage and interference voltage when the magnetic field is switched on.

Figure 7.14(a) shows the induced field in the form of a d.c. pulse. Figure 7.14(b) illustrates the voltage at the sensors in which the measured voltage V_m is superimposed on the spurious unbalanced offset voltage V_u. By taking (and storing) samples during the periods A and B, the mean value V_m may be obtained by algebraic subtraction of the two values:

V_m = (V_u + V_m) – V_u

This method assumes that the value of the electrochemical interference voltage remains constant during this measuring period between the samples A and B. However if the interference voltage changes during this period serious errors are likely to occur. Figure 7.15 shows the unbalanced offset voltage as a steadily increasing ramp. Here, the error is as high as the amount by which the unbalanced voltage has changed during the measuring periods A and B and could result in an induction error of as much as 100 %.

One method of overcoming this problem is by a method of linear interpolation as illustrated in Figure 7.16. Prior to the magnetic induction the unbalanced voltage A is measured. During the magnetic induction phase the value B (which is the sum of unbalanced voltage and flow signal) is measured and then, after magnetic induction, the changed unbalanced voltage C is measured.

The mean value (A + C)/2 of the balanced voltage prior to and after magnetic induction is electronically produced and subtracted from the sum signal measured during magnetic induction. So, the exact flow signal:

Vm = B – (A + C)/2

is obtained which is free from the unbalanced voltage. This method corrects not only the amplitude of the d.c. interference voltage, but also its change ,with respect to time.

7.10 Bipolar pulse operation

An alternative method of compensation is shown in Figure 7.17 using an alternating (or bipolar) d.c. pulse. Under ideal or reference conditions, the values of V₁ and V₂ would be equal and would both have the value Vm, the measured value. Thus:

V₁ – V₂ = (V_m) – (-V_m)
              = 2V_m

If, now, the zero or no-flow signal is off-set by an unbalanced voltage in, for example, a positive direction (Figure 7.18) , then:

            V₁ = V_u + V_m

and      V₂ = V_u – V_m

and      V₁– V₂ = (V_u +V_m) – (V_u – V_m)

                          = 2V_m

Again, linear interpolation methods may be applied as illustrated in Figure 7.19 where five separate samples are taken during each measurement cycle. A zero potential measurement is taken at the commencement of the cycle; a second measurement at the positive peak; a third at zero potential again; a fourth at negative peak and finally another zero measurement at the completion of the cycle. The result, in this case, will be:

2 V_m = (V₁ – (Z₁ + Z₂)/2 – (V₂ – (Z₂ + Z₃)/2)

7.11 Meter sizing

Generally the size of the primary head is matched to the nominal diameter of the pipeline. However, it is also necessary to ensure that the flow rate of the medium lies between the minimum and maximum full scale ranges of the specific meter. Typical values of the minimum and maximum full scale ranges are 0,3 and 12 m/s respectively.

Experience has also shown that the optimum flow velocity of the medium through an electromagnetic flowmeter is generally 2 to 3 m/s — dependent on the medium. For example, for liquids having solids content, the flow velocity should be between 3 to 5 m/s to prevent deposits and to minimise abrasion.

Knowing the volumetric flowrate of the medium in, for example, cubic metres per hour, and knowing the pipe diameter, it is easy to calculate and thus check to see if the flow velocity falls within the recommended range. Most manufacturers supply nonograms or tables that allow users to ascertain this data at a glance.

Occasionally, in such cases where the calculated meter size needs to be smaller than that of the media pipe size, a transition using conical sections can be installed .The cone angle should be 8 ° or less and the pressure drop resulting from this reduction can, again, be determined from manufacturers’ tables (Figure 7.20).

7.12 Conclusion

The electromagnetic (EM) flowmeter is regarded by many users as the universal answer to more than 90% of all flowmetering applications. Some of the many benefits offered by the EM flowmeter include:

• no pressure drop;
• short inlet/outlet sections (5D/2D);
• relationship is linear (not square root);
• insensitive to flow profile changes (laminar to turbulent) including many non-Newtonian liquids;
• rangeability of 30:1 or better;
• inaccuracy of better than ±0,5% of actual flow over full range;
• no recalibration requirements;
• bi-directional measurement
• no taps, or cavities;
• no obstruction to flow;
• not limited to clean fluids;
• high temperature capabilities;
• high pressure capabilities;
• volumetric flow;
• can be installed between flanges; and
• can be made from corrosion resistance materials at low cost.

Table of contents

Ultrasonic Flowmeters

8.1 Introduction 3

8.2 Doppler method 3

8.3 Transit time meter 5

8.4 Flow profile 7

8.5 Frequency difference 8

8.6 Clamp on instruments 9

8.7 Velocity of Sound Measurement 10

8.7.1 Factors influencing the velocity of sound 10

8.8 Beam scattering 11

8.9 Summary 11

8.9.1 Advantages 11

8.9.2 Disadvantages 12

8.9.3 Application limitations 12

Chapter 8

Ultrasonic Flowmeters

Objectives

When you have completed this chapter you should be able to:

• Explain the principle of Doppler flow measurement
• Describe the difference between transit time and frequency difference meters
• Examine the effects of profile on the accuracy and show how multi-beam paths may be use to increase the accuracy and make the measurement largely profile independent
• Describe the use of clamp-on meters
• Explain the concept of cross correlation technology

8.1 Introduction

Ultrasonic flowmeters, suitable for both liquids and gases, have been available for more than twenty years and are currently the only truly viable non-intrusive measuring alternative to the electromagnetic flowmeter.

Unfortunately, although originally hailed as a general panacea for the flow measurement industry, lack of knowledge and poor understanding of the limitations of early instruments (especially the Doppler method) often lead to its use in unsuitable applications.

Nonetheless, the ultrasonic meter is probably the only meter capable of being used on large diameter pipes (above 3 m bore) at a reasonable cost and performance (around 1%).

In essence there are three basic principles used in ultrasonic metering: the Doppler method; the time-of-flight method; and the frequency difference method.

8.2 Doppler method

Doppler flowmeters are based on the Doppler effect — the change in frequency that occurs when a sound source and receiver move either towards or away from each other. The classic example is that of an express train passing through a station. To an observer, standing on the platform, the sound of the train appears to be higher as the train approaches and then falls as the train passes through the station and moves away. This change in frequency is called the Doppler shift.

In the Doppler ultrasonic flowmeter, an ultrasonic beam (usually of the order of 1 to 5 MHz) is transmitted, at an angle, into the liquid (Figure 8.1). Assuming the presence of reflective particles (dirt, gas bubbles or even strong eddies) in the flowstream, some of the transmitted energy will be reflected back to the receiver. Because the reflective particles are moving towards the sensor, the frequency of the received energy will differ from that of the transmitted frequency (the Doppler effect).

This frequency difference, the Doppler shift, is directly proportional to the velocity of the particles.

Assuming that the media velocity (v) is considerably less than the velocity of sound in the media (C), the Doppler frequency shift (Δf) is given by:

Δf = 2f_t v cosθ / c

where f_t is the transmitted frequency. From this it can be seen that the Doppler frequency, Δf, is directly proportional to flow rate.

The velocity of sound in water is about 1500 m/s. If the transmitted frequency is 1 MHz, with transducers at 60°, then for a media velocity of 1 m/s the Doppler shift is around 670 Hz.

Since this technique requires the presence of reflecting particles in the media, its use in ultra-clean applications or, indeed, with any uncontaminated media, is generally, precluded. Although some manufacturers claim to be able to measure ‘non-aerated’ liquids, in reality such meter rely on the presence of bubbles due to micro-cavitation originating at valves, elbows or other discontinuities.

In order for a particle to be ‘seen’, it needs to be approximately 1/10 larger than the wavelength of the acoustic frequency in the liquid. In water, a 1 MHz ultrasonic beam would have a wavelength of about 1,5 mm and so particles would need to be larger than 150 μm in order to reflect adequately.

Whilst air, oil particle and sand are excellent sonic reflectors, the presence of too may particles can attenuate the signal so that very little of the signal reaches the receive transducer.

Probably the single biggest drawback of this technology is that in multiphase flows, the particle velocity may bear little relationship to the media velocity. Even in single phase flows, because the velocity of the particles is determined by their location within the pipe, there may be several different frequency shifts — each originating at different positions in the pipe. As a result, the Doppler method often involves a measurement error of 10 % or even more.

Generally, Doppler meters should not be considered as high performance devices and are cost effective when used as a flow monitor. They work well on dirty fluids and typical applications include sewage, dirty water, and sludge. Doppler meters are sensitive to velocity profile effects and they are temperature sensitive.

8.3 Transit time meter

The ultrasonic transit time measuring method is based on the fact that, relative to the pipe and the transducers, the propagation speed of an ultrasonic pulse travelling against the media flow will be reduced by a component of the flow velocity. Similarly, the speed of propagation of the pulse travelling downstream is increased by the fluid velocity. The difference between these two transit times can be directly related to the flow velocity.

In practice, the meter comprises two transducers (A and B) mounted at an angle to the flow and having a path length L (Figure 8.2) — with each acting alternately as the receiver and transmitter. The transit time of an ultrasonic pulse, from the upstream to the downstream transducer, is first measured and then compared with the transit time in the reverse direction.

Mathematically:

where:

T_AB = upstream travel time

T_BA = downstream travel time

L      = path length through the fluid

C      = velocity of sound in medium

v      = velocity of medium.

The difference in transit time ΔT is:

Since the velocity of the medium is likely to be much less than the velocity of sound in the medium itself (15 m/s compared to 1500 m/s), the term v² cos² θ will be very small compared with C² and may thus be ignored for all practical flow velocities. Thus:

This shows that the flow velocity v is directly proportional to the transit time difference ΔT.

This also illustrates that v is directly proportional to C² (the square of the speed of sound) which will vary with temperature, viscosity, and material composition.

Fortunately, it is possible to eliminate the variable C² from the equation:

where T_M is the mean transit time given by:

Since both the length L and the angle θ are likely to remain constant it is only necessary to calculate the sum and difference of the transit times in order to derive the flow rate independent of the velocity of sound in the media.

The accuracy of measurement is determined by the ability of the instrument to measure accurately the transit time. In a 300 mm diameter pipe, for example, with the transducers set at 45 °, and the media flowing at 1 m/s, the transit time is about 284 μs and the time difference ΔT is less than 200 ns. This means that in order to measure the velocity with a full scale accuracy of 1 %, must be at the very least down to 2 ns. With smaller diameter pipes, the measurement accuracy would need thus to be in the picosecond range. Obviously, with longer path lengths, this stringent time measurement requirement becomes easier to meet and performance thus tends to be better with large bore pipes.

As distinct from Doppler meters, transit time meters work better on clean fluids and typical applications include: water, clean process liquids, liquefied gases and natural gas pipes.

8.4 Flow profile

If, as shown in Figure 8.3, a single ultrasonic path is used the measurement is very much determined by the flow profile, with a laminar-to-turbulent error of up to 33%.

This error can be reduced by using a dual path, as shown in Figure 8.4, by which the laminar-to-turbulent error may be reduced to 0,5%.

A new multi-channel custody-transfer ultrasonic flowmeter makes use of ten sensors to form five measurement paths located in the cross section of the flowtube (Figure 8.5) — thus providing a measurement that is essentially independent of the flow profile — with accuracies to 0,15% and repeatability down to 0,02%.

8.5 Frequency difference

The frequency difference or ‘sing-around’ flowmeter makes use of two independent measuring paths — with each having a transmitter (A and A’) and a receiver (B or B’) (Figure 8.6). Each measuring path operates on the principle that the arrival of a transmitted pulse at a receiver triggers the transmission of a further pulse. As a result, a pair of transmission frequencies is set up — one for the upstream direction and another for the downstream direction. The frequency difference is directly proportional to the flow velocity.

Thus:

The frequency difference ΔF is given by:

The main advantage of this system is that because the frequency difference is directly proportional to flow, no maths function is required. Further, the measurement is independent of the velocity of sound in the medium.

8.6 Clamp on instruments

Transducers that are clamped externally to the walls of the pipe provide portable non-intrusive flow measurement systems that can be installed within a few minutes to virtually any pipe. Pipe materials include: metal, plastic, ceramic, asbestos cement and internal and externally coated pipes.

Because the ultrasonic pules must traverse the pipe wall and any coatings, the thicknesses must, of course, be known. In addition, the presence of deposits on the inside pipe surface will affect the transmitted signal strength and, therefore, performance.

Despite these obstacle, modern clamp-on ultrasonic meters incorporating microprocessor technology that allows the transducer mounting positions and calibration factors to be calculated for each individual application and provides measuring accuracy of 1 to 3% — depending on the application.

8.7 Velocity of Sound Measurement

Because ultrasonic meters measure volumetric flow which is, in most cases, not relevant for plant operation purposes, their output is correlated to mass flow — assuming a fixed actual density (reference density) under operating conditions. Consequently, deviations in actual density will cause a misreading in mass flow which is inversely proportional to the deviation compared with the reference density.

Since the velocity of sound is a characteristic property of a fluid, its measurement, in conjunction with the temperature and pressure of the fluid, can be used as a measure/indication of:

— actual flowing density
— concentration (e.g. for fluids consisting of two distinctive components);
— molecular weight (W pressure, temperature, Cp/Cv ratio and compressibility are known).

Furthermore, since deviations of the velocity of sound signal/range will indicate a change in fluid composition, its output may thus be used as an ‘interface detector’ — alerting operators to different plant operating conditions and/or feed stock changes or changes in composition e.g. contamination in heavy crude.

Since the signal strength will also be measured, deviations in signal strength could indicate viscosity changes, an increased level of solids (crystal formation, catalyst carry over) and/or bubbles (flashing off of dissolved gases under changed pressure/temperature conditions) in the fluid.

In applications where it is required to determine changes in the constituency of the medium, the instrument should be capable of determining and displaying the speed of sound through the medium as a separate parameter.

8.8 Beam scattering

As indicated earlier, beam scattering/dispersion may occur if the fluid contains too many particles (crystals, catalyst particles). Further, as soon as the fluid ceases to be single phase, beam scattering may occur under bubble flow or mist flow conditions.

Bubble flow could appear with liquids operating close to their boiling point where only a marginal pressure decrease could cause the liquid to evaporate and form bubbles.

Another flashing off phenomena (not so well recognised as boiling off) occurs if gas is dissolved in liquid. Generally, as the pressure decreases or the temperature rises, the dissolved gas can no longer be contained in the liquid and will flash off until a new equilibrium is reached.

Typical examples of gases soluble in liquid are:

— H₂S in water
— H₂S in DlPA (diisopropylamine)
— CO/C0₂ in water
— C0₂ in methanol

In order to minimise or prevent bubble flow, the meter should be moved to a location in the line with a higher pressure, e.g. downstream of a pump

In immiscible mixtures (e.g. water/oil), beam scattering should be avoided by thorough upstream agitation to ensure that no oil droplets in water or water droplets in oil are present at the meter.

Product layering may also introduce beam scattering and should be avoided by proper mixing. Product layering occurs not just as a result of poorly mixed products, but at locations where cold and hot streams are mixed.

Layering will most likely occur directly downstream of a tie-in of a cold stream with a hot stream, of the same product, as a result of density differences. To avoid product layering, the fluid should be thoroughly mixed upstream of the meter using reducers (d/D ≤ 0.7) or static mixers.

8.9 Summary

Apart from not obstructing the flow, ultrasonic flowmeters are not affected by corrosion, erosion or viscosity. Most ultrasonic flowmeters are bi-directional, and sense flow in either direction.

8.9.3 Application Limitations

For the transit time meter, the ultrasonic signal is required to traverse across the flow, therefore the liquid must be relatively free of solids and air bubbles. Anything of a different density (higher or lower) than the process fluid will affect the ultrasonic signal.

Turbulence or even the swirling of the process fluid can affect the ultrasonic signals. In typical applications the flow needs to be stable to achieve good flow measurement, and typically allowing sufficient straight pipe up and downstream of the transducers does this. The straight section of pipe required upstream and downstream is dependent on the type of discontinuity and varies for gas and liquid as shown in Tables 8.1 and 8.2.

Table 8.3 provides a list of the liquid media that can be measured using ultrasonic meters.

D = internal diameter of pipe

D = internal diameter of pipe

Substance	Formula	Sound velocity (m/s)	Substance	Formula	Sound velocity (m/s)
Acetic acid	CH3OOH	1159 (at 20°C)	Chloroform	CHCl3	931 (at 20°C)
Acetic anhydride	(CH3CO)2O	1180 (at 20°C)	1-Chloro-propane	C3H7Cl	1058
Acetic acid, ethyl ester	C4H8O2	1085	Cinnamic aldehyde	C9H8O	1554
Acetic acid, methyl ester	C3H6O2	1211	Colamine	C2H7NO	1724
Acetone	C3H6O	1190 (at 20°C)	m-Cresol	C7H8O	1500 (at 20°C)
Acetonitrile	C2H3N	1290	Cyanomethane	C2H3N	1290
Acetonylacetone	C3H6O	1399	Cyanohexane	C6H12	1284 (at 20°C)
Acetylene dichloride	C2H2Cl2	1015	Cyclohexanol	C6H12O	1454
Acetylene, tetrabromide	C2H2Br4	1027	Cyclohexanone	C6H10O	1423
Acetylene, tetrachloride	C2H2Cl4	1147	Decane	C10H22	1252
Alcohol	C2H6O	1207	n-Decylene	C10H20	1235
Alkazene-13	C15H24	1317	Diacetyl	C4H6O2	1236
Alkazene-25	C10H12Cl2	1307	Diamylamine	C10H23N	1256
2-Amino-ethanol	C2H7NO	1724	1, 2 Dibromo-ethane	C2H4Br2	995
2- Aminotilidine	C7H9N	1618	trans-1, 2 Dibromoethene	C2H2Br2	935
4- Aminotilidine	C7H9N	1480(at -33°C)	Dibutyl phthalate	C6H22O4	1408
Ammonia	NH3	1729	Dichloro-t-buthl alcohol	C4H8Cl2O	1304
t-Amyl alcohol	C5H12O	1204	2,3 Dichlorodixane	C4H6Cl2O2	1391
Aminobenzene	C6H5NO2	1639	Dichlorodifluormethane (Freon 12)	CCl2F2	774.1
Azine	C6H5N	1415	1, 2 Dichloro ethane	C2H4Cl2	1193
Benzene	C6H6	1306	Dichloro-fluoromethane (Freon 21)	CHCl2F	891 (at 0°C)
Bromine	Br2	889	1-2-Dichlorohexafluorocyclobutane	C4Cl2F6	669
Bromo-benzene	C6H5Br	1170	1-3-Dichloro-isobutane	C2H8Cl2	1220
1-Bromo-butane	C4H9Br	1019	Dichloro methane	CH2Cl2	1070
Bromo-ethane	C2H5Br	900	Diethyl ether	C2H10O	985
Bromoform	CHBr3	918	Diethylene glycol	C2H10O3	1586
n-Butane	C4H10	1085 (at -5°C)	Diethylene glycol, monoethyl ether	C6H14O3	1458
sec-Butylalcohol	C4H10O	1240	Diethylenimide oxide	C4H9NO	1442
n-Butyl bromide	C4H9Br	1019 (at 20°C)	1, 2-Dimethyl-benzene	C8H10	1331.5
n-Butyl chloride	C4H9Cl	1140	2, 2-Dimthyl-butane	C6H14	1079
Butyl oleate	C22H42O2	1404	Dimethyl ketone	C3H6O	1174
2, 3 Butyl glycol	C4H10O2	1484	Dimethyl pentane	C7H16	1063
Carbinol	CH4O	1076	Dimethyl phthalate	C8H10O4	1463
Carbitol	C6H14O3	1458	Dioxane	C4H8O2	1376
Carbon dioxide	CO2	839 (at -37°C)	Dodecane (23)	C12H26	1279
Carbon disulphide	CS2	1158 (at 20°C)	1, 2-Ethanediol	C2H6O2	1658
Carbon tetrachloride	CCl4	938 (at 20°C)	Ethanenitrile	C2H3N	1290
Cetane	C16H34	1338 (at 20°C)	Ethanoic anhydride (22)	(CHCO)2O	1180
Chloro-benzene	C6H5Cl	1289	Ethanol amide	C2H7NO	1724
1-Chloro-butane	C4H9Cl	1140	Ethyl acetate	C4H8O2	1164 (at 20°C)
Ethyl alcohol	C2H6O	1207	2-Methyl-butane	C5H12	980
Ethyl benzene	C8H10	1338 (at 20°C)	Methyl carbinol	C2H6O	1207
Ethyl Bromide	C2H5Br	900 (at 20°C)	Methyl-chloroform	C2H3Cl3	985
Ethyl iodide	C2H5I	876 (at 20°C)	Methyl-cyanide	C2H3N	1290
Ethyl ether	C4H10O	985	3-Methyl-cyclohexanol	C7H14	1400
Ethylene bromide	C2H4Br2	995	Methylene chloride	CH2Cl2	1070
Ethylene chloride	C2H4Cl2	1193	Methylene iodide	CH2I2	980
Ethylene glycol	C2H6O2	1666 (at 20°C)	Methyl formate	C2H4O2	1127
d-Fenochone	C10H16O	1320	Methyl iodide	CH3I	978
Fluoro-benzene (46)	C6H5F	1189	α-Methyl napthalene	C11H10	1510
Formaldehyde, methyl ester	C2H4O2	1127	2-Methyl phenol	C7H8O	1541 (at 20°C)
Formamide	CH3NO	1622	Morpholine	C4H9NO	1442
Furfural	C5H4O2	1444	Naptha	–	1225
Furfuryl alcohol	C5H6O2	1450	Nitrobenzene	C6H5NO2	1473 (at 20°C)
Gallium	Ga	2870 (at 30°C)	Nitromethane	CH3NO2	1300
Glycerol	C3H8O3	1904	Nonane	C9H2O	1207
Heptane	C7H16	1131	1-Nonene	C9H18	1207
Hexadecane	C16H34	1338	0ctane	C8H16	1172
Hexalin	C6H12O	1454	Oil, car (SAE 20/30)	–	870
Hexane	C6H14	1112	Oil, Castor	C11H10O10	1477
2, 5-Hexanedione	C6H10O2	1399	Oil, Diesel	–	1250
n-Hexanol	C6H14O	1300	Oil, (Lubricating X200)	–	1530
Hexahydrobenzene	C6H12	1248	2, 2-0xydiethanol	C4H10O3	1586
Hexahydrophenol	C6H12O	1454	Pentachloro-ethane	C2HCl5	1082
2-Hydroxy-toluene	C7H8O2	1541 (at 20°C)	Pentane	C5H12	1020
Iodo-benzene	C6H5I	1114 (at 20°C)	Perchlorocyclopentadience	C5Cl6	1150
Iodo-ethane	C2H5I	876 (at 20°C)	Perchloro-ethylene	C2Cl4	1036
Iodo-methane	CH3I	978	Perchloro-1-Hepten	C7F14	583
Isobutyl acetate	C6H12O	1180 (at 27°C)	Perfluoro-n-Hexane	C6F14	508
Isobutanol	C4H10O	1212	Phene	C6H6	1306
Isopentane	C5H12	980	β-Phenyl acrolein	C9H8O	1554
Isopropanol	C3H8O	1170 (at 20°C)	Phenyl amine	C6H5NO5	1639
Kerosene	–	1324	Phenyl bromide	C6H5Br	1170 (at 20°C)
Ketohexamethylene	C6H10O	1423	Phenyl chloride	C6H5Cl	1273
Mercury	Hg	1451 (at 20°C)	Phenyl iodide	C6H5I	1114 (at 20°C)
Mesityloxide	C6H16O	1310	Phenyl methane	C7H8	1328 (at 20°C)
Methanol	CH4O	1076	3-Phenyl propenal	C9H8O	1554
Methyl acetate	C3H6O2	1181 (at 20°C)	Phthalardione	C8H4O3	1125(at 152°C)
o-Methyl aniline	C7H9O	1618	Pimelic ketone	C6H10O	1423
Methyl benzene	C7H8	1328 (at 20°C)	Propane	C3H8	1003
1,2,3-Propanetriol	C3H8O3	1904	Tetraethylene glycol	C8H18O	1586
1-Propanol	C3H6O	1222	Tetrahydro-1, 4-isoxazine	C4H9NO	1442
n-Propyl-acetate	C5H10O2	1280	Toluene	C7H9	1328 (at 20°C)
n-Propyl-alcohol	C3H8O	1225	Toluidine	C7H9N	1618
Propyl chloride	C3H7Cl	1058	Tribromo-methane	CHBr3	918
Propylene	C3H6	963	1, 1, 1-Trichloro-ethane	C2H3Cl3	985
Pyridine	C6H5N	1415	Trichloro-ethene	C2HCl3	1028
Refrigerant 11	CCl3F	828.3 (at 0°C)	Trichloro-fluoromethane (Freon 11)	CCl3F	828 (at 0°C)
Refrigerant 12	CCl2F2	774(at -40°C)	Trichloro-methane	CHCl3	979
Refrigerant 21	CHCl2F	891 (at 0°C)	Triethyl-amine	C6H15N	1123
Refrigerant 22	CHClF2	893.9(at 50°C)	Triethylene glycol	C6H14O4	1608
Refrigerant C318	CF8	574 (at -10°C)	Trinitrotoluene	C7H5(NO2)3	1610 (at 81°C)
Silicone (30 cp)	–	990	Turpentine	–	1255
Sulphuric Acid	H2SO4	1257.6	Water, distilled	H2O	1482 (at 20°C)
1,1,2,2-Tetrabromo-ethane	C2H2Br4	1027	Water, heavy	D2O	1388 (at 20°C)
Tetrachloroethane	C2H2Cl4	1170	Water, sea	–	1520 (at 20°C)
Tetrachloro-ethene	C2Cl4	1036 (at 20°C)	Wood Alcohol	CH4O	1076
Tetrachlormethane	CCl4	926	m-Xylene	CH10	1343 (at 20°C)
Tetradecane	C14H3O	1331 (at 20°C)	Xylene hexafluoride	C8H4O6	879

Table of contents

Mass Flow Measurement

9.1 Introduction 3

9.2 The Coriolis force 4

9.3 A practical system 6

9.4 Multiple phase flow 8

9.5 Density Measurement 9

9.6 Loop arrangements 9

9.7 Straight through tube 10

9.8 Application in the food industry 11

9.9 Applications in the chemical industry 12

9.10 Summary of Coriolis mass measurement 13

9.10.1 Advantages 14

9.10.2 Disadvantages 14

9.10.3 Application limitations 14

9.11 Thermal mass meters 14

9.11.1 Heat loss or ‘hot wire’ method 14

9.11.1.1 Advantages 16

9.11.1.2 Disadvantages 16

9.11.2 Temperature rise method 17

9.11.2.1 Disadvantages 17

9.11.3 External temperature rise method 17

9.11.3.1 Advantages 18

9.11.3.2 Disadvantages 18

9.11.4 Capillary-tube meter 19

9.11.5 Liquid mass flow 20

Chapter 9

Mass Flow Measurement

Objectives

When you have completed this chapter you should be able to:

• Appreciate the need for mass flow measurement
• Describe the basic concept of Coriolis force
• Demonstrate how the Coriolis force will attempt to slow down the rotation of a rotating pipe
• Show how the basic theory may be applied to a practical system
• Describe how density measurement is accomplished a Coriolis meter
• Examine various pipe configurations
• Describe the straight-through pipe system
• Show how the Coriolis meter can be applied in the food and chemical industries

9.1 Introduction

In many industries, particularly the chemical industry, most chemical reactions are largely based on their mass relationship. Consequently, by measuring the mass flow of the product it is possible to control the process more accurately. Further, the components can be recorded and accounted for in terms of mass.

Mass flow is a primary unit of flow measurement and is unaffected by viscosity, density, conductivity, pressure and temperature. As a result it is inherently more accurate and meaningful for measuring material transfer.

Traditionally, mass flow has been measured inferentially. Electromagnetic, orifice plate, turbine, ultrasonic, venturi, vortex shedding, etc, all measure the flow of the medium in terms of its velocity through the pipe (e.g. metres per second). However, because the dimensions of the pipe are fixed, we can also determine the volumetric flow rate (e.g. litres per second). Further, by measuring density and multiplying it by the volumetric flow rate, we can even infer the actual mass flow rate. However, such indirect methods commonly result in serious errors in measuring mass flow.

Consequently, possibly the most significant advance in flow measurement over the last few years has been the introduction of the Coriolis mass flowmeter. Not only does this technology allow mass flow to be measured directly but Coriolis meters are readily able to cope with the extremely high densities of, for example, dough, molasses, asphalt, liquid sulphur, etc, found in many industries.

9.2 The Coriolis force

The Coriolis meter is based on the Coriolis force— sometimes, incorrectly, known as gyroscopic action.

Consider two children, Anne and Belinda, sat on a rotating platform. Anne is situated mid-way between the axis and the outer edge of the platform while Belinda is sat at the outer edge itself (Figure 9.1). If Anne now throws a ball directly to Belinda, Belinda will fail to receive the ball!

The reason will have nothing to do with Anne’s ability to throw a straight ball (we’ll assume she’s a perfect pitcher) or Belinda’s ability to catch a ball (we’ll assume she’s a perfect catcher). The reason is due to what is termed the Coriolis effect.

What Anne ignored is that although the platform is rotating at a constant angular speed (ω) she and Belinda are moving at different circular or peripheral speeds. Indeed, the further you move away from the axis, the faster your speed. In fact, the peripheral speeds of each are directly proportional to the radius i.e.:

v = r.ω

where:

v = peripheral velocity

r = radius

ω = angular speed.

In this case, Belinda at the edge of the platform will have a peripheral speed of twice that of Anne (Figure 9.2). Thus, when Anne throws the ball radially outwards towards Belinda, the ball initially has not only the velocity (v) radially outwards, but also a tangential velocity v_A due to the rotation of the platform. If Belinda had this same velocity v_A the ball would reach her perfectly. But Belinda’s speed (v_B) is twice that of v_A. Thus when the ball reaches the outer edge of the platform it passes a point that Belinda has already passed and so the ball passes behind her.

Consequently, to move the ball from Anne to Belinda its peripheral speed needs to be accelerated from v_A to v_B. This acceleration is a result of what is termed the Coriolis force, named after the French scientist who first described it, and is directly proportional to the product of the mass in motion, its speed and the angular velocity of rotation:

F_cor = 2mωv

where:

F_cor = Coriolis force

v = peripheral velocity

ω = angular speed

m = the mass of the ball

Looking at this from another point, if we could measure the Coriolis force and knowing the peripheral velocity and the angular speed, we could determine the mass of the ball.

How does this relate to mass measurement of fluids?

Consider a simple, straight liquid-filled pipe rotating around axis A, at an angular velocity ω (Figure 9.3). With no actual liquid flow, the liquid particles move on orbits equivalent to their distance r from the axis of rotation. Thus, at distance r₁, the tangential velocity of a particle would be r1.ω whilst at double the distance r₂, the tangential velocity would also double to r₂.ω.

If now, the liquid flows in a direction away from the axis A, at a flow velocity v, then as each mass particle moves, for example, from r₁ to r₂ it will be accelerated by an amount equivalent to its movement along the axis from a low to a higher orbital velocity. This increase in velocity is in opposition to the mass inertial resistance and is felt as a force opposing the pipe’s direction of rotation — i.e. it will try to slow down the rotation of the pipe. Conversely, if we reverse the flow direction, particles in the liquid flow moving towards the axis are forced to slow down from a high velocity to a lower velocity and the resultant Coriolis force will try to speed up the rotation of the pipe.

Thus, if we drive the pipe at a constant torque, the Coriolis force will produce either a braking torque or an accelerating torque (dependent on the flow direction) that is directly proportional to the mass flow rate.

Although the possibility of applying the Coriolis effect to measure mass flow rate was recognised many years ago, it is little more than twenty years since the first practical design was devised.

During this development period, many pipe arrangements and movements have been devised — with the major drawback of early systems lying in their need for rotational seals. This problem was overcome by using oscillatory movement rather than rotational.

9.3 A practical system

One of the simplest arrangements that incorporates all the positive features of a Coriolis-based mass flow meter is illustrated in Figure 9.4. Here, a tubular pipe, carrying the liquid, is formed in a loop and vibrated around the z axis. The straight parts of the pipe, A-B and C-D, oscillate on the arcs of a circle and without any flow will remain parallel to each other throughout each cycle.

If a liquid now flows through the tube in the direction shown, then the fluid particles in section A-B will move from a point having a low rotary velocity (A) to a point having a high rotary velocity (B). This means that each mass particle must be accelerated in opposition to the mass inertial resistance. This opposes the pipe’s direction of rotation and produces a Coriolis force in the opposite direction. Conversely, in section C-D, the particles move in the opposite direction — from a point having a high rotary velocity (C) to a point having a low rotary velocity (D).

The resultant effect of these Coriolis forces is to delay the oscillation in section A-B and accelerate it in section C-D. As a result section A-B tends to lag behind the undisturbed motion whilst section C-D leads this position. Consequently, the complete loop is twisted by an amount that is directly and linearly proportional to the mass flow rate of the fluid —

with the twisting moment lent to the pipe arrangement being measured by sensors. Figure 9. 5 shows a typical arrangement.

Because of this twisting motion, one of the major design factors of the oscillating tube is to prevent the pipe fracturing because of stress ageing. Here, computer simulation has allowed a geometric design to be developed for thick-walled tubes that does not expose them to bending stress but to torsional strain applied evenly to the cross-section of the tube.

A further factor in reducing stress fractures is to limit the oscillation amplitude to approximately 1 mm that, in an optimally designed system, would be about 20 % of the maximum permitted value. Thus, because the distortion caused by the Coriolis forces is about 100 times smaller (a magnitude of about 10 μm) a measurement resolution of ± 0,1 % amounts to only a few nanometres.

9.4 Multiple phase flow

Whilst fundamentally suitable for both gaseous and liquid media, in practice the Coriolis technique is really only suitable for gases having similar mass flow rates typical of a liquid media. These are generally only obtained with high density gases.

Mixtures having low admixtures of finely injected gas in liquids or fine grain solid admixtures, react almost like a single phase liquid in that the admixtures merely alter the density. A Coriolis mass measurement is thus still effective.

At higher levels of non-homogeneity, two problem areas occur. First, a non-homogenous mixture results in an irregular fluctuating density and, thus, a constantly fluctuating resonant frequency that can put the system out of phase.

A second problem is that the Coriolis method assumes that all particles of the medium are accelerated on orbits in accordance with the movement of the pipes. With high proportions of gas, particles in the middle of the pipe will no longer complete the movement of the pipe. Conversely, the Coriolis forces of the mass particles in the centre of the pipe will no longer effect the pipe walls. The result is that the measuring value will be systematically reduced.

Most Coriolis-based systems can still tolerate an air-water gas volume of between 4 and 6%. However, because the behaviour of liquid-gas mixtures depends on the distribution of bubbles, and the velocity of sound depends very largely on the materials involved, these figures cannot simply be transferred to other mixtures. With liquids having a lower surface tension than water, for example, considerably higher proportions of gas can be tolerated.

The conditions for solids in water are a great deal more favourable and many good systems can tolerate suspensions of fine grain solids of up to 20% in water without any difficulty.

9.5 Density Measurement

The measurement of mass flow by the Coriolis meter is, fundamentally, independent of the density of the medium. However, the resonant frequency of the oscillating pipe will vary with density — falling as the density increases. In many instruments this effect is used to provide a direct measurement of density by tracking the resonant oscillation frequency.

The temperature of the pipe system changes with the temperature of the measured medium and alters its modulus of elasticity. This not only alters the oscillation frequency but also the flexibility of the loop system. Thus, the temperature must be measured as an independent quantity and used as a compensating variable. The temperature of the medium is, therefore, also available as a measured output.

9.6 Loop arrangements

There are many different designs of Coriolis Mass Flowmeter, in the majority of which the primary sensor involves an arrangement of convoluted tubes through which the measured fluid flows.

In any arrangement requiring the tube to be bent to form the desired convolutions, the outside wall is stretched and becomes thinner whilst the inner wall becomes thicker. This distortion will vary from one tube to another and, when the flowmeter requires two such convoluted tubes, it becomes difficult to balance them both dimensionally and dynamically.

Furthermore, if the fluid to be measured is abrasive, this already weakened part of the flowmeter is likely to be most severely stressed. Abrasive material can also cause erosion that will change the stiffness of the resonant elements and so cause measurement errors.

In the parallel loop arrangement (Figure 9.6) the flow is split at the inlet to follow parallel paths through the two sections. The advantage of this is that the total cross-sectional area of the flow path is the sum of the cross-sections of both pipes. At the same time, since each pipe has a relatively small cross section it may be designed with to have a high flexibility — thus increasing the sensitivity to the Coriolis effect.

A disadvantage of this arrangement is that the action of splitting and then re-combining the flow introduces a significant pressure drop. Furthermore, the flow may not be divided equally, in which case an unbalance is generated — especially if solids or gases are entrained in the liquid flow. The same reasoning applies if the balance of the split is disturbed by partial or complete blockage of one section — again leading to measurement errors. The balance may also be disturbed by separation of the components in a two-phase flow, such as air or solids entrained in liquid flow. A similar problem exists with shear sensitive fluids.

In the serial arrangement (Figure 9.7) the total length of the pipe is considerably greater due to the second loop and must therefore have a larger cross-sectional area to reduce the pressure loss. This however leads to increased rigidity that makes it less sensitive to the Coriolis effect at low flow rates. At high flow rates however, there is less pressure drop, and the pipe is easier to clean.

9.7 Straight through tube

The development of a straight through tube mass flowmeter, without any loops or bends, is based on the fact that a vibrating tube, fixed at its ends, also has a rotational movement about the fixed points and thereby generates a Coriolis force.

In the first of such designs, as shown in Figure 9.8, two tubes are vibrated at their resonant frequency. Infrared sensors are place at two exactly defined locations at the inlet and outlet of the pipe to detect the phase of the pipe oscillation. At zero flow the oscillation of the system is in phase. When liquid flows into the system the flowing medium is accelerated on the inlet and decelerated on the outlet and the oscillation of the system is out of phase. The measured phase difference is proportional to mass flow.

In comparison with the ‘looped’ type Coriolis mass flowmeter, the straight through pipe obviously offers a much lower pressure loss and since it has no bends or loops, it is easier to clean.

Although this design avoids many of the problems associated with the convoluted tube meter, the flow splitter still causes a pressure drop and an unbalance can still occur due to a partial or complete blockage of one section.

Subsequently single straight tube designs have been introduced with no bends or splitters

9.8 Application in the food industry

The special requirements of the food and beverage industries are both demanding and varied. The most obvious requirement is for approved quick release sanitary fittings that allow the instrument to be rapidly removed for cleaning and which can prevent bacterial entrapment. Often there is also a requirement for the system to be automatically self draining when installed vertically (Figure 9.9).

The instrument must also often cater for Clean-in-Place (CIP) and Steam-in-Place (SIP) requirements. It should thus be capable of working with high material temperatures (e.g. up to 130 °C) and should feature high temperature shock resistance — allowing the system to be cleaned with super-heated steam. And where the system is required to be cleaned with a ‘pig’ — prohibiting the use of a flow splitter is prohibited.

9.9 Applications in the chemical industry

Not only should the mass flow meter be able to work with material temperatures of up to 150 °C but it should also cater for liquid heating/cooling and electrical heating of the primary sensing head. This is particularly useful in the measurement of media that liquefies only at high temperatures.

A case in point would be the measurement of liquid sulphur which has its minimum viscosity at 145 °C. Thus, the whole installation requires controlled heat tracing with the mass flow meter head maintaining the media at 145 °C. When production stops and the process cools down, the sulphur solidifies. Consequently, another important feature of the instrument in this application is that it should again empty automatically when installed vertically.

Another important feature, particularly relevant to the petrochemical industry, is the availability of an explosion proof model up to the highest attainable temperature (T6). This means that media with extremely low ignition temperatures can be measured without danger.

9.10 Summary of Coriolis mass measurement

Coriolis meters provide direct, in-line and accurate mass flow measurements that are independent of temperature, pressure, viscosity and density. Mass flow, density and temperature can be accessed from the one sensor. They can also be used for almost any application when calibrated.

For critical control, mass flow rate is the preferred method of measurement and because of their accuracy Coriolis meters are becoming very common for applications requiring very tight control. Apart from custody transfer applications, they are used for chemical processes and expensive fluid handling.

9.11 Thermal mass flowmeters

Thermal mass flow measurement, which dates back to the 1930’s, is a quasi-direct method, suited, above all, for measuring gas flow. Thermal mass flow meters infer their measurement from the thermal properties of the flowing medium (such as specific heat and thermal conductivity) and hence are capable of providing measurements which are proportional to the mass of the medium.

In the ranges normally encountered in the process industry, the specific heat c_p of the gas is essentially independent of pressure and temperature and is proportional to density and therefore to mass.

The two most commonly used methods of measuring flow using thermal techniques are either to measure the rate of heat loss from a heated body in the flow stream; or to measure the rise in temperature of the flowing medium when it is heated.

9.11.1 Heat loss or `hot wire’ method

In its simplest form a hot body (a heated wire, thermistor, or RTD) is placed in the main stream of the flow (Figure 9.10). According to the first law of thermodynamics, heat may be converted into work and vice versa. Thus, the electrical power (I²R ) supplied to the sensor is equal to the heat convected away from it.

Since it is the molecules (and hence mass) of the flowing gas that interact with the heated boundary layer surrounding the velocity sensor and convect away the heat, the electrical power supplied to the sensor is a direct measure of the mass flow rate.

The rate of heat loss of a small wire is given by:

H/t = T[K + 2(πKC_VdρV)^½]

where:

H = heat loss

t = time

T = temperature

K = thermal conductivity

Cv = specific heat

ρ = density

V = velocity

d = wire diameter

In practice, a second ‘temperature sensor’ is immersed in the flow to monitor the gas temperature and automatically correct for temperature changes (Figure 9.11). The mass measuring RTD has a much lower resistance than the temperature RTD and is self heated by the electronics. In a constant temperature system, the instrument measures I²R and maintains the temperature differential between the two sensors at a constant level.

Complete hot wire mass flowmeters (Figure 9.12) are available for pipes up to 200 mm diameter (size DN 200).

Above this size insertion probes are used which incorporate a complete system at the end of rod. Here, in a practical modern industrial meter, a typical sensor comprises a reference grade platinum resistance temperature detector (RTD) wound on a ceramic mandrel and inserted into an encasement or thermowell.

The main limitation of this method is that by its very ‘point’ measurement it is affected by the flow profile within the pipe as well as by the media viscosity and pressure. Further, since the measurement is determined by the thermal characteristics of the media, the system must thus be calibrated for each particular gas — with each mass flow/temperature sensor pair individually calibrated over its entire flow range.

The measured value, itself, is primarily non-linear and thus requires relatively complex conversion. On the positive side, however, this inherent non-linearity is responsible for the instrument’s unique wide rangeability (1000:1) and low speed sensitivity (60 mm/s).

Such instruments also have a fast response to velocity changes (typically 2 seconds) and provide a high level signal, ranging from 0,5 to 8 W over the range of 0 to 60 m/s.

9.11.1.1 Advantages

— Fast response times, < 0.5 ms.

9.11.1.2 Disadvantages

— Require 10 diameters of straight pipe upstream.
— Have similar limitations to pitot tubes.

9.11.2 Temperature rise method

In this method, the gas flows through a thin tube in which the entire gas stream is heated by a constantly powered source — with the change in temperature being measured by RTDs located upstream and downstream of the heating element (Figure 9.13). Because of the heat requirements this method is used for very low gas flows.

Here, the mass flow rate q_m is:

q_m =k. q_Q/c_p.ΔT

where:

k = constant

q_Q = the heat input (W)

c_p = specific heat capacity of the gas (J/kg.K)

ΔT = temperature difference (°C)

9.11.2.1 Disadvantages

— Suitable for low gas flows only.
— Subject to erosion and corrosion.
— More tapping points, increased chances of leakage.

9.11.3 External temperature rise method

An alternative arrangement is often used in which the heating element and temperature sensors are mounted external to the pipe. In the arrangement shown in Figures 9.14 and 9.15, the heating elements and temperature sensors are combined such that the RTD coils are used to direct a constant amount of heat through the thin walls of the sensor tube into the gas. At the same time, the RTD coils sense changes in temperature through changes in their resistance.

9.11.3.1 Advantages

— Non contact, non intrusive sensing
— No obstruction to flow
— Reduced maintenance

9.11.3.2 Disadvantages

— Suitable for low gas flows only
— Subject to erosion and corrosion

9.11.4 Capillary-tube meter

In a typical capillary-tube thermal mass flowmeter the media divides into two paths, one (m₂) through the bypass and the other (m₁) through the sensor tube (Figure 9.16).

As the name implies, the role of the bypass is to bypass a defined portion of the flow so that a constant ratio of bypass flow to sensor flow (m₂/m₁) is maintained.

This condition will only apply if the flow in the bypass is laminar so that the pressure drop across the bypass is linearly proportional to the bypass flow. An orifice bypass, for example, has non-laminar flow so that the ratio of total flow to sensor flow is non-linear.

One solution lies in the use of multiple disks or sintered filter elements. Another solution is the bypass element used by Sierra (Figure 9.17) which comprises a single machined element having small rectangular passages with a high length-to-width ratio. This element provides pure laminar flow and is easily removed and cleaned.

With a linear pressure drop (P1-P2) maintained across the sensor tube, a small fraction of the mass flow passes through the sensor tube. The sensor tube has a relatively small diameter and large length-to-diameter ratio in the range of 50:1 to 100:1 — both features being characteristic of capillary tubes. These dimensions reduce the Reynolds number to a level of less than 2 000 to produce a pure laminar flow in which the pressure drop (P₁ – P₂) is linearly proportional to the sensor’s mass flow rate (m₁).

In actual operation, the long length-to-diameter ratio of the tube ensures that the entire cross-section of the stream is heated by the coils — with the mass flow carrying heat from the upstream coil to the downstream coil. This means the first law of thermodynamics can be applied in its simplest form.

This method is largely independent of the flow profile and the media viscosity and pressure. This means that the flow calibration for any gas can be obtained by multiplying the flow calibration for a convenient reference gas by a constant K factor. K-factors are now available for over 300 gases, giving capillary-tube meters almost universal applicability.

Although the output is not intrinsically linear with mass flow, it is nearly linear over the normal operating range. Accurate linearity is achieved with multiple-breakpoint linearization (for example at 0,25, 50, 75 and 100% of full scale).

In addition to its applicability to very low gas flows, the capillary tube method may also be use for larger flows by changing the bypass to effect a higher or lower value of the bypass ratio (m₂/m₁).

9.11.5 Liquid mass flow

Although the main application of the thermal mass flow meter lies with gases, the same technology may also be applied to the measurement of very low liquid flows e.g. down to 30 grams/hour.

A typical meter is shown in Figure 9.18. Here, the inlet and outlet of the sensor tube are maintained at a constant temperature by a heat sink — with the mid-point of the sensor tube heated to a controlled level e.g. 20°C above the temperature of the inlet-outlet heat sink. These two locations, together with the flow tube, are mechanically connected by a thermally conductive path.

In this manner, the flowing fluid is slightly heated and cooled along the sensor zones, 1 and 2 respectively, to create an energy flow perpendicular to the flow tube. Two RTDs (T₁ and T₂), located at the mid-point of the sensor tube determine the temperature difference. This temperature difference is directly proportional to the energy flow and is, therefore, directly proportional to the mass flow times the specific heat of the fluid.

Table of contents

Open Channel Flow Measurement

10.1 Introduction 3

10.2 The Weir 3

10.2.1 Rectangular weir 5

10.2.2 Trapezoidal (Cipolletti) weir 6

10.2.3 Triangular or V- notch weir 6

10.2.4 Application limitations 7

10.2.4.1 Advantages 7

10.2.4.2 Disadvantages 7

10.3 The flume 7

10.3.1 Flume flow considerations 8

10.3.2 Venturi flume meter 8

10.3.3 Parshall venturi flume 9

10.3.4 Application limitations 11

10.3.4.1 Advantages 11

10.3.4.2 Disadvantages 11

10.4 Level measurement 11

10.4.1 Float measurement 11

10.4.2 Capacitive measuring systems 12

10.4.3 Hydrostatic pressure measurement 13

10.4.4 Bubble injection 14

10.4.5 Ultrasonic 14

10.5 Linearization 15

10.5.1 Non-linear scale 15

10.5.2 Mechanical cam 15

10.5.3 Software 16

Chapter 10

Open Channel Flow Measurement

Objectives

When you have completed this chapter you should be able to:

• Understand the need for open flow measurement
• Explain the functioning of the basic rectangular weir and where the trapezoidal and v-notch weirs are applied
• Describe the differences between the basic venturi flume and the Parshall flume
• Examine the various method from measuring the head including: float, capacitive, hydrostatic, bubble injection and ultrasonics
• Explain the need for linearization and the various options available

10.1 Introduction

In many applications, liquid media is distributed in open channels. Open channels are found extensively in water irrigation schemes, sewage processing and effluent control, water treatment and mining beneficiation.

The most commonly used method of measuring flow in an open channel is through the use of a hydraulic structure (known as a primary measuring device) that changes the level of the liquid. By selecting the shape and dimensions of the primary device (a form of restriction) the rate of flow through or over the restriction will be related to the liquid level in a known manner. In this manner, a secondary measuring element may be used to measure the upstream depth and infer the flow rate in the open channel.

In order that the flow rate can be expressed as a function of the head over the restriction, all such structures are designed so that the liquid level on the upstream side is raised to make the discharge independent of the downstream level. The two primary devices in general use are the weir and the flume.

10.2 The weir

A weir (Figure 10.1) is essentially a dam mounted at right angles to the direction of flow, over which the liquid flows.

The dam usually comprises a notched metal plate — with the three most commonly used being: the rectangular weir; the triangular (or V-notch) weir; and the trapezoidal (or Cipolletti) weir —each having an associated equation for determining the flow rate over the weir that is based on the depth of the upstream pool. The crest of the weir, the edge or surface over which the liquid passes, is usually bevelled — with a sharp upstream corner.

For the associated equation to hold true and accurate flow measurement determined, the stream of water leaving the crest (the nappe), should have sufficient fall (Figure 10.2). This is called free or critical flow, with air flowing freely beneath the nappe so that it is aerated. Should the level of the downstream water rise to a point where the nappe is not ventilated, the discharge rate may be inaccurate and dependable measurements cannot be expected.

10.2.1 Rectangular weir

The rectangular weir was probably the earliest type in use and, due to its simplicity and ease of construction is still the most popular type.

In its simplest form (Figure 10.3 (a)), the weir extends across the entire width of the channel with no lateral contraction. The discharge equation (head vs. flow rate) of such a restriction, without end contractions, is:

q = k L h^1,5

where:

q = flow rate;

k = constant;

L = length of crest; and

h = the head.

Generally, this means that for a 1 % change in flow, there will be a 0,7 % change in the level.

A problem with rectangular weirs without contraction is that the air supply can become restricted and the nappe clings to the crest. In such cases a contracted rectangular weir (Figure 10.3 (b)) is used where end contractions reduce the width and accelerate the channel flow as it passes over the weir and provides the needed ventilation. In this case the discharge equation of such a restriction, with end contractions, becomes:

q = k (L – 0,2 h) h^1,5

where: q = flow rate;

k = constant;

L = length of crest; and

h = the head.

The rectangular weir can normally handle flow rates in the range of 1:20 from about 0 – 15 l/s up to 10 000 l/s or more (3 m crest length).

10.2.2 Trapezoidal (Cipolletti) weir

In the trapezoidal type of weir (Figure 10.4) the sides are inclined to produce a trapezoidal opening. When the sides slope one horizontal to four vertical the weir is known as a Cipolletti weir and its discharge equation (head vs. flow rate) is similar to that of a rectangular weir with no end contractions:

q = k L h^1,5

The trapezoidal type of weir has the same flow range as a rectangular weir.

10.2.3 Triangular or V- notch weir

The V-notch weir (Figure 10.5) comprises an angular v-shaped notch — usually of 90° — and is particularly suited for low flows.

A major problem with both the rectangular and trapezoidal type weirs is that at low flow rates the nappe clings to the crest and reduces the accuracy of the measurement.

In the V-notch weir, however, the head required for a small flow is greater than that required for other types of weirs and freely clears the crest — even at small flow rates.

The discharge equation of the V-notch weir is given by:

q = k h^2,5

where:

q = flow rate;

k = constant; and

h = the head.

This equates to a 0,4 % change in height for a 1 % change in flow.

V-notch weirs are suitable for flow rates between 2 and 100 I/s and, for good edge conditions, the flow range is 1: 100. Higher flow rates can be obtained by placing a number of triangular weirs in parallel.

10.3 The flume

The second class of primary devices in general use is the flume (Figure 10.6). The main disadvantage of flow metering with weirs is that the water must be dammed, which may cause changes in the inflow region. Further, weirs suffer from the effects of silt build-up on the upside stream. In contrast, a flume measures flow in an open channel in which a specially shaped flow section restricts the channel area and/or changes the channel slope to produce an increased velocity and a change in the level of the liquid flowing through it.

Major benefits offered by the flume include: a higher flow rate measurement than for a comparably sized weir; a much smaller head loss than a weir; and better suitability for flows containing sediment or solids because the high flow velocity through the flume tends to make it self-cleaning.

The major disadvantage is that a flume installation is typically more expensive than a weir.

10.3.2 Venturi flume meter

The most common flume is the Venturi flume ( Figure 10.7) whose interior contour is similar to that of a Venturi flow tube with the top removed: normally consisting of a converging section, a throat section, and a diverging section.

The rectangular venturi flume, with constrictions at the side, is the most commonly used since it is easy to construct. In addition, the throat cross section can also be trapezoidal or U-shaped. Trapezoidal flumes are more difficult to design and construct, but provide a wide flow range with low pressure loss. A U-shaped section is used where the upstream approach section is also U-shaped and gives higher sensitivity — especially at low (tranquil) flows.

Although the theory of operation of flumes is more complicated than that of weirs, it can be shown that the volume flow rate through a rectangular Venturi flume is given by:

q = k h^1,5

where:

q = the volume flow;

k = constant determined by the proportions of the flume; and

h = the upstream fluid depth.

10.3.3 Parshall venturi flume

The Parshall Venturi Flume (Figure 10.8) differs from the conventional flat bottomed venturi flume in that it incorporates a contoured or stepped floor that ensures the transition from sub-critical to supercritical flow. This allows it to function over a wide operating range whilst requiring only a single head measurement. The Parshall Venturi flume also has better self-cleaning properties and relatively low head loss.

Parshall Venturi flume are manufactured in a variety of fixed sizes and are usually made of glass fibre reinforced polyester. The user need only install it in the existing channel.

Because of its slightly changed shape, the discharge equation of the Parshall Venturi flume changed slightly to:

q = k hⁿ

where:

q = flow rate;

h = the head; and

k and n are both constants determined by the proportions of the flume.

Generally, the exponent n varies between 1,522 and 1,607, determined mainly by the throat width.

10.4 Level measurement

Whilst a weir or a flume restricts the flow and generates a liquid level which is related to the flow rate, a secondary device is required to measure this level.. Several measuring methods exist:

10.4.1 Float measurement

Float measurement is a direct measurement method in which the height of the float is proportional to the water level (Figure 10.9). This height is mechanically transmitted via either a cable and pulley or a pivoting arm, and converted into an angular position of a shaft that is proportional to liquid level. Alternatively, the mechanical movement may be electrically linearised and converted to a standardised output signal.

Floats are not only affected by changes in ambient air temperature, but are also subject to build up of grease and other deposits that can alter the immersion depth of the float and thus affect the measured value.

Floats generally require the use of a stilling well and, since this method has moving parts that are subject to wear, periodic maintenance and repair is required.

10.4.2 Capacitive measuring systems

The principle of capacitive level measurement is based on the change in capacitance between an insulated probe immersed in the liquid and a grounding plate or tube which is also in contact with the liquid (Figure 10.10). The PVC- or Teflon-coated probe and the grounding plate form the plates of a capacitor and the liquid forms the dielectric. As the liquid level changes, it alters the dielectric constant of the capacitor and, therefore, its capacitance. By measuring the capacitance a reading can be obtained that can be directly related to level and the flow.

The main advantages of this system are that there are no moving parts; no mains power is required at the measuring point; and the distance between the probe and the control room can be up to 600 m.

The main disadvantage is that accuracy is affected by changes in the characteristics of the liquid. Further, despite the very smooth surface of the Teflon or PVC coating, waste water containing grease can still lead to deposits on the measuring probe which affect the measured value.

10.4.3 Hydrostatic Pressure Measurement

This method makes use of a submerged sealed pressure transducer to measure the hydrostatic pressure of the liquid above it (Figure 10.11). The hydrostatic pressure is the force exerted by a column of water above a reference point and is proportional to the height.

The transducer comprises a membrane which is firmly attached to the channel wall — with an oil fill transmitting the pressure on the membrane to a capacitive metering cell.

Submerged pressure transducers are not affected by wind, steam, turbulence, floating foam and debris, or by deposits or contamination.

However, because they are submerged, the transducers may be difficult to install in large channels with high flow, and may require periodic maintenance in flow streams with high concentrations of suspended solids or silt. Further, accuracy may be affected by changes in the temperature of the process medium.

10.4.4 Bubble injection

Like the submerged pressure transducer, the bubble injection method or ‘bubbler’ measures the hydrostatic pressure of the liquid (Figure 10.12). The system comprises a pressure transducer connected to a ‘bubble tube’ which is located in the flow stream and whose outlet is at the lowest point.

Air or other gas, at a constant pressure, is applied to the tube so that bubbles are released from the end of the bubble tube at a constant rate. The pressure measured by the transducer, which is required to maintain the bubble rate, is proportional to the liquid level.

Because the pressure transducer is not in contact with the fluid, it is not subject to chemical or mechanical attack. Additionally the cost for providing explosion proof protection is minimal.

When used in channels with high concentrations of grease, suspended solids, or silt, bubblers may require occasional maintenance — although periodic air purges of the bubble tube often minimise this problem. Additional maintenance is also required to regenerate desiccators that prevent moisture from being drawn into the air system of a bubbler.

10.4.5 Ultrasonics

Ultrasonic level measurement makes use of a transducer, located above the channel, which transmits a burst of ultrasonic energy that is reflected from the surface of the water (Figure 10.13). The time delay from the transmitted pulse to the received echo is converted into distance and hence determines the liquid level.

Ultrasonic sensors have no contact with the liquid; are easy to install; require minimal maintenance; and are not affected by grease, suspended solids, silt, and corrosive chemicals in the flow stream.

Modern ultrasonic systems are also capable of providing very high level measuring accuracies (down to ± 0,25%).

10.5 Linearization

Open channel flow measurement does not end with the measurement of level, since it still remains to convert the measured liquid level into a corresponding flow rate. This conversion or linearization must be carried out according to the level-flow rate relationship for the primary measuring device being used and can be accomplished in several ways:

Notes:

1. Marks will be deducted for incorrect answers

2. There may be more than one correct answer

Chapter 1

1. In the SI system, dynamic viscosity is measured in:

(a) centipoise

(b) pascals/second

(c) pascal.second

(d) centistoke

2. Which of the following is true:

(a) kinematic viscosity is related to a density and measured in centipoise

(b) dynamic viscosity is related to acceleration due to gravity and is measured in poise

(c) kinematic viscosity is related to density and is measured in Stokes

(d) kinematic viscosity is related to acceleration due to gravity and is measured in centistokes

3. Kinematic viscosity is:

(a) measured in m2/s and given by v = μ/ρ

(b) measured in m/s and given by μ = v/ρ

(c) measured in m.s and given by ρ = μ/v

(d) measured in m2/s and given by v = μ2/ρ

4. Which one of the following is true:

(a) in a Newtonian fluid, the shear stress is indirectly proportional to the shear rate.

(b) an ideal plastic exhibits a linear relationship between shear stress and shear rate.

(c) in a pseudoplastic substance, the viscosity decreases as the shear stress increases.

(d) dilatant materials exhibit a linear relationship between shear stress and shear rate and a zero yield stress

5. The Reynolds number of a fluid:

(a) increases with an increase in viscosity

(b) increases as the pipe diameter increases

(c) decreases with an increase in density

(d) increases as a function of the acceleration due to gravity

6. A fully developed parabolic flow profile is termed:

a) turbulent

b) axis-asymmetrical

c) laminar

d) disturbed

7. Volumetric flow:

a) describes the speed at which a fluid passes a point along the pipe

b) represents the total volume of fluid flowing through a pipe per unit of time

c) is the flow velocity in a localised region or point, in the fluid

d) is obtained by averaging the velocity over the velocity profile

8. The mass flow rate, W, is given by:

a) W = v.A/ρ

b) W = Q/ρ

c) W = v.A. μ

d) W = v.A.ρ/μ

Chapter 2

9. Positive displacement meters are also referred to as:

(a) indirect volumetric totalizers

(b) direct volumetric totalizers

(c) direct averaging velocity totalizers

(d) indirect averaging velocity totalizers

10. Sliding vane meters are:

(a) affected by viscosity and are suitable for accuracies of 1%

(b) affected by viscosity and have a rangeability of 20:1

(c) are not affected by viscosity and have a high repeatability of ± 0.05%.

(d) are only suitable for low temperature service up to 50°

11. The main features of the Oval gear flowmeter include:

(a) High accuracy; low pressure drop and viscosity independence

(b) High accuracy, high pressure drop and viscosity dependence

(c) High accuracy, low pressure drop and viscosity dependence

(d) Low accuracy, high pressure drop and viscosity dependence

12. The lobed impeller meter is characterised by:

(a) Mainly used with gases at high operating pressures up to 8 MPa and having poor accuracy at low flow rates

(b) Mainly used with liquids at high operating pressures up to 8 MPa and having high accuracy at low flow rates

(c) Mainly used with gases at low operating pressures up to and having poor accuracy at low flow rates

(d) Mainly used with gases at high operating pressures up to 8 MPa and having high accuracy at low flow rates

13. The rotating piston meter:

a) is particularly suitable for accurately measuring large volumes with performance largely unaffected by viscosity

b) is particularly suitable for accurately measuring small volumes with performance largely unaffected by viscosity

c) is particularly suitable for accurately measuring small volumes with performance affected by viscosity

d) is particularly suitable for accurately measuring large volumes with performance affected by viscosity

14. The nutating disk meter is characterised by:

a) Simplicity, low-cost and short meter life

b) Complex design, high-cost and long meter life

c) Simplicity, low-cost and long meter life

d) Simplicity, high-cost and long meter life

Chapter 3

15. Inferential meters are:

a) direct volumetric totalizers, in which the enclosed volume is geometrically defined

b) direct volumetric totalizers, in which the enclosed volume is not geometrically defined

c) indirect volumetric totalizers, in which the enclosed volume is not geometrically defined

d) indirect volumetric totalizers, in which the enclosed volume is geometrically defined

16. In addition to their high accuracies, turbine meters are characterised by:

(a) Rangeability of 5:1 and suitability for pressures of up to 64 MPa at very low flow rates.

(b) Rangeability up to 20:1 and suitability for pressures of up to 100 kPa at very low flow rates.

(c) Rangeability up to 20:1 and suitability for pressures of up to 64 MPa but only at very high flow rates.

(d) Rangeability up to 20:1 and suitability for pressures of up to 64 MPa at very low flow rates.

17. Turbine meters are:

(a) Not suitable for high viscous fluids or with swirling fluids; require 10 diameter upstream and 5 diameter downstream of straight pipe; and are only suitable for clean liquids and gases.

(b) Suitable for high viscous fluids and swirling fluids; require 10 diameter upstream and 5 diameter downstream of straight pipe; and are only suitable for clean liquids and gases.

(c) Suitable for high viscous fluids and swirling fluids; require 20 diameter upstream and 15 diameter downstream of straight pipe; and are only suitable for clean liquids and gases.

(d) Not suitable for high viscous fluids or with swirling fluids; require 10 diameter upstream and 5 diameter downstream of straight pipe; and are suitable for ‘dirty’ liquids and gases.

18. The vertical turbine Woltman meter:

(a) is widely used for measurement of non-conductive liquids and offers the advantage of minimal bearing friction and low pressure drop.

(b) is suitable for high viscosity oil measurement and offers the advantage of minimal bearing friction but at the expense of a high pressure drop.

(c) is widely used as a domestic water meter and offers the advantage of minimal bearing friction but at the expense of a high pressure drop.

(d) is widely used as a domestic water meter and offers the advantage of minimal bearing friction and low pressure drop.

19. The impeller type meter, typified by the Pelton wheel turbine:

(a) is able to measure extremely high flow rates up to 200 litres/min, coupled with a turn-down ratio of up to 50:1.

(b) is able to measure extremely low flow rates down to 0,02 litres/min, coupled with a turn-down ratio of up to 50:1.

(c) is able to measure extremely low flow rates down to 0,02 litres/min, coupled with a turn-down ratio of up to 100:1.

(d) is able to measure extremely high flow rates up to 100 litres/min, coupled with a turn-down ratio of up to 10:1.

Chapter 4

20. In a vortex meter:

(a) Vortices are generated by the bluff body and are swept downstream to form the Karman Vortex Street. Vortices are shed alternately from either side of the bluff body at a frequency that, within a given Strahal factor, is proportional to the mean flow velocity in the pipe.

(b) Vortices are generated by the bluff body and are swept downstream to form the Strahl Vortex Street. Vortices are shed alternately from either side of the bluff body at a frequency that, within a given range, determined by the Karman factor, is proportional to the mean flow velocity in the pipe.

(c) Vortices are generated by the bluff body and are swept downstream to form the Karman Vortex Street. Vortices are shed alternately from either side of the bluff body at a frequency that, within a given Reynolds number range, is proportional to the mean flow velocity in the pipe.

(d) Vortices are generated by the bluff body and are swept downstream to form the Karman Vortex Street. Vortices are shed alternately from either side of the bluff body at a frequency that, within a given Reynolds number range, is proportional to the mass flow velocity in the pipe.

21. The frequency of oscillation of a bluff body is:

(a) proportional to the flow velocity and Reynolds Number and inversely proportional to the diameter of the bluff body

(b) proportional to the flow velocity and Strouhal factor and inversely proportional to the diameter of the pipe

(c) proportional to the flow velocity and Strouhal factor and inversely proportional to the diameter of the bluff body

(d) inversely proportional to the flow velocity and Strouhal factor and directly proportional to the diameter of the bluff body

22. The major advantage of the vortex precession Swirlmeter over vortex shedding is that:

(a) It requires only five diameters of straight line upstream of the meter; it features linear flow measurement and a rangeability between 1:5; and installation may be at any angle in the pipeline.

(b) It requires only three diameters of straight line upstream of the meter; it features linear flow measurement and a rangeability up to 1:30; and installation may be at any angle in the pipeline.

(c) It requires only three diameters of straight line upstream of the meter; is suitable for highly viscous materials; and installation may be at any angle in the pipeline.

(d) It requires only five diameters of straight line upstream of the meter; it features a rangeability of up to 1:30; and installation may be at any angle in the pipeline.

23. The fluidic meter is:

(a) based on the Coanda effect; may be used with fairly viscous media; and requires no recalibration during its expected lifetime.

(b) based on the Karman Street effect; may be used with fairly viscous media; and requires no recalibration during its expected lifetime.

(c) based on the Coanda effect; may be used with very low viscous media; and requires no recalibration during its expected lifetime.

(d) based on the Coanda effect; may be used with fairly viscous media; but requires constant recalibration.

24. The vortex meter cannot measure flow:

(a) at very high flow rates — corresponding to a Reynolds number between 50 000 and 100 000.

(b) at very high flow rates — corresponding to a Reynolds number between 5 000 and 10 000.

(c) down to very low flow rates — corresponding to a Reynolds number between 5 000 and 10 000.

(d) down to very low flow rates — corresponding to a Reynolds number between 50 000 and 100 000.

Chapter 5

25. In a differential flow meter, the difference between the upstream static pressures and the pressure at or immediately downstream of the restriction can be related to flow by the expression:

(a)

(b)

(c)

(d)

26. Major features of the orifice plate are:

(a) it is easily fitted between adjacent flanges; its performance changes with time; and it provides a long term accuracy of ± 2 to 3%.

(b) it is easily fitted between adjacent flanges; its performance does not change with time; and it provides a long term accuracy of μ 0,6%

(c) it is easily fitted between adjacent flanges; its performance does not change with time; and it provides a long term accuracy of about ± 2 to 3%.

(d) it is easily fitted between adjacent flanges; its performance changes with time; and it provides a long term accuracy of about μ 0,6%

27. The quadrant edge orifice plate:

(a) has an eccentric opening with a square upstream edge that produces a coefficient of discharge that is practically constant for Reynolds numbers from 300 to 25 000, and is therefore useful for use with low viscosity fluids or at low flow rates.

(b) has a concentric opening with a rounded upstream edge that produces a coefficient of discharge that is practically constant for Reynolds numbers from 300 to 25 000, and is therefore useful for use with high viscosity fluids or at low flow rates.

(c) has an eccentric opening with a square upstream edge that produces a coefficient of discharge that is practically constant for Reynolds numbers from 300 to 2 000, and is therefore useful for use with high viscosity fluids or at low flow rates.

(d) has a concentric opening with a rounded upstream edge that produces a coefficient of discharge that is practically constant for Reynolds numbers from 300 to 25 000, and is therefore useful for use with very low viscosity fluids or at very high flow rates.

28. Vena contracta taps are:

(a) normally located one pipe diameter upstream and about ½-pipe diameter downstream and should not be used for pipe sizes over 150 mm diameter

(b) normally located about ½-pipe diameter upstream and about one pipe diameter downstream and should not be used for pipe sizes under 150 mm diameter

(c) normally located about ½-pipe diameter upstream and about one pipe diameter downstream and should not be used for pipe sizes over 150 mm diameter

(d) normally located one pipe diameter upstream and about ½-pipe diameter downstream and should not be used for pipe sizes under 150 mm diameter

29. Flange taps are:

(a) commonly used for pipe sizes of 200 mm and greater and are, typically, located 25 mm either side of the orifice plate

(b) commonly used for pipe sizes of 50 mm and less and are, typically, located 25 mm either side of the orifice plate

(c) commonly used for pipe sizes of 200 mm and greater and are, typically, located 75 mm either side of the orifice plate

(d) commonly used for pipe sizes of 50 mm and greater and are, typically, located 25 mm either side of the orifice plate

30. When compared to the orifice plate, the venturi tube is:

(a) small and inexpensive and exhibits less significant pressure drop across restriction; less unrecoverable pressure loss; and requires less straight pipe up and downstream

(b) small and inexpensive and exhibits less significant pressure drop across restriction; less unrecoverable pressure loss; and requires less straight pipe up and downstream

(c) bulky and expensive and exhibits a very high pressure drop across restriction; a high unrecoverable pressure loss; and requires less straight pipe up and downstream

(d) bulky and expensive and exhibits less significant pressure drop across restriction; less unrecoverable pressure loss; and requires less straight pipe up and downstream

31. When compared with the standard venturi, the flow nozzle:

(a) is used mainly in low velocity applications; the permanent pressure loss is increased from between 30 to 80% of the measured differential pressure; it is usually only half the cost; and it requires far less space for installation.

(b) is used mainly in high velocity applications; the permanent pressure loss is decreased from between 30 to 80% of the measured differential pressure; it is usually only half the cost; and it requires far less space for installation.

(c) is used mainly in high velocity applications; the permanent pressure loss is increased from between 30 to 80% of the measured differential pressure; it is usually double the cost; and it requires more space for installation.

(d) is used mainly in high velocity applications; the permanent pressure loss is increased from between 30 to 80% of the measured differential pressure; it is usually only half the cost; and it requires far less space for installation.

32. The major advantages of the target meter include:

(a) wide size availability; free passage of particles or bubbles; and no pressure tap or lead line problems.

(b) ability to cope with highly viscous fluids at high temperatures; free passage of particles or bubbles; and no pressure tap or lead line problems.

(c) wide size availability; wide flow range; and no pressure tap or lead line problems.

(d) ability to cope with highly viscous fluids at high temperatures; free passage of particles or bubbles; and low head loss.

33. In the Pitot tube a small sample of the flowing medium impinging on the open end of the tube:

(a) is brought to rest — transforming the kinetic energy of the fluid into potential energy in the form of a head pressure (also called stagnation pressure).

(b) is accelerated — transforming the kinetic energy of the fluid into potential energy in the form of a head pressure (also called stagnation pressure).

(c) is brought to rest — transforming the potential energy of the fluid into kinetic energy in the form of a head pressure (also called stagnation pressure).

(d) is accelerated — transforming the kinetic energy of the fluid into potential energy in the form of a head pressure (also called stagnation pressure).

34. Multi-port averaging devices, such as the ‘Annubar’ are used mainly:

(a) for metering flows in large bore pipes — offering a very low pressure drop and application on a wide range of fluids.

(b) for metering flows in small bore pipes — offering a very low pressure drop and application on a wide range of fluids.

(c) for metering flows in large bore pipes — but at the expense of a very high pressure drop and restricted application

(d) for metering flows in large bore pipes — offering a very low pressure drop and application on very highly viscous fluids.

Chapter 6

35. In the variable area flowmeter the fluid or gas:

(a) flows upwards through a tube, carrying the conical float upwards. A balance is reached when the upward force on the float, created by differential pressure across the annular gap between the float and the tube, equals the weight of the float.

(b) flows upwards through a conical tube, carrying the float upwards. A balance is reached when the upward force on the float, created by differential pressure across the annular gap between the float and the tube, equals the weight of the float.

(c) flows upwards through a tube, carrying the conical float upwards.. A balance is reached when the differential pressure across the annular gap between the float and the tube, equals the viscosity of the float.

(d) flows upwards through an inverted conical tube, carrying the float upwards. A balance is reached when the differential pressure across the annular gap between the float and the tube, equals the density of the float.

36. A major advantage of the variable area flowmeter is that:

(a) the flow rate is indirectly proportional to the orifice area so that it is unnecessary to carry out viscosity corrections

(b) the flow rate is indirectly proportional to the orifice area so that it is unnecessary to carry out density corrections

(c) the flow rate is directly proportional to the orifice area so that it is unnecessary to carry out square root extraction.

(d) the flow rate is directly proportional to the orifice area so that it is unnecessary to carry out density corrections

37. The slots in the float head of a ‘Rotameter’ cause:

(a) the float to become viscosity independent

(b) the float to become density independent

(c) the float to rotate and centre itself and prevent it sticking to the walls of the tube

(d) the float to rotate and produce an output that is linear

38. The main advantages of the variable area meter include:

(a) linear float response to flow rate change; 10 to 1 flow range or turn down ratio; ease of installation and maintenance; simplicity; high accuracy; and low cost.

(b) linear float response to flow rate change; 100 to 1 flow range or turn down ratio; ease of installation and maintenance; simplicity; high low-flow accuracy; and low cost.

(c) linear float response to flow rate change; 10 to 1 flow range or turn down ratio; ease of installation and maintenance; simplicity; high low-flow accuracy; and low cost.

(d) square law float response to flow rate change; 10 to 1 flow range or turn down ratio; ease of installation and maintenance; simplicity; high low-flow accuracy; and low cost.

39. The main disadvantages of the variable area meter include:

(a) limited accuracy; low turn-down ratio of 3:1; fluid must be clean, no solids content; and operation in vertical position only

(b) limited accuracy; susceptibility to changes in temperature, density and viscosity; square law response; and operation in vertical position only

(c) limited accuracy; susceptibility to changes in temperature, density and viscosity; fluid must be clean, no solids content; and operation in horizontal position only

(d) limited accuracy; susceptibility to changes in temperature, density and viscosity; fluid must be clean, no solids content; and operation in vertical position only

Chapter 7

40. Faraday’s law of induction that states that:

(a) if a conductor is moved through a magnetic field a voltage will be induced in it that is proportional to the velocity of the conductor.

(b) if a conductor is moved through a magnetic field a voltage will be induced in it that is proportional to the length of the conductor.

(c) if a conductor is moved through a magnetic field a voltage will be induced in it that is proportional to the strength of the magnetic field.

(d) if a conductor is moved through a magnetic field a voltage will be induced in it that is proportional to the conductivity of the medium.

41. The characteristics of Teflon PTFE, the most widely used liner material, include:

(a) very high pressure capability (200 MPa); excellent anti-stick characteristics; inert to a wide range of acids and bases; and approved in food and beverage applications.

(b) very high temperature capability (180°C); excellent anti-stick characteristics; high abrasion resistance; and approved in food and beverage applications.

(c) very high temperature capability (180°C); poor anti-stick characteristics; inexpensive; and approved in food and beverage applications.

(d) average temperature capability (40°C); excellent anti-stick characteristics; inert to a wide range of acids and bases; and approved in food and beverage applications.

42. The main differences between hard rubber and soft rubber liners is that:

(a) Soft rubber is an inexpensive general purpose liner whose main application lies in the water and waste water industries; whilst hard rubber is an expensive liner whose main application lies in the chemical industry.

(b) Soft rubber is an expensive general purpose liner whose main application lies in slurries; whilst soft rubber is a relatively inexpensive liner whose main application lies in waste water industries

(c) Soft rubber is an expensive liner whose main application lies in the chemical industries; whilst soft rubber is relatively inexpensive whose main application lies in slurries.

(d) Soft rubber is an inexpensive general purpose liner whose main application lies in the water and waste water industries; whilst soft rubber is relatively inexpensive whose main application lies in slurries.

43. Fused aluminium oxide liners are:

(a) highly recommended for very abrasive and/or corrosive applications and high temperatures up to 180°C; and are used extensively in the potable water industry

(b) highly recommended for very abrasive and/or corrosive applications and high temperatures up to 180°C; and are used extensively in the chemical industry

(c) highly recommended for high pressure applications and high temperatures up to 180°C; and are used extensively in the chemical industry

(d) only suitable for non-abrasive applications and low temperatures up to 80°C; and are used extensively in the chemical industry

44. In a ‘characterised field’:

(a) the magnetic flux density (B) is constant over the entire plane

(b) the magnetic flux density (B) is marked by an increase in the x-direction and a decrease in the y-direction

(c) the magnetic flux density (B) is marked by an decrease in the x-direction and an increase in the y-direction

(d) the magnetic flux density (B) is marked by an increase in the x-direction and is constant in the y-direction

45. Volumetric flow measurement in a partially filled pipe is not valid because:

(a) the cross sectional area of the media is unknown

(b) the induced potential at the electrodes is no longer proportional to the media velocity

(c) the reduction in magnetic flux reduces the limit for conductivity

(d) the conductive path length is reduced

46. `Empty Pipe Detection’ is used to:

(a) indicate that the volume reading is correct and to ‘freeze’ the signal of the standby line flowmeter when using a two-line standby system

(b) indicate that the volume reading is incorrect and to produce a fully characterised field

(c) indicate that the volume reading is incorrect and to ‘freeze’ the signal of the standby line flowmeter when using a two-line standby system

(d) indicate that the volume reading is correct

47. Which of the following statements is correct:

(a) the pulsed d.c. field is designed to overcome the problems associated with a non-characterised field

(b) the pulsed d.c. field is designed to overcome the problems associated with high liquid conductivities

(c) the pulsed d.c. field is designed to overcome the problems associated with both a.c. and d.c. interference.

(d) the pulsed d.c. field is designed to overcome the problems associated with half or semi-filled pipes

48. Which of the following statements is correct:

(a) The electromagnetic flowmeter is characterised by: no pressure drop; short inlet/outlet sections (5D/2D); linear relationship; insensitive to flow profile changes (laminar to turbulent); rangeability of 30:1 or better; inaccuracy of better than ±0,5% of actual flow over full range

(b) The electromagnetic flowmeter is characterised by: high pressure drop; short inlet/outlet sections (5D/2D); linear relationship; insensitive to flow profile changes (laminar to turbulent; rangeability of 30:1 or better; inaccuracy of better than ±0,5% of actual flow over full range

(c) The electromagnetic flowmeter is characterised by: no pressure drop; inlet/outlet sections (10D/5D); linear relationship; insensitive to flow profile changes (laminar to turbulent; rangeability of 30:1 or better; inaccuracy of better than ±0,5% of actual flow over full range

(d) The electromagnetic flowmeter is characterised by: no pressure drop; square root relationship; insensitive to flow profile changes (laminar to turbulent); rangeability of 30:1 or better

49. Which of the following statements is correct:

(a) The main drawbacks of the electromagnetic flowmeter are: requires calibration and unsuitable for non-conductive fluids

(b) The main drawbacks of the electromagnetic flowmeter are: non-linear relationship; unsuitable for non-conductive fluids; and highly sensitive to flow profile changes

(c) The main drawbacks of the electromagnetic flowmeter are: long inlet/outlet sections (10D/5D); unsuitable for non-conductive fluids; and highly sensitive to flow profile changes

(d) The main drawbacks of the electromagnetic flowmeter are: square root relationship; unsuitable for non-conductive fluids; and highly sensitive to flow profile changes

Chapter 8

50. Doppler ultrasonic meters make use of the principle that:

(a) the change in velocity is directly proportional to the velocity of the particles flowing in the medium

(b) the change in frequency is directly proportional to the velocity of the particles flowing in the medium

(c) the change in frequency is directly proportional to the resonant frequency of the particles flowing in the medium

(d) the change in velocity is directly proportional to the resonant frequency of the particles flowing in the medium

51. Which of the following statements is correct:

(a) Doppler ultrasonic meters require an uncontaminated medium

(b) Doppler ultrasonic meters require the presence of reflecting particles in the media

(c) Doppler ultrasonic meters provide an accuracy of ± 1% if properly calibrated

(d) Doppler ultrasonic meters may only be used with high viscosity media

52. Which of the following statements is correct:

(a) Doppler meters should not be considered as high performance devices and are cost effective when used as a flow monitor.

(b) Doppler meters are insensitive to velocity profile effects and are temperature independent

(c) Doppler meters work well on dirty fluids and typical applications include sewage, dirty water, and sludge.

(d) Doppler meters are sensitive to velocity profile effects and are temperature sensitive.

53. Which of the following statements is correct:

(a) The ultrasonic transit time meter measures the transit time of an ultrasonic pulse, from the upstream to the downstream transducer

(b) The ultrasonic transit time meter measures the transit time of an ultrasonic pulse, from the downstream to the upstream transducer

(c) The ultrasonic transit time meter compares the difference between the transit time of an ultrasonic pulse from the upstream to the downstream transducer with the transit time of an ultrasonic pulse, from the downstream to the upstream transducer

(d) The ultrasonic transit time meter measures the transit time of an ultrasonic pulse in either direction and calculates the Doppler shift

54. The ultrasonic transit time meter calculates:

(a) the sum and difference of the transit times in order to derive the flow rate independent of the density of the media.

(b) the sum and difference of the transit times in order to derive the flow rate independent of the viscosity of the media

(c) the sum and product of the transit times in order to derive the flow rate independent of the velocity of sound in the media

(d) the sum and difference of the transit times in order to derive the flow rate independent of the velocity of sound in the media

55. Which of the following statements is correct:

(a) Transit time meters work better on dirty fluids and typical applications include: water, sewage and slurries

(b) Transit time meters work better on clean fluids and typical applications include: water, clean process liquids, liquefied gases and natural gas pipes.

(c) Transit time meters work better on fluids with high entrained gas content and typical applications include: water, clean process liquids, liquefied gases and natural gas pipes.

(d) Transit time meters are not suitable for use on gases

56. The laminar-to-turbulent error of a single ultrasonic path is:

(a) very much determined by the flow profile

(b) independent of the flow profile

(c) very much determined by the density of the product

(d) very much determined by the velocity of sound in the medium

57. On transit-time clamp-on ultrasonic meters the following factors must be known:

(a) thickness of coating; pipe wall material; the speed of sound in the medium; the pipe wall thickness; the thickness of any deposits on the inside pipe surface

(b) the pipe wall thickness; thickness of coating; pipe wall material; the thickness of any deposit on the inside pipe surface

(c) thickness of coating; pipe wall material; the thickness of any liner; the pipe wall thickness; the medium characteristics; the material of construction of any liner

(d) the pipe wall thickness; thickness of coating; pipe wall material; the thickness of any deposits on the inside pipe surface

58. Which of the following is true:

(a) measurement of the velocity of sound provides indication of: actual flowing density; velocity profile; and molecular concentration

(b) measurement of the velocity of sound, in conjunction with temperature and pH, provides indication of the : actual flowing density; concentration; and molecular conductivity

(c) measurement of the velocity of sound, in conjunction with temperature and conductivity, provides empty pipe detection

(d) measurement of the velocity of sound, in conjunction with temperature and pressure, provides indication of: actual flowing density; concentration; and molecular weight

59. Some of the advantages of ultrasonic flowmeters include:

(a) suitable for large diameter pipes; low cost; no obstructions; no pressure loss; no moving parts; long operating life; fast response.

(b) suitable for very small diameter pipes; suitable for partially filled pipes; no obstructions; no pressure loss; no moving parts; long operating life; fast response.

(c) suitable for dirty liquids; no obstructions, no pressure loss; no moving parts; long operating life; fast response.

(d) suitable for large diameter pipes; no obstructions, no pressure loss; no moving parts; long operating life; fast response.

60. The straight section of pipe required upstream and downstream of an ultrasonic flowmeter used on liquids is:

(a) 20 D upstream and ≥ 10 downstream from an elbow; ≥ 30 D upstream and ≥ 10 downstream from a T-junction; and ≥ 50 D upstream and ≥ 20 downstream from a valve

(b) 10 D upstream and ≥ 5 downstream from an elbow; ≥ 10 D upstream and ≥ 5 downstream from a T-junction; and ≥ 30 D upstream and ≥ 10 downstream from a valve

(c) 20 D upstream and ≥ 10 downstream from an elbow; ≥ 10 D upstream and ≥ 10 downstream from a T-junction; and ≥ 30 D upstream and ≥ 10 downstream from a valve

(d) 10 D upstream and ≥ 5 downstream from an elbow; ≥ 50 D upstream and ≥ 10 downstream from a T-junction; and ≥ 30 D upstream and ≥ 10 downstream from a valve

Chapter 9

61. Conventional mass-flow measurement entails:

(a) measurement of velocity and cross sectional area — assuming a constant density

(b) measurement of velocity and viscosity — assuming a constant cross sectional area

(c) measurement of velocity, density and viscosity — assuming a constant cross sectional area

(d) measurement of velocity and density — assuming a constant cross sectional area

62. Which of the following statements is correct for a Coriolis meter:

(a) because the measurement of mass flow is independent of the density of the medium, density cannot be measured.

(b) because the resonant frequency varies with density — falling as the density increases — density is measured by tracking the resonant oscillation frequency of the oscillating pipe

(c) the resonant frequency of the oscillating pipe varies with density and temperature — increasing as the density increases

(d) the resonant frequency of the oscillating pipe varies with density, viscosity, conductivity and temperature — increasing as the density increases

63. The parallel loop arrangement is characterised by:

(a) a small total cross-sectional area that increases the pressure drop; a low sensitivity; and a flow divider that increases the pressure drop and makes cleaning difficult

(b) a large total cross-sectional area that reduces the pressure drop; a high sensitivity; and a flow divider that increases the pressure drop and makes cleaning difficult

(c) a small total cross-sectional area that reduces the pressure drop; a low sensitivity; and a flow divider that increases the pressure drop and makes cleaning difficult

(d) a large total cross-sectional area that increases the pressure drop; a high sensitivity; and a flow divider that decreases the pressure drop but makes cleaning difficult

64. The series loop arrangement is characterised by:

(a) increased rigidity that makes it less sensitive to the Coriolis effect at low flow rates; less pressure drop at high flow rates; and the pipe is easier to clean.

(b) decreased rigidity that makes it more sensitive to the Coriolis effect at low flow rates; more pressure drop at high flow rates; and the pipe is more difficult to clean.

(c) increased rigidity that makes it more sensitive to the Coriolis effect at low flow rates; less pressure drop at high flow rates; and the pipe is easier to clean.

(d) decreased rigidity that makes it less sensitive to the Coriolis effect at low flow rates; less pressure drop at high flow rates; and the pipe is more difficult to clean.

65. Which of the following characterise the Coriolis meter:

(a) high accuracy capability; independent of temperature, pressure, density, conductivity and viscosity; not suitable for high densities

(b) high accuracy capability; independent of temperature, pressure, and density; sensor capable of transmitting mass flow, density and temperature information; high density capability; conductivity independent; capable of measuring low mass flow rates; dependent on conductivity and viscosity

(c) high accuracy capability; independent of temperature, pressure, density, conductivity and viscosity; sensor capable of transmitting mass flow, density, temperature and viscosity information; high density capability; conductivity independent; capable of measuring low mass flow rates

(d) high accuracy capability; independent of temperature, pressure, density, conductivity and viscosity; sensor capable of transmitting mass flow, density and temperature information; high density capability; conductivity independent; capable of measuring low mass flow rates

Chapter 9

66. The three most commonly used weirs are:

(a) the rectangular; the V-notch; and the Cipolletti

(b) the venturi; the V-notch; and the Cipolletti

(c) the trapezoidal; the V-notch; and the Cipolletti

(d) the rectangular; the Parshall; and the Cipolletti

67. The discharge equation of the V-notch weir is given by:

(a) q = k (1-a) h2,5

(b) q = k (1-a) h1,5

(c) q = k h1,5

(d) q = k h2,5

68. When compared with a weir, major features of the flume include:

(a) a higher flow rate measurement; a much smaller head loss; better suitability for flows containing sediment; and cheaper

(b) a higher flow rate measurement; a much higher head loss; better suitability for flows containing sediment; and more expensive

(c) a higher flow rate measurement; a much smaller head loss; better suitability for flows containing sediment; and more expensive

(d) a lower flow rate measurement; a much smaller head loss; better suitability for flows containing sediment; and more expensive

67. The discharge equation of the Parshall Venturi flume is:

(a) q = (k – 1)hn where n varies between 1,522 and 1,607

(b) q = (k – 1)hn where n varies between 2,522 and 2,607

(c) q = k hn where n varies between 2,522 and 2,607

(d) q = k hn where n varies between 1,522 and 1,607

68. Features of the flume include:

(a) no erosion; sensitive to dirt and debris; very low head pressure loss; simple operation and maintenance; high installation costs

(b) no erosion; not sensitive to dirt and debris; very low head pressure loss; simple operation and maintenance; high installation costs

(c) no erosion; not sensitive to dirt and debris; very high pressure loss; simple operation and maintenance; high installation costs

(d) no erosion; not sensitive to dirt and debris; very low head pressure loss; simple operation and maintenance; low installation costs