Centrifugal pump efficiency is the ratio of Hydraulic power delivered by the pump to the brake horsepower supplied to the pump.
 
Hydraulic Power (Power Output from Pump):
Centrifugal Pump consumes energy to develop the discharge pressure and to deliver flow. Therefore Hydraulic Horsepower of the Pump depends on these two parameters. Power Output from Pump = (P2–P1) * Q
P2: Pump Discharge pressure in N/m2
P1: Pump suction pressure in N/m2
Q: Flow delivered by pump in m3/s
 
Brake Horse Power (Power Input to Pump):
This is the power given to the pump through Electric Motor. Power output from the electric driver is calculated by the formula
Power Input to Pump = 1.732 * V * I * PF * Motor Efficiency * Coupling Efficiency
V: Measured Voltage of Motor in Volt
I: Measured Current of Motor in Ampere
PF: Power Factor
Motor Efficiency May be considered as design efficiency or may be obtained from Motor efficiency calculation data through tests
Coupling Efficiency is obtained from Supplier Manual
Centrifugal pump efficiency equation
Centrifugal pump efficiency = Power Output from Pump/ Power Input to Pump * 100
 
Centrifugal Pump Efficiency and Discharge Temperature
Actual Power required in pump can also be derived from Heat balance across the pump.
Difference in Heat flow Outlet and Heat flow inlet is the actual power required for the pump. This indicates the fall in centrifugal pump efficiency increases the temperature of liquid at the pump discharge
 
Factors Influencing Centrifugal Pump Efficiency
1. In Recirculation lines Minimum Thermal flow is maintained to avoid Cavitation during low flow operation of the pump. This will also result in lowering the efficiency.
2. Internal Surface Roughness. Smooth surface finish in pump internals gives high efficiency
3. Increase in Wear Ring Clearances decreases the efficiency of Centrifugal pump. Wear rings are used reduce clearance between Pump impeller and Pump casing
4. Increase in viscosity decreases the pump efficiency
5. Mechanical losses in Couplings, Bearings, Packings etc will decrease the efficiency
6. Impeller Trimming will also decrease efficiency
 
Source: https://www.chemicalengineeringsite.com/centrifugal-pump-efficiency-calculation/388