Pump power calculation

The efficiency of pump (εp) is defined as the ratio of power transferred to water to the power supplied to the pump. The latter is equal to the brake horsepower of motor (PM). If gear box is used to reduce motor speed, the gear box efficiency (~95%) must be multiplied to PM to obtain the real power input to pump.

The efficiencies of commonly used centrifugal pumps range up to 75% for mixed liquor and 85% for clean water, if the pumps are used at preferred operating conditions with respect to flow rate and differential pressure. In field condition, however, the flow rate and the differential head pressure often do not fall into the preferred ranges. Moreover motor speed may be reduced occasionally to accommodate the dry weather flow, which not only reduces the efficiency of variable speed drive (VFD) but also reduces pump efficiencies. If VFD was not used, throttling, bypassing, recirculation, etc. are performed to accommodate various flow demand, but these methods cause more dramatic efficiency loss. Overall, pump efficiency likely ranges 35- 70% in field condition especially when flow rate changes periodically with frequent on and off (Kaya, 2008).

The power consumption of pump (Pp) can be calculated by dividing the energy transferred to liquid (ΔPQL) by pump efficiency (εp) and motor efficiency (εM) as equation (1).

1    ———————————      (1)


g     : Gravity acceleration ( 9.8 m/s2 )
Δh  : Vertical height difference between water intake level and discharge pipe exit (m)
P0   : Power consumption of pump (W)
ΔP  : differential pressure between pump inlet and outlet (Pa)
QL  : liquid flow rate (m3/s)
vL   : liquid velocity in pump outlet (m/s)
ρ     : liquid density (kg/m3)
εp   : pump efficiency (-)
εM  : motor efficiency (-)

In practical situation, the velocity head,vl2 , is negligible comparing to the pressure head, deltap, unless the liquid velocity, vL, is very high such as >3-5m/s. As a result, velocity head can be neglected in pump energy calculation in most situations in MBR except for the pump used to circulate mixed liquor through tubular membrane. The elevation head, , can be included in the pressure head by considering the total pressure difference in between the feed water intake and the water discharge instead of the pressure difference between immediate inlet and outlet of the pump.

© Seong Hoon Yoon