Hydraulic, brake, and electrical input power, wire-to-water efficiency, and annual energy cost from your duty point
Understand the three kinds of pump power, wire-to-water efficiency, and how affinity-law speed reduction cuts energy cost
Power grows at every stage of the pumping chain because each component adds its own loss:
The useful energy actually added to the fluid: WHP = Q·H·SG / 3960 (Q gpm, H ft).
The shaft power the driver delivers: BHP = WHP / η_pump. The pump's hydraulic and mechanical losses make BHP larger than WHP.
The power drawn from the line: kW = BHP·0.7457 / (η_motor·η_vfd). Motor and drive losses make it larger still.
Wire-to-water efficiency is the product of the three component efficiencies:
A pump set running well lands around 60–75%. The two biggest energy levers are running near the best-efficiency point (BEP) and, for variable duty, using a variable-frequency drive — at reduced speed the affinity laws make power fall with the cube of speed.
Wire-to-water efficiency is the overall efficiency of a pumping system from the electrical input at the wire to the hydraulic energy delivered to the water (fluid). It is the product of the pump efficiency, the motor efficiency, and the variable-frequency-drive efficiency: η_wtw = η_pump × η_motor × η_vfd. A typical electric pump set lands around 60–75% wire-to-water; the remaining input energy is lost as heat in the pump, motor, and drive.
The biggest lever is matching the pump to the system so it runs near its best-efficiency point (BEP) instead of being oversized and throttled. Other proven measures: install a variable-frequency drive so flow reductions follow the affinity laws (power varies with the cube of speed), trim or change impellers, use premium-efficiency (IE3/IE4) motors, fix worn wear rings and internal clearances, and reduce system head by removing unnecessary restrictions. Multiply the input power by your operating hours and electricity rate to see the annual dollar impact of each change.
Hydraulic (water) power, WHP = Q·H·SG/3960, is the useful energy added to the fluid. Brake power, BHP = WHP/η_pump, is the larger shaft power the driver must deliver because the pump is not perfectly efficient. Electrical input power, kW_in = BHP·0.7457/(η_motor·η_vfd), is the still-larger power drawn from the line after motor and drive losses. Each stage adds loss, so WHP < BHP < input power.