Pump power calculation

Hydraulic Pump Power

The ideal hydraulic power to drive a pump depends on

• the mass flow rate the
• liquid density
• the differential height

- either it is the static lift from one height to an other or the total head loss component of the system - and can be calculated like

P_h(kW) = q ρ g h / (3.6 10⁶)

        = q p / (3.6 10⁶)                  (1)

where

P_h(kW) = hydraulic power (kW)

q = flow (m³/h)

ρ = density of fluid (kg/m³)

g = acceleration of gravity (9.81 m/s²)

h = differential head (m)

p = differeential pressure (N/m², Pa)

The hydraulic Horse Power can be calculated as:

P_h(hp) = P_h(kW) / 0.746                                  (2)

where

P_h(hp) = hydraulic horsepower (hp)

Or - alternatively

P_h(hp) = q_gpm h_ft SG / (3960 η)                              (2b)

where

q_gpm = flow (gpm) 

h_ft = differential head (ft)

SG = Specific Gravity (1 for water)

η = pump efficiency

Example - Power pumping Water

1 m³/h of water is pumped a head of 10 m. The theoretical pump power can be calculated as

P_h(kW) = (1 m³/h) (1000 kg/m³) (9.81 m/s²) (10 m) / (3.6 10⁶) 

    = 0.027 kW

Shaft Pump Power

The shaft power - the power required transferred from the motor to the shaft of the pump - depends on the efficiency of the pump and can be calculated as

P_s(kW) = P_h(kW) / η                                     (3)

where

P_s(kW)  = shaft power (kW)

η = pump efficiency