# Pump Power Calculator

### 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 10^{6})

= q p / (3.6 10^{6}) (1)

where

P_{h(kW)}= hydraulic power (kW)

q = flow (m^{3}/h)

ρ = density of fluid (kg/m^{3})

g = acceleration of gravity (9.81 m/s^{2})

h = differential head (m)

p = differential pressure (N/m^{2}, 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, SI Units

*1 m ^{3}/h* of water is pumped a head of

*10 m*. The theoretical pump power can be calculated as

*P _{h(kW)} = (1 m^{3}/h) (1000 kg/m^{3}) (9.81 m/s^{2}) (10 m) / (3.6 10^{6})^{ }*

* = 0.027 kW*

### Example - Power pumping Water, Imperial Units

*600 gpm* of water is pumped a head of *110 ft*. The efficiency ofthe pump i s *60% (0.6)* and the specific gravity of water is *1*. The pump shaft power can be calculated as

*P _{h(kW)} = (60 gpm) (110 ft) (1) / ((3960) (0.6))^{ }*

* = 27.8 hp*

### 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

### Online Pump Calculator - SI-units

The calculator below can used to calculate the hydraulic and shaft power of a pump:

### Online Pump Calculator - Imperial units

The calculator below can used to calculate the hydraulic and shaft power of a pump using Imperial units:

- Specific weight of water is 62.4 lb/ft
^{3} - Check the relation between Density, Specific Weight and Specific Gravity
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