# Pumps - Power Calculator

## Calculate pumps hydraulic and shaft power.

### 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= q ρ g h / (3.6 10_{h(kW)}^{6})

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

where

P= hydraulic power (kW)_{h(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/ 0.746_{h(kW)}(2)

where

P= hydraulic_{h(hp)}horsepower (hp)

Or - alternatively

P= q_{h(hp)}_{gpm}h_{ft}SG / (3960η)(2b)

where

q_{gpm}= flow (gpm)

h_{ft}=differential head(ft)

SG =(1 for water)Specific Gravity

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= shaft power (kW)_{s(kW)}

η = pump efficiency

### Online Pump Calculator - SI-units

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

*q - flow (m ^{3}/h)*

*ρ - density of fluid (kg/m ^{3})*

*g - gravity (m/s ^{2})*

*h - differential head (m) *

*η - pump efficiency*

### Online Pump Calculator - Imperial units

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

*q - flow capacity (gpm)*

*γ* - specific weight of fluid (lb/ft^{3})

*g - gravity (ft/s ^{2})*

*h - differential head (ft) *

*η - pump efficiency*

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