 # Pump power

### Definition and calculation of pump hydraulic power and shaft power

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1. Definition of pump hydraulic and shaft power
2. Calculation of pump hydraulic power and shaft power
3. Calculation of pump installed power
4. Step by step example of calculation of pump power
5. Excel pump power calculator

## 1. Definition

### What is the pump hydraulic power ? What is the pump shaft power ?

2 types of powers are associated with a pump : the hydraulic power and the shaft power.

In order to size properly the motor of the pump, it is necessary to know the power to be transmitted to the shaft. The shaft power is dependent on the hydraulic power, the power to be transmitted to the fluid, and the efficiency of the pump which takes into account all the losses that happens when converting the shaft power to the hydraulic power. The shaft power is also called the absorbed power.

The pump efficiency is given by the manufacturer, as a function of the pump capacity and can be determined from the pump characteristic. Figure 1 : pump shaft and hydraulic power

## 2. Calculation of hydraulic and shaft power

### How to calculate the pump hydraulic power ?

The hydraulic pump power calculation is done thanks to the pump flowrate, the pump head and the density of the fluid being pump. Pump power formula is the following :

Phydraulic = Q.H.ρ/367

In case the density is changing significantly when the fluid goes through the pump, the density at the inlet is used. Equation 1 : Pump Hydraulic Power equation

With
Q : pump capacity in m3/h
H : pump head in m
ρ : volumetric mass density in kg/l
Hydraulic Power in kW

The expression above is specified not in SI units but to give directly the results in kW, please pay attention to the units.

### How to calculate the pump shaft power ?

The pump shaft power is also called the absorbed power. It is the power that needs to be actually applied at the coupling / shaft to get the considered flow and head. It includes some losses and is therefore higher than the hydraulic power.

Pshaft = Phydraulic / η Equation 2 : Pump Shaft Power

With :
Pshaft = pump shaft power in kW
Phydraulic = pump hydraulic power in kW
η = pump efficiency

## 3. Calculation of the installed power

The shaft power is used to calculate the motor required for a pump. To calculate the actual electrical power, additional losses (electrical motor efficiency for instance) but also some margins to start the pump from a standstill and to consider that the circuit characteristic may not be exactly the one calculated or that the pump will age, have to be considered. Suppliers will advise a certain overdesign for the actual installed power of a pump, typically 10-50% depending on the power and the technology of the pump.

For centrifugal pumps, the following coefficients are common :

 Shaft power in kW Coefficient to consider for installed power <1 2-1.5 1-5 1.5-1.2 5-50 1.2-1.15 >50 1.1

## 4. Step by step example of calculation of pump power

A pump has to deliver 100 m3/h of water at 2 bar g and 20c, from a tank at atmospheric pressure. The pump is connected to a pipe of same diameter DN100 at the inlet and outlet of the pump. The pump efficiency is 75%.

Step 1 : calculate the pump head

The pump is delivering fluid at 2 bar g from a tank at atmospheric pressure. The velocity of fluid at the inlet and outlet is the same a water is considered incompressible and the temperature increase very low.

H = (pd-ps)*10.2/d+(ud2-us2)/(2g)

H = (2-0)*10.2/0.998 = 20.44 m

STEP 2 : Calculate the hydraulic power

The hydraulic power is calculated thanks to : Q*ρ*H/367

In this case Hydraulic power = 100*9.98*20.44/367 = 5.56 kW

STEP 3 : calculate the shaft power

The shaft power is calculated by dividing the hydraulic power by the pump efficiency.

This gives 5.56/0.75 = 7.4 kW

STEP 4 : calculate the installed power

The installed power is calculated by multiplying the shaft power by the coefficient advised in paragraph 3. In this example, the power is in between 5-50 kW, which means that the installed power should be 15 to 20% higher than the shaft power

This gives an installed power = 7.4*1.2 = 8.88 kW

## 5. Pump power Excel calculator

Please access here the pump power Free Excel calculation tool : tool access 