 # Pump efficiency calculation

### How to calculate the efficiency of a pump ?

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1. Definition of pump efficiency
2. Hydraulic efficiency calculation
3. Mechanical efficiency calculation
4. Volumetric efficiency calculation
5. Pump overall efficiency
6. Pump manufacturers

## 1. Definition of pump efficiency

This page is explaining what is the efficiency of a pump and how to calculate it.

Pumps are fitted with an electrical drive which delivers a certain power, however all this power is not transferred to the fluid, only some of it. There are indeed losses in every components of the pump, which means that the total power input to the fluid is less than the pump power. The efficiency of the pump is then the ratio in between the power actually gained by the fluid and the the power supplied at the shaft of the pump.

There are actually 3 efficiencies that can be calculated, all related to different types of energy losses :

• Hydraulic efficiency
• Mechanical efficiency
• Volumetric efficiency

Those 3 efficiencies then combine to constitute the pump overall efficiency.

## 2. Hydraulic efficiency calculation

The fluid needs to circulate in the pump in order to gain power, as for any fluid flow, the fluid will lose energy when it has to flow against the walls of the pump, change direction, or accelerate. There is an overall energy gain but the flow of the fluid leads to some losses called hydraulic losses. Hydraulic losses can be calculated with the following formula :

Eh = W/(W+Wh)

With :

Eh = hydraulic efficiency (-)
W = the actual specific work given to the fluid by the pump (J/kg)
Wh = the specific work that was lost by the fluid during pumping (J/kg)

## 3. Mechanical efficiency calculation

Like every rotating equipment, even the best designed pumps have mechanical losses due to friction / heat at their bearing, in the shaft, in the coupling. The mechanical efficiency can be calculated with the following equation :

Em = (P-Pm)/P

With :

Em = mechanical efficiency (-)
P = total shaft power (kW)
Pm = power lost in the mechanical parts of the pump (kW)

## 4. Volumetric efficiency calculation

Pumps are bringing liquid from the inlet of the pump, to the outlet of the pump, however, as the pressure at the outlet is higher than the inlet, the fluid tends to go back in the reverse direction, leading to "leakages" in the volute of the pump. A little bit of liquid leaks back which means that it needs to be propelled 2 times, it's a loss called volumetric loss. It can be expressed the following way :

Ev = Q/(Q+Qv)

With :

Ev = volumetric efficiency (-)
Q = total volumetric flow pumped out (m3/s)
Qv = leakage (m3/s)

## 5. Pump overall efficiency

The individual efficiencies are rarely considered in practice, what give the manufacturers are a pump efficiency that actually is the combination of them.

E = Poutput_to_fluid / Pinput_at_shaft_coupling = Eh*Em*Ev

Once the required power has been calculated for an application, then it must be divided by the pump overall efficiency to calculate the actual power to install.

References of pump efficiency : depending on the pump design and the pump speed, the typical pump efficiency will be 80-90% for a single stage pump and 70-90% for multi stage high pressure pumps. The efficiency can be increased slightly by using a diffuser.

## 6. Manufacturers

If you have calculated the pump you need for your application and would need to know the efficiency of actual pumps that could fit your needs, you can contact the pumps GrosClaude : https://www.pompes-grosclaude.com/en/home/

(Note that MyEngineeringTools has no link with this company)