# Pump calculations

In order to make the most common pump calculations, we have created an overview of pump formulas with a brief explanation on each. All mentioned formulas are based on theoretical pumping technology and are given as a simple aid for making pump calculations. In practice, additional factors can have an influence and may lead to deviations from theoretical values. If you have any questions or are unable to solve your issue, please contact us for personal pump advice.## Pump power calculation

The pump power is shown in the pump curve or in the specifications of the pump. The absorbed pump power, also called shaft power, is given in kW and can be easily calculated using the following formula:**P = (Q x H x SG) ÷ (**

**η**

**x 3670)**

P = pump power kW

Q = pump capacity m3/h

H = pump head mwc

SG = weight medium kg/m3

η = pump efficiency %

3670 = fixed factor

## Pump affinity laws

The affinity laws for pumps express the relationship between the several variables involved in pump performance. The below calculation applies to centrifugal pumps and gives a good indication of the differences in pump capacity, pump head and absorbed pump power when changing the pump speed but with the impeller diameter remaining unchanged.- The capacity changes in proportion to the pump speed:

**Q**

_{1 }÷ Q_{2}= N_{1}÷ N_{2}- The head is proportional to the square of the pump speed:

**H**

_{1 }÷ H_{2 }= (N_{1}÷ N_{2})^{2}- The power is proportional to the cube of the pump speed

**P**

_{1 }÷ P_{2 }= (N_{1}÷ N_{2})^{3}Q = pump capacity m

^{3}/h

H = pump head mwc

P = pump power kW

N = pump speed rpm

## Pump efficiency calculation

The most commonly used formula to calculate pump efficiency at any duty point in the pump curve is**Ƞ = Q x H ÷ 3,67 x P**

η = pump efficiency %

Q = pump capacity m3/h

H = pump head mwc

P = pump power kW

3,67 = fixed factor

Expanded formula for calculating the total pump efficiency:

**η**=

**η**

**h**x

**η**

**v**x

**η**

**m**

- Hydraulic pump efficiency
**ηh**. Is the ratio between the manometric head and the theoretical head of the pump caused by internal frictional and vortex losses. - Volumetric pump efficiency
**ηv**. The actual volume flow of the pump is lower than the theoretical volume flow because a small part of the liquid returns internally to the suction side. - Mechanical pump efficiency
**ηm**. Is the ratio between the theoretical and the actual absorbed pump power due to friction losses in the bearings and wheel friction (impeller resistance in the surrounding fluid).

**Motor efficiency**, losses occur in all drives and motors. To calculate the total efficiency of a pumpset, the motor efficiency factor must also be included in the calculation.

## Fuel consumption diesel driven pumps calculation

When calculating the fuel consumption of diesel driven pumps, we assume that the specific weight of a liter of diesel is 835 grams (measured at 15°C). The formula to calculate the fuel consumption on a duty point of the pump:**L/h = P**

_{ }x BSFC**÷**

**835**

P = Pump power in kW

BSFC = Specific fuel consumption in g/kWh (specified by the engine manufacturer)

835 = Specific weight of diesel in grams/L

**Engine consumers**, the diesel engine itself also has a few additional consumers of fuel, such as the alternator and the cooling fan. In order to accurately calculate the fuel consumption of diesel driven pumps, we recommend that you add an extra 5-6% for these components.

## CO_{2} emission calculation formula for diesel driven pumps

During the process of burning fossil fuels, CO_{2}is produced. The abbreviation stands for carbon dioxide and is a compound of carbon and oxygen. When too much CO

_{2}is released into the air, it has major harmful effects to our planet. Therefore, it is good to know how to calculate CO

_{2}emissions for diesel driven pumps.

For the CO

_{2}emission calculation we assume that the specific gravity of a liter diesel fuel is 835 grams. Normal diesel fuel consists of 86.2% carbon (C), so we calculate 720 grams of carbon per liter of diesel. The combustion process requires 1920 grams of oxygen (O

_{2}) per liter. The total of 720 + 1920 = 2640 grams of CO

_{2}/liter diesel.

So the formula for calculating CO

_{2}emissions of a diesel driven pump is: actual fuel consumption in

**L/hour x 2640 grams ÷ 1000 = CO**.

_{2}kg/hour*CO*

_{2}emission calculation example:*A diesel driven pump runs at a duty point where the engine consumes 8 liters of diesel per hour. CO*

_{2}emissions = 8 x 2640 ÷ 1000 = 21 kg/hour.## Maximum suction lift pump calculation

Particularly when working with mobile pumps it is useful to know how to easily calculate the maximum suction height of the pump. For this you need the following information:- Actual air pressure (weight of air)
- The NPSHr curve of the pump
- The pipe resistance in the suction pipe

**L = P(h) – NPSHr – hf**

Actual air pressure

**P(h)**, also known as the atmospheric pressure, which is an average of 1000 hPa = 1.0 bar = 10 mwc in the Netherlands. In the mountains the atmospheric pressure is reduced and depends on the difference in height compared to sea level. The current air pressure also determines the theoretical maximum achievable suction height of a pump.

The

**NPSHr**value can be found in the performance curves of the pump. Here you can read the internal suction losses of the pump in order to be able to run without cavitation. The value depends on the capacity to be pumped.

Calculating the resistance

**hf**in the suction pipe is the sum of the friction loss in the hose or pipe and the total resistance of the accessories used.

With the maximum suction height

**L,**we refer to the vertical height difference between the liquid to be drawn and the center line of the centrifugal pump.

*There are a number of factors influencing the maximum suction height of the pump that are not included in the calculation. For example, the temperature of the liquid plays a role, when the liquid temperature rises above 20°C the available suction height starts to decrease rapidly*

*.*

## Power generator calculation for electric pumps with frequency inverter

Many electric pumps are controlled by a frequency inverter, also called variable fequency drive. Mobile electric pumps often require a (standby) power generator to be installed. How much kVA power should the power generator have available? That all depends on the type of frequency inverter.Formula for a 6-pulse frequency inverter:

**kVA =**

**P ÷ 0,65 x 1,25**

Formula for a 12-pulse frequency inverter:

**kVA =**

**P ÷ 0,8 x 1,25**

kVA = Power generator

P = Pump power in kW