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Pump Formulas

In order to make the most common pump formulas, we have created an overview of pump calculations 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 formulas. 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.

Centrifugal Pump Power Formula

The pump power is shown in the pump curve chart or in the cutsheet. The required pump power, also called shaft power, is given in brake horsepower – bhp – and can be easily calculated using the following pump power formula: P = (Q x H x SG) ÷ (3960 η) 

P = pump power         bhp
Q = pump flow            gpm
H = pump head           feet
SG = specific gravity of the fluid kg/dm3     
η = pump efficiency   %  
3960 = constant factor

Pump Power Formula Example

We are using a BA150E D285 for pumping water at an operating point of 1600 gpm @ 90 feet. The pump efficiency at that point is 80 % according to the curve chart. The specific gravity of water is 1 kg/dm3  (62.4 lb/ft3).

BBA Pumps ModelBA150E D285
Operating point example1600 gpm @ 90 feet
Specific gravity of water1 kg/dm3
Pump efficiency at operating pointη is 80 %
Q x H x SG = 1600 x 90 x 1144,000
Constant factor x η = 3960 x 80%3168
Pump power = 144,000 ÷ 3168P = 45.5 bhp 

Centrifugal Pump Affinity Laws

The affinity laws for centrifugal 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 held constant.

- The capacity changes in proportion to the pump speed:  Q÷ Q2 = N1 ÷ N2 
- The head is proportional to the square of the pump speed: H÷ H= (N1 ÷ N2)2 
- The power is proportional to the cube of the pump speed: P÷ P= (N1 ÷ N2)3 

Q = pump flow            gpm
H = pump head          feet
P = pump power         bhp
N = pump speed         rpm

Pump Affinity Laws Example

We are using a BA150E D285 for pumping water. The pump curve chart shows the maximum pump speed of 1900 rpm. With that reference pump speed we can easily calculate the performance at the proposed speed of e.g. 1500 rpm.

BBA Pumps modelBA150E D285
Proposed operational speed N11500 rpm
Reference pump speed N21900 rpm
Calculated ratio 1500 ÷ 1900 = 0.79
Operating point Q1 @ H11600 gpm @ 90 feet at 1900 rpm
Qx 0.79 = Q2Q= 1600 gpm x 0.79 = 1264 gpm
Hx (0.79)2 = H2H= 90 feet x 0.62 = 56 feet
Px (0.79)3 = P2P= 45.5 bhp x 0.49 = 22.3 bhp
Calculated point Q@ H2 1264 gpm @ 56 feet at 1500 rpm

Head Feet to PSI Formula

Dynamic head to psi or static head to psi. For converting head feet to psi, it does not matter whether it is dynamic or static. Pump head is regularly expressed in feet. This is because we always test pumps with water. We then call the measured pressure on the discharge side of the pump foot of water column. The formula to convert dynamic head or static head from feet to psi: H = ft x 0.433

H = pump head          
ft = feet
0.433 = constant factor

Fuel Consumption Engine Driven Pumps Formula

For the fuel consumption calculation of diesel driven pumps, we assume that the specific weight of diesel is 7 lb. per US gallon (measured at 60 °F). Then formula to calculate the diesel consumption on an operating point of a centrifugal pump is: Gal/h = BSFC x BHP ÷ 7 

BSFC = Fuel consumption in lb/hp-hr (specified by the engine manufacturer)
BHP = Required pump brake horsepower at the operating point (specified in pump curves)  
7 = Fuel specific weight of diesel in lb. per US gallon

Fuel Consumption Formula Example

We are using a BA150E D285 for pumping water at an operating point of 1600 gpm @ 90 feet. The required pump brake horsepower at that point is 47 bhp according to the curve chart. Fuel consumption specified by the engine manufacturer Hatz is 0.36 lb/hp-h.

BBA Pumps modelBA150E D285
Operating point Q @ H 1600 gpm @ 90 feet at 1900 rpm
Required brake horsepower47 bhp
BSFC fuel consumption0.36 lb/hp-h
Gal/h = 0.36 x 47 ÷ 7Gal/h = 2.4 

Pump Sizing Formula

In order to make the optimal formula of the size of the pump requires extensive knowledge about liquids and pump technology. One of the key considerations in optimization is to choose an operating point at Best Efficiency Point in the pump curve chart. Though, our portable pumps are supplied to operate over a wide range, even at the end of the rating curve. If the NPSH available is sufficient to prevent cavitation, the pump will give satisfactory operation.

Please contact us and let our experienced pump experts advise you on the best pump for your application. Our experience can save you money and its given free of charge.

Coming Soon More Pump Formulas…