Pump Power Calculation Formula | Specific speed of a centrifugal pump

In this article discussed about pump basic formulas with examples like pump power calculation formula, specific speed of centrifugal pump and affinity laws for centrifugal and displacement pumps. Also provided online calculator for pump power calculation

Pump Efficiency and Pump Power Calculation Formulas with Examples

Efficiency and Input Power of the Pump

The work performed by the pump is equal to the weight of liquid pumped in Unit time multiplied by total Head in meters. However the pump capacity in M3/hr and liquid specific gravity are used rather than weight of liquid pumped for work done by the pump.

The input power “P” of a pump is the mechanical power in kW or Watt taken by the shaft or coupling. So the input power of the pump also called Break Horse Power (BHP).

Pump input BHP is the power delivered to the pump shaft and is designated as brake horsepower.  so pump input power also called as pump shaft power.

Pump output power is called as Water Horse Power (WHP ) or Hydraulic power and it is useful work delivered by the pump.  and is usually expressed by the formula

Hydraulic power Ph = Flow rate  X  Total developed head  X  Density  X  Gravitational constant

Pump Efficiency is the ratio of pump input and output power.

i.e Efficiency of the pump is the ratio water horse power to break horse power.

 Pump \ Efficiency =\frac{Pump \ Output}{Pump \ Input} \ \times \ 100 \ = \frac{Water \ Horse \ Power}{Break \ Horse \ Power} \ \times 100 \ = \frac{Hydraulic \ Power}{Pump \ Shaft \ Power} \times 100

Pump input power calculation formula or pump shaft power calculation formula

Pump Input Power = P

Formula – 1

P in Watt = \frac{ Q \ \times H \ \times\ \rho \ \times \ g }{ 100 \ \times \ \eta }

Here

Q = Flow rate in m3/sec

H = Total developed head in meters

\rho = Density in kg/m3

g = Gravitational constant = 9.81 m/sec2

η  = Efficiency of the pump ( between 0% to 100%)

Formula – 2

P in kW = \frac{ Q \ \times H \ \times\ \rho \ }{ 367 \ \times \ \eta }

Here

Q = Flow rate in m3/hr

H = Total developed head in meters

\rho = Density in kg/dm3 (1 kg/m3 = 0.001 kg/dm3)

η  = Efficiency between 0 and <1 (not in %)

Formula – 3

P in kW = \frac{ Q \ \times H \ \times\ \rho \ }{ 102 \ \times \ \eta }

Here

Q = Flow rate in Lt./sec ( 1 m3/sec = 3.6 x Lt./sec)

H = Total developed head in meters

\rho = Density in kg/dm3 (1 kg/m3 = 0.001 kg/dm3)

η  = Efficiency of the pump ( between 0% to 100%)

Formula – 4

P in Hp = \frac{ Q \ \times H \ \times\ \rho \ }{ 75 \ \times \ \eta }

Here

Q = Flow rate in Lt./sec

H = Total developed head in meters

\rho = Density in kg/dm3

η  = Efficiency of the pump ( between 0% to 100%)

Formula – 5 ( USCS units )

P in Hp = \frac{ Q \ \times H \ \times\ \rho \ }{ 3960 \ \times \ \eta }

Here

Q = Flow rate in gpm

H = Total developed head in feet

\rho = Density in lb/ft3

η  = Efficiency of the pump ( between 0% to 100%)

For an electric-motor-driven pumping unit, the overall efficiency is

Overall efficiency =   pump efficiency x   motor efficiency

The overall efficiency then becomes what is commonly called “wire-to-water” efficiency, which is expressed by the formula

Overall Efficiency = \frac{Water \ Horse \ Power}{Electric \ Power \ Input}

Specific Speed of Pump

The specific speed “Nq” is a parameter derived from a dimensional analysis which allows a comparison of impellers of various pump sizes even when their operating similar Q -H range.  The specific speed can be used to classify the optimum impeller design.

Specific Speed of pump (Nq) is defined as the speed in RPM at which a geometrically similar impeller would run if it were reduced proportionately in size so as to delivered 75 kg of water per second to the height of 1 m.

Nq is also defined as the theoretical rotational speed at which a geometrically similar impeller would run if it were of such a size as to produce 1 m of head at a flow rate of 1 m3/sec at the best efficiency point.

The specific speed can be made a truly dimensionless characteristic parameter while retaining the same numerical value by using following equation.

Metric System

Nq = \frac{3.65 \ \times \ N \ \times \ Q \ ^{0.5}}{H \ ^{0.75}}   = \frac{ 333 \ \times \ n \times \ \sqrt{Q}}{(g \times H ) \ ^{3/4}}

Where Nq = Dimensionless parameter

N = RPM of pump

n = Rev/sec of Pump

Q =  Flow rate in m3/sec

H = Head in meters

g = Gravitational constant ( 9.81 m/sec2)

British Units

Nq = \frac{ \ N \ \times \ Q \ ^{0.5}}{H \ ^{0.75}}

Where N = RPM of pump

Q =  Flow rate in Gallons per minute (GPM)

H = Head in feet

Note:

1. For multistage pumps the developed head (H) at best efficiency

2. Consider half total discharge in case of double suction impeller.

Approximate reference values  for specific speed of centrifugal pump (Nq):

Radial high head impeller – up to approx. 25

Radial medium head impeller – up to approx. 40

Radial low head impeller – up to approx. 70

Mixed flow impeller – up to approx. 160

Axial flow impeller (propeller) – approx. from 140 to 400

Affinity laws for pumps – Please go through the below link

Affinity laws for centrifugal pumps | Positive displacement pump affinity laws | Pump affinity laws with example

Why to select pump with better efficiency

Pump Efficiency is the most important factor while calculating power consumption. So while selection of the higher rating of pump always choose best efficiency pump set.

The following formula to help  which type of efficiency rating pump is best

N  = \frac{ \eta _{2} - \ \eta _{1} }{ \eta _{1} } \ \times P \ \times \ T

N = Number units power saving per year in  KWH

\eta _{2} & \eta _{1} = Higher and lower overall efficiency of two pump sets.

P = Power input in kW to motor (related to low efficiency pump)

T = Running hours per year

Pump efficiency calculation example

\eta _{2} & \eta _{1} = 75% and 65% respectively

P = Power input = 40 kW

T = 3000 hours per year

N = 18461 Units (KWH)

So for same rating pump efficiency will increase by 10% then power saving will be 18461 KWH per year.

Centrifugal pump power calculation online

 Note : 1000 kg/m3 = 1 kg/dm3

Pump Efficiency and Pump Power Calculation Formulas with Examples

Related Article:

Pump Vapour pressure calculation | Water Vapour Pressure Table at Different temperatures

Classification of pumps | Types of pumps and their working principles

Unit Conversion Factors and Tables for Engineering Design Calculations

NPSH calculation | Pump suction and delivery lines head loss with online calculator 

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Post Author: siva alluri

The aim of this Blog "sugarprocesstech" is Providing basic to advance knowledge in sugar process industry and providing maximum calculation regarding capacity and equipment design online calculators .

3 thoughts on “Pump Power Calculation Formula | Specific speed of a centrifugal pump

    Pranjal saxena

    (September 29, 2018 - 5:52 am)

    Dear sir, please specify the Units in formula (Hydraulic power Ph = Flow rate X Total developed head X Density X Gravitational constant) and also Describe how to convert in kW.

      siva alluri

      (September 29, 2018 - 3:51 pm)

      Formulas also covered in this article

    Mallappa.undi

    (October 6, 2018 - 1:17 am)

    How to calculate gear box power?

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