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 M^{3}/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 powe**r 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** = {Pump Output / Pump Input} × 100

= {Water Horse Power / Break Horse Power} × 100

= {Hydraulic Power / Pump Shaft Power} × 100

**Pump input power calculation formula or pump shaft power calculation formula**

Pump Input Power = P

**Formula – 1**

Here

Q = Flow rate in m^{3}/sec

H = Total developed head in meters

**ρ** = Density in kg/m^{3}

g = Gravitational constant = 9.81 m/sec^{2}

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

**Formula – 2**

Here

Q = Flow rate in m^{3}/hr

H = Total developed head in meters

**ρ** = Density in kg/dm^{3} (1 kg/m^{3} = 0.001 kg/dm^{3})

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

**Formula – 3**

Here

Q = Flow rate in Lt./sec ( 1 m^{3}/sec = 3.6 x Lt./sec)

H = Total developed head in meters

**ρ **= Density in kg/dm^{3} (1 kg/m^{3} = 0.001 kg/dm^{3})

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

**Formula – 4**

Here

Q = Flow rate in Lt./sec

H = Total developed head in meters

**ρ **= Density in kg/dm^{3}

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

**Formula – 5 ( USCS units )**

Here

Q = Flow rate in gpm

H = Total developed head in feet

**ρ ** = Density in lb/ft^{3}

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

### 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 m ^{3}/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**

Where Nq = Dimensionless parameter

N = RPM of pump

n = Rev/sec of Pump

Q = Flow rate in m^{3}/sec

H = Head in meters

g = Gravitational constant ( 9.81 m/sec^{2})

**British Units**

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

#### 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 = Number units power saving per year in KWH

**η _{2} & **

**η**= Higher and lower overall efficiency of two pump sets.

_{1}P = Power input in kW to motor (related to low efficiency pump)

T = Running hours per year

**Pump efficiency calculation example**

**η _{2} & **

**η**= 75% and 65% respectively

_{1 }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/m ^{3} = 1 kg/dm^{3}*

**Related Article:**

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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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