In this article provided pump related formulas like fluid flow rate and velocity, power calculation, Specific Speed of Pump (Nq), Total Head, Pump Torque and temperature rise, Net Positive Suction Head, Affinity laws for pump, Pump Efficiency & Overall Efficiency of the Pump

## Basic required formulas for the operation of Pump

### Formulas regarding product while pumping

**Volume of the fluid (Q )**

**Velocity of the Fluid ( V )**

Here

V = Velocity of fluid in m/sec

Q =Volume of Fluid (m^{3}/sec)

A = Pipe line area (m^{2})

V = Velocity of fluid in m/sec

Q =Volume of Fluid in m^{3}/hr

A = Pipe line dia in mm

**Reynolds Number of the fluid**

Here

D = Dia of the tube in meters

V = fluid velocity in m/sec

ρ= density of the fluid (kg/m^{3})

μ = Absolute viscosity in Pas

**Absolute viscosity of the fluid (μ )**

μ = ** υ x ρ**

where:**υ** = Kinematic viscosity (mm^{2}/s)

ρ = density of the fluid in kg/m^{3}

μ = Absolute viscosity of the fluid in mPas

**Darcy Friction Factor**

where:

f_{d} = friction factor (Darcy)

Re = Reynolds number

### Pump Power Calculation

**Hydraulic Pump Power **

The ideal hydraulic power to drive a pump depends on liquid density , differential height to lift the material and flow rate of the material.

Here

Hydraulic power in watt

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

H = Total head in meters = Discharge head + Suction head

ρ = Density of the Fluid kg/dm^{3} (1 kg/m^{3} = 0.001 kg/dm^{3})

g = Acceleration due to gravity (m/sec^{2})

**Pump Power input or Pump shaft Power**

The pump power input of a centrifugal pump is the mechanical energy at the pump coupling or pump shaft absorbed from the drive.

Here

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

H = Total head in meters = Discharge head + Suction head

ρ = Density of the Fluid ( kg/dm^{3})

η_{p} =Pump efficiency

Here

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

H = Total head in meters = Discharge head + Suction head

ρ = Density of the Fluid ( kg/dm^{3 })

η_{p} =Pump efficiency

**Pump input power from pump shaft power**

**Pump input power from current and voltage**

Here all efficiencies are in decimals

### Specific Speed of Pump (**Nq)**

Specific Speed of pump (Nq) is identifies the geometrical similarity of pumps. It is useful to comparing different pump designs irrespective of pump size

Nq = =

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})

**Suction Specific Speed at best efficiency point**

Ns = Suction Specific speed of pump (Dimensionless parameter)

N = RPM of the pump

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

NPSH = Net positive section head in meters

### Total Head

In pumping system, Head means it is a height of a liquid coloumn.

In vertical pipe any liquid coloumn of water exerts a certain pressure (force per unit area) on a horizontal surface at the bottom area, this pressure is expressed in metres of liquid column or kg/cm^{2}.

H = H_{t} – (±H_{s})

where:

H_{t} = total discharge head

H_{s} = total suction head

**Total Discharge Head**

H_{t} = h_{t} + h_{ft} + p_{t}

where:

h_{t} = static discharge head

h_{ft} = pressure drop in discharge line

p_{t} = Pressure head in delivery

p_{t} > 0 for pressure

p_{t} < 0 for vacuum

p_{t} = 0 for open tank

**Total Suction Head**

H_{s} = h_{s} + h_{fs} + (± p_{s})

where:

h_{s} = static suction head

h_{f}_{s} = pressure drop in suction line

p_{s} = Pressure head in suction

p_{s} > 0 for pressure

p_{s} < 0 for vacuum

p_{s} = 0 for open tank

**Pressure Head for Pump**

*Pressure Head* of the pump suction must be considered according to the** condition of source tank.**

Pressure head calculated as per pumping system source tank is *under some gauge pressure* **or** *vacuum* open or open to* atmospheric *than pressure head is calculated in **metres of water column** (MWC) of Feet of water column of liquid.

**Velocity head**

Here Hv = Velocity head in meters

V = Fluid velocity in m/sec

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

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

d = pipe inside diameter in mm

**Shutoff head :**

Shutoff head of the centrifugal pump is the maximum head that can be developed by a pump operating at a set speed

Please go through the below link for more information about pump head

Pressure Head | Velocity head | Static Suction Head Calculation of PUMP

### Pump Torque and temperature rise

Temperature rise in pumps can be calculated as per the below formula

Here

**Δ**T = Temperature rise in the pump (in ^{o}C)

P = brake power (kW)

ηp =Pump efficiency

Cp = specific heat of the fluid (kJ/kg ^{o}C)

Q = Flow rate of the pump (m^{3}/second)

ρ = fluid density (kg/m^{3})

### Net Positive Suction Head

**Net Positive Suction Head Required (NPSHr ):**

The amount of NPSH the pump requires to avoid cavitation is called Net Positive Suction Head Required (NPSHr). This value of the pump is determined based on actual pump test by the vendor.

**Net Positive Suction Head Available( NPSHa) :**

Net positive suction head available is the difference between the saturation pressure and the pump suction pressure for the liquid being pumped.

The amount of Net positive suction head available (NPSHa) to the pump from the suction line is termed NPSHa.

*NPSHa = Absolute Pressure head + Static head (difference in elevation) – Vapor pressure head – Friction head loss in the piping, valves and fittings.*

Net positive suction head available must be greater than or equal to the net positive suction head required to avoid cavitation. It can be stated mathematically as shown below.

NPSH a ≥ NPSH

Please go through the below link for more information about NPSH

Formulas of pump NPSH and head loss calculation in suction and delivery line

### Affinity laws for pumps

**Change in Diameter**

D = Diameter of the impeller (inch or mm)

Q = Flow rate (gpm or m^{3}/hr)

H = Head (ft or m)

P = Power ( hp or kW)

**Change in Speed**

N = Pump speed (RPM)

Q = Flow rate (gpm or m^{3}/hr)

H = Head (ft or m)

P = Power ( hp or kW)

Please go through the below link for more information about affinity laws

Affinity laws, Affinity laws for centrifugal pumps & Positive displacement pump with example

### Pump Efficiency & Overall Efficiency of the Pump

Generally for any system efficiency means the ratio of output and input

Efficiency of the system =

**Pump Efficiency** can be defined as a ratio of pump input and output power.

i.e Efficiency of the pump defined as the ratio of *water horse power to break horse power.*

Hydraulic power in Watt =

Here

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

H = Total developed head in meters

= Density in kg/m^{3}

Hydraulic power in kW =

Here

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

H = Total developed head in meters

= Density in kg/dm^{3} (Conversion : 1 kg/m^{3} = 0.001 kg/dm^{3})

Pump shaft power means it is an input to pump often is the output of motor.

In case of gear drive or pulley drive, efficiency of these drives will also have to be taken into account

Output of motor = (kW input to motor) x motor efficiency (η_{m})

Input to motor is measured directly in kW.

Then

Pump efficiency η_{p} =

**Overall Efficiency of the pumping system**

Overall efficiency (**η**_{overall}) = Pump efficiency (η_{p}) x Motor efficiency (η_{m})

Overall efficiency (**η**_{overall}) =

**Related Articles:**

Classification of pumps | Types of pumps and their working principles

NPSH Calculation |Head loss in suction and delivery line

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

Affinity Laws for Centrifugal and Positive displacement pumps

Pump Efficiency and Pump Power Calculation Formulas with Online Calculator

Pressure head, Velocity Head formulas with examples

Unit Conversion Factors and Tables for Engineering Design Calculations

## 3 thoughts on “Pump Related formulas | Power calculation, Total Head, NPSH, Affinity laws”

## joel

(September 20, 2022 - 5:11 am)very handy to speed up calculation

## siva alluri

(October 1, 2022 - 3:31 pm)welcome

## Debasis Maitra

(December 8, 2022 - 11:07 am)Can we calculate head of a pump with the the help of impeller diameter or any other simple method for pump discharge head calculation.