# Pump specific work

### What is the power gained by a fluid when pumped ?

1. Introduction
2. Pump specific work calculation
3. Power gained by the fluid
4. Specific work and power gained calculation example : step by step guide
5. Manufacturers

## 1. Introduction

This page is explaining how to calculate the specific work of a pump as well as the power gained by a fluid when it goes through a pump.

Pumping a fluid means bringing it from certain conditions of pressure to another, higher pressure. It means that the pump must deliver a work in order for the fluid to gain energy. The work is often presented as a specific work, which means an energy per unit of fluid (J/kg).

## 2. Pump specific work calculation

The pump specific work, which means the Joules input per kg of fluid, can be calculated with the following formula :

W=H.g

With :

W = specific work of the pump in J/kg
H = actual head rise (m)
g = gravity acceleration = 9.81 m.s-2

## 3. Power gained by the fluid

The power gained by the fluid is then the product of the specific work by the mass flow rate of the fluid. The power gained by the fluid can be calculated with the following equation :

P = m.W

With :

P = power gained by the fluid (W)
m = mass flow rate (kg/s)
W = pump specific work (J/kg)

## 4. Specific work and power gained calculation example : step by step guide

A pump is pumping a liquid from atmospheric conditions to 2 bar abs, the fluid process is water at 25c which has a specific gravity of 999 kg/m3, the flow is 10 m3/h.

### Step 1 : calculate the head rise

The actual head rise is expressed by H = (P2-P1)/(ρ.g), here assuming that the references points before and after the pump are equal and the velocity is also equal (same pipe size and incompressible fluid).

H = (2.105-1.105)/(9.81*999) = 10.2 m

### Step 2 : calculate the specific work

The specific work can be calculated with the equation in paragraph 2 :

W = g.H = 9.81*H = 100.1 J/kg

### Step 3 : calculate the power gained by the fluid

The mass flowrate of the fluid can be calculated thanks to the volumetric flowrate and the density of the fluid : m = 10*999/3600 = 2.775 kg/s.

The power gained by the fluid can be calculated with the equation in paragraph 3 :

P = m.W = 2.775*100.1 = 277.7 W

## 5. Manufacturers

If you are interested in getting pump characteristics to estimate the head and size of the pump you need for your application, you can contact the pumps GrosClaude : https://www.pompes-grosclaude.com/en/home/

(Note that MyEngineeringTools has no link with this company)