Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Turbo Machines - Specific Work done by Pumps, Compressors or Fans

Calculate specific work done by pumps, fans, compressors or turbines.

Sponsored Links

Specific work is work per unit weight. Specific work in turbo machines as fans, pumps, compressors or turbines has the SI-units

  • Nm/kg = J/kg = m2/s2

Specific Work of a Pump or Fan

Specific work of a pump or fan working with an incompressible fluid can be expressed as:

w = (p2 - p1) / ρ                                   (1)


w = specific work (Nm/kg, J/kg, m2/s2)

p = pressure (N/m2)

ρ = density (kg/m3)

Specific Work of a Turbine

Specific work of a turbine with an incompressible fluid can be expressed as:

w = (p1 - p2) / ρ                                      (2)

Specific Work of a Compressor

A compressor works with compressible fluids and the specific work for an isentropic compressor process can be expressed with the help of

p1 v1κ = p2 v2κ                                        (3)


v = volume (m3)

κ = cp / cv - ratio of specific heats (J/kg K)

Specific work:

w = κ / (κ -1) R T1 [( p2 / p1)((κ-1)/κ) - 1]                                     (4)


R = individual gas constant (J/kg K)

T = absolute temperature (K)

Specific Work of a Gas Turbine

A gas turbine expands a compressible fluid and the specific work can be expressed as

w = κ / (κ -1) R T1 [1 - ( p2 / p1)((κ-1)/κ)]                                     (5)

Head in Turbomachines

The specific work can on basis of the energy equation be expressed with the head as:

w = g h                                         (6)


h head (m)

g = acceleration of gravity (m/s2)

Transformed to express head:

h = w / g                                         (7)

Example - Specific Work of a Water Pump

A water pump works between 1 bar (105 N/m2) and 10 bar (10 105 N/m2). The specific work can be calculated with (1):

w = (p2 - p1) / ρ

    = ((10 105 N/m2) - (105 N/m2)) / (1000 kg/m3)

    = 900 Nm/kg

Dividing by acceleration of gravity the head can be calculated using (7):

hwater = (900 Nm/kg) / (9.81 kg/s2)

    = 91.74 (m) water column

Example - Specific Work of an Air Compressor

An air compressor works with air at 20 oC compressing the air from 1 bar absolute (105 N/m2) to 10 bar (10 105 N/m2). The specific work can be expressed with (4):

w = κ / (κ -1) R T1 [( p2 / p1)((κ-1)/κ) - 1]

    = ((1.4 J/kg K) / ((1.4 J/kg K) - 1 )) (286.9 J/kg K) ((273 K) + (20 K)) [((10 105 N/m2) / (105 N/m2))(((1.4 J/kg K) - 1)/(1.4 J/kg.K)) - 1 ]

    = 273826 Nm/kg


κair = 1.4 (J/kg K) - ratio of specific heat air

Rair = 286.9 (J/kg K) - individual gas constant air

Dividing by acceleration of gravity the head can be calculated using (7):

hair = (274200 N m/kg) / (9.81 kg/s2)

    = 27951 (m) air column

Sponsored Links

Related Topics

Related Documents

Sponsored Links

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro .Add the Engineering ToolBox extension to your SketchUp from the SketchUp Pro Sketchup Extension Warehouse!

About the Engineering ToolBox!


We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.

Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.

Google use cookies for serving our ads and handling visitor statistics. Please read Google Privacy & Terms for more information about how you can control adserving and the information collected.

AddThis use cookies for handling links to social media. Please read AddThis Privacy for more information.


This page can be cited as

  • Engineering ToolBox, (2004). Turbo Machines - Specific Work done by Pumps, Compressors or Fans. [online] Available at: [Accessed Day Mo. Year].

Modify access date.

. .


3D Engineering ToolBox - draw and model technical applications! 2D Engineering ToolBox - create and share online diagram drawing templates! Engineering ToolBox Apps - mobile online and offline engineering applications!

Scientific Online Calculator

Scientific Calculator

3 10

Sponsored Links