Head Rise and the Energy Equation for a Pump or a Fan

The energy equation can be used to calculate the actual head rise in a pump or fan

Actual Head Rise of a Pump or Fan

Using the Energy Equation the head rise through a pump or fan can be expressed as:

ha = (p2 - p1) / γ + h2 - h1 + (v22 - v12) / 2 g         (1)

where

ha = actual head rise

p = pressure

h = elevation height

γ = ρ g = specific weight

v = velocity

g = acceleration of gravity

The actual head rise can be expressed as:

ha = hshaft - hloss         (2)

where

hshaft = shaft work in the pump or fan

hloss = head loss through the pump or fan

The head loss - hloss - through a pump or fan is related to the

  • skin friction in the blade passages and is proportional to volume flow - q2.
  • flow separation
  • impeller blade casing clearance flows
  • other three dimensional flow effects

Actual Head Rise for an Inline Pump

For a very common installation - the inline pump or fan - where the inlet velocity and the outlet velocity are the same (v2 = v1), and the inlet and outlet elevation are the same (h2 = h1), the generic equation (1) can be modified to:

ha = (p2 - p1) / γ         (3)

Specific Work

By multiplying (3) with acceleration of gravity - g -, specific work - w - of the pump or fan may be calculated:

w = ha g         (4)

where

w = specific work

Example - Head Rise of an Inline Pump

An inline water pump works between the pressure 1 bar (1 105 N/m2) and 10 bar (10 105 N/m2). Density of water is 1000 kg/m3. The actual water head (water column) can be calculated using (3):

hwater = (p2 - p1) / γ

    = (p2 - p1) / ρ g

    = ((10 105 N/m2) - (1 105 N/m2)) / (1000 kg/m3) (9.81 m/s2)

    = 91.7 m - water column

Example - Head Rise of an Fan

An inline fan working with hot air with density ρ = 1,06 kg/m3 add a pressure of 400 Pa (N/m2) to the flow.

The air head (air column) can be calculated with (3):

hair = (p2 - p1) / ρ g

    = (400 N/m2) / (1.06 kg/m3) (9.81 m/s2)

    = 38.5 m - air column

The water head (water column) can be calculated with (3) using the density of water:

hwater = (p2 - p1) / ρ g

    = (400 N/m2) / (1000 kg/m3) (9.81 m/s2)

    = 0.041 m

    = 41 mm - water column

Measuring pressure with water column in an U-tube manometer is common in air distribution applications as ventilation and air condition systems.

Related Topics

  • Pumps - Piping systems and pumps - centrifugal pumps, displacement pumps - cavitation, viscosity, head and pressure, power consumption and more

Related Documents

Tag Search

  • en: head rise pump fan energy equation
  • es: bomba de elevación ecuación de la energía del ventilador cabeza
  • de: Kopf steigen Pumpe Ventilator Energiegleichung

Search the Engineering ToolBox

- "Search is the most efficient way to navigate the Engineering ToolBox!"

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/Plugin - 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 Extension Warehouse!

Translate the Engineering ToolBox!
About the Engineering ToolBox!

close