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 with 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

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