# Compressibility Factor Pressure For Calculating Fan Power

1. May 8, 2013

### Aperture Labs

What is the correct type of pressure (static or total) used in the compressibility factor, KP, when calculating fan power? Howden's Fan Engineering book seems to indicate total pressures should be used, but I also have a PDF from Howden that indicates static pressures should be used. Online searching has shown mixed answers. For my calculation, I did it both ways and the difference was small enough to be considered negligible by engineering judgement, however, I would still like to know the correct calculation.

The equations I am using are:

H = (Q*PT*KP) / (6356*NT)

Where,

H = fan shaft power [hp]
NT = fan total efficiency [%]
Q = fan inlet volumetric flow [acfm]
PT = fan total pressure [in. w.c.]
6356 is a conversion factor
KP = compressibility factor [dimensionless]

KP = $\gamma$/($\gamma$-1) * [(p2/p1)^(($\gamma$-1)/$\gamma)$-1] / ((p2/p1)-1)

Where,

p2 = total or static pressure at the fan outlet [in. w.c.]
p1 = total or static pressure at the fan inlet [in. w.c.]

2. May 9, 2013

### SteamKing

Staff Emeritus
It's going to depend on what velocities are produced by the fan. In flow calculations, a gas can be treated like an incompressible fluid when the flow velocity is below 0.3 M (for air at sea lever, 0.3 M is about 100 m/s).

3. May 9, 2013

### Aperture Labs

1.) Are you saying that if my gas velocities have a Mach # less than 0.3 I may treat the gas as incompressible with negligible difference in results, and the KP factor does not need to be considered?

2.) Per my work standards I'm required to treat it as compressible. So even if #1 above is correct, I'm still stuck trying to figure out if I should use total or static pressures in the compressibility equation.

3.) A small addendum to the compressibility factor equation shown in blue:

KP = γ/(γ-1) * [(p2/p1)^((γ-1)/γ)-1] / ((p2/p1)-1)

Where,

p2 = total or static absolute pressure at the fan outlet [in. w.c.]
p1 = total or static absolute pressure at the fan inlet [in. w.c.]​

4. May 9, 2013

### SteamKing

Staff Emeritus
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