Compressibility Factor Pressure For Calculating Fan Power

[Aperture Labs]

What is the correct type of pressure (static or total) used in the compressibility factor, K_P, 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*P_T*K_P) / (6356*N_T)

Where,

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

K_P = \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.]

 

[SteamKing]

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).

 

[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 K_P 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.]​

 

[SteamKing]

1. Yes I am.
2. and 3. Knock yourself out.

The first paragraph of this article I think says it all:

http://en.wikipedia.org/wiki/Compressible_flow