## Calculation of Fan work by VdP and the adiabatic process where PV^(gamma) = Constant; which is OK?

## Calculation of Fan work by VdP and the adiabatic process where PV^(gamma) = Constant; which is OK?

(OP)

Dear forum

I have been trying to calculate the work done by a fan on a gas flow in two ways, but I get two different values of power.

The first method is the W=V * dP

(I guess this is assuming isothermal compression). I then use the power calculated as a measure of the internal energy increase and calculate the outlet temperature this way.

The second method I used is adiabatic compression. Seems on for an insulated fan.

I followed https://en.wikipedia.org/wiki/Adiabatic_process but did not arrive to the same fan work.

My question is when to use the first method and when to use the second.

What about for a compressor, I guess the same model shall be used for this?

I have been trying to calculate the work done by a fan on a gas flow in two ways, but I get two different values of power.

The first method is the W=V * dP

(I guess this is assuming isothermal compression). I then use the power calculated as a measure of the internal energy increase and calculate the outlet temperature this way.

The second method I used is adiabatic compression. Seems on for an insulated fan.

I followed https://en.wikipedia.org/wiki/Adiabatic_process but did not arrive to the same fan work.

My question is when to use the first method and when to use the second.

What about for a compressor, I guess the same model shall be used for this?

## RE: Calculation of Fan work by VdP and the adiabatic process where PV^(gamma) = Constant; which is OK?

## RE: Calculation of Fan work by VdP and the adiabatic process where PV^(gamma) = Constant; which is OK?

## RE: Calculation of Fan work by VdP and the adiabatic process where PV^(gamma) = Constant; which is OK?

Fan Engineering, an Engineer's Handbook on Fans and Their applications.Edited by Robert Jorgensen

Published by BUFFALO FORGE COMPANY,

Buffalo, New YorkFan Engineeringand it dates back to the 1930's! Is it still published?Tunalover

Electro-Mechanical Product Development

UMD 1984

UCF 1993

~~copy is dated 1983.~~show us your calc's in both cases (for example for air) and someone may help.

In the case of the isothermal approximation, integrate between the limits of P1 and P2 to get the total work of compression - here V = nRT/P, so dW = nRT dP/P, then integrate between limits and divide the result by isothermal compression eff.

I think I am a bit further now in my understanding. When I was comparing the

1. adiabatic model

2. and the isothermal model

I was making one crucial mistake (I think); I used the same efficiency coefficient. But in fact for the isothermal model I should use the static fan efficiency (with static head) and for the adiabatic model I should use the isentropic efficiency (which is not known to me because as Chicopee says industry standard is to provide the efficiency as static or total)

The numericla difference in static efficiency and isentropic effieciency should explain why I get different values of power of the two calculations. So if I could get the isentropic efficiency from the vendor it would be of lower magnitude than the static???

Efficiency as ist approximation = 0.65

After the fan total pressure is estimate is refined we select the fan using manufacturer (like Twin City) computer program. We yry to pick the most efficient fan that would fit.