When to use mass flow averaging
 

I am studying CFX tutorial 9, flow through a pipe with a butterfly valve.

In this tutorial, the flow is assumed to be incompressible.

I'm trying to find out when its necessary to use mass flow averaging over area averaging.

My question is, which averaging method (area averaging or mass flow averaging) would provide the best results for calculating the average pressure at a location down the pipe, and why?

In addition, which would be most suitable to calculate the average velocity and why.

Its the why thats the main thing im trying to find out. Am hoping some knowlegeable people out there can help me!

Area averaging simply averages over the area (no surprises there) as:
integral of variable dA/total area

Mass flow averaging is:
integral of rho*normal velocity*variable dA/total mass flow

If the integration surface is normal to the flow then in incompressible flow the results are identical. If the surface is not normal to the flow the results can differ because mass flow includes a normal velocity bit but area averaging does not. In compressible flow they are both different as rho is not constant.

To find a representative pressure downstream from a valve it is best to use area averaging. The reason has nothing to do with the explanation above - simply because pressure is not advected with the flow and is an area-based thing then use an area integral to average. Something like temperature is advected with the flow and if you use mass flow average you are effectively working out the total enthalpy across the surface which is a physically relevant quantity.

thanks for your help on this. much appreciated