Compressible Flow Pressure Drop Equations

[brysoncook]

Hello all,

I have been searching and can not seem to find any equations to calculate the pressure drop around pipe bends for compressible flow. I was hoping to end up solving for a pressure differential using the fluid properties (including flowrate/velocity), pipe diameter, bend radius, and pipe roughness. I'm trying to equalize the pressure drop across multiple pipes with different geometry, but with the same fluid properties and initial pressure. Depending on the structure of the equations, perhaps I can eliminate several of the parameters that are held constant. Thanks for your help,

--Bryson

 

[katmar]

If the pressure drop is less than 10% of the absolute pressure you can safely use the Darcy-Weisbach incompressible flow equation. Any errors introduced by this assumption are likely to be less than the uncertainties in the fluid physical properties, pipe dimensions, roughness etc.

Because you seem to more interested in the differences in pressure drop between the different bends I suspect that you could extend this assumption up to a pressure drop of around 25% of the absolute pressure without introducing significant errors.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[davefitz]

Usually the design case boundary conditions are : equal inlet pressure + equal outlet pressure==> equal DP is a given boundary condition, the unknown value is the flow per branch for teh case of unequal geometries.

If you want to exactly calculate the balance flow for this case, yould likely either need to run a 3D CFD model or run a scaled down physical model. Although there are posted standard loss coefficients for elbows, these loss coefficients are not accurate in the case of multiple out of plane elbows- you can only account for pre-swirldue to an upstream elbow using 3D CFD or a scale model.