air pressure differential calculation verfication

[freeweel]

hi,
here is a description of what i am trying to accomplish: design a spreadsheet to show air pressure differential from pipe “A” to pipe “B”. pipe “A” is larger diameter than pipe “B”. this is to act as a quick reference for our manufacturing facilities. i am trying to keep this as simple as possible. any input would be greatly appreciated.

i have modeled my spreadsheet as a venturi tube problem using bernoulli’s equation. i am assuming incompressible flow to simplify calculations and because i do not know the flow rate (at the moment, we have no flowmeters in-house and i’m not aware of any at the plants). for the density calculation, i used: rho = P1/(R*T), (assume T = 68F = 528R).

i have the spreadsheet configured so that i can input any pipe dia., inlet pressure, and flow rate and it will output P2 (pressure in pipe “B”). here is an example of my given and calculated values:

given: dia. pipe ”A” = .250 in
dia. Pipe “B” = .215 in
flow rate = 22.5 cfm
inlet pressure (P1) = 100 psi

calculated: outlet pressure (P2) = 44.66 psi

have i oversimplified this problem and made poor assumptions? also, would this same method work if pipe "B" dia. was a nozzle open to atmosphere?

please let me know if more info is necessary. thnx

 

[pmureiko]

Your assumption of the gas being non-compressible is generally good up to a 10% pressure drop. In this case the pressure drop is 45% and you will need to take into account the compressible nature air and may have problems with sonic flow.

 

[JeffHofacre]

I have solved problems like this by breaking the pipe into 10 or more pieces. You then iterate your flow assuming sonic flow at the discharge. Breaking the pipe into pieces you can use the incompressible formulas because it limits the pressure drop per section. This works real well in Mathcad but should also work in a spreadsheet. The density has to be recalculated for each of the sections. This density would then be used in the next calculation. Also the velocity needs to be checked in order to not be exceeding sonic.

My work was based on guidelines given in Crane Flow of Fluids tech paper 410. I have also checked my results using compressible flow formulas from "Streeter - Fluid Mechanics"and have achieved results within 10%.

I can't say incompressible flow is quicker to calculate but it is easier for most people to understand. In my company I only know a handful of engineers that can understand compressible flow.

Concluding, in order to be accurate break your pipe into an adequate number of sections to limit the % pressure drop per section.

 

[freeweel]

thnx for the input guys. i guess i'm going to delve a little deeper into calculation now. send out the cavalry if i'm not back in 20 min.....

 

[Cockroach]

Here is the text reference for you, from the "master" in the measurement industry.

Flow Measurement Engineering Handbook
Miller, Richard W
McGraw-Hill, 1996 (Third Edition)
ISBN 0-07-042366-0

Cut to the chase and don't fool around. I have modeled many cases from Miller and have found most other designers do too, particularly when it comes to software.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[freeweel]

thnx for pointing me to the handbook...all the reviews i've seen are great. i actually found a copy through the local library network and have it on order right now.