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Validity of using xxpansion factor Y for a branched system.

Validity of using xxpansion factor Y for a branched system.

Validity of using xxpansion factor Y for a branched system.

(OP)
Hello,


   Imagine a piping network with a source that begins as a pipe with losses, valves etc.. and branches into two with their own respective losses and such.

If I am to calculate the flow rate through one branch, is it safe for me to use equation 3-19 of crane's and finding Y through table on A-22, but, I will say that the system "K" for that one branch actually begins at the source up through the single line and into one of the branches.

I do the same for the other branch, and I can calculate flow rate for each branch. Remember, that is only flow rate for each branch and is not valid for source line flow (which will be the additive sum of the branch flows).

This is how I am visualizing solving a branched network for compressible flow with equation 3-19 and Y.

Please discuss this with me.


   Thank you!!

 

RE: Validity of using xxpansion factor Y for a branched system.

No, the flowrates in each, every and all branches are the result of the upstream and downstream pressures on each branch.  It appears in your configuration, you know the upstream pressure of two branches forming at your fitting, but you don't know the downstream pressure of either branch.   

**********************
"Pumping accounts for 20% of the world's energy used by electric motors and 25% to 50% of the total electrical energy usage in certain industrial facilities." - DOE statistic  (Note: Make that 99.99% for pipeline companies) http://virtualpipeline.spaces.live.com/

RE: Validity of using xxpansion factor Y for a branched system.

(OP)
I have the downstream pressure of the branches and the upstream source pressure.  

RE: Validity of using xxpansion factor Y for a branched system.

Purrrfect.

Now write some simultaneous nonlinear equations in terms of flow (1 for each branch) and solve them simultaneously.  

**********************
"Pumping accounts for 20% of the world's energy used by electric motors and 25% to 50% of the total electrical energy usage in certain industrial facilities." - DOE statistic  (Note: Make that 99.99% for pipeline companies) http://virtualpipeline.spaces.live.com/

RE: Validity of using xxpansion factor Y for a branched system.

(OP)
Oh great....  :(

So equation 3-20 is valid for this type of computation?

I have K for each branch and the source line, I have specific volume of the inlet (required by eq. 3-20), I can find Y. Now what should I use for my diameter in eq. 3-20 since the diameter changes throughout the line? Should I just use the smallest diameter in the line?


   Thanks,


      - Dan

RE: Validity of using xxpansion factor Y for a branched system.

Equation 3-19 is for liquid flow and has no Y.  I think you meant equation 3-20.

Quote (dbecker):

I will say that the system "K" for that one branch actually begins at the source up through the single line and into one of the branches.

No, that's not right.  By mass balance the flow rate in the main = the flow rate in branch 1 + the flow rate in branch 2. Or, wmain = w1 + w2.  By doing what you propose, w1 is being used to characterize the flow in the main, which is not true.

You need to break the problem up into 3 sections, the main, branch 1, and branch 2.  While this will yield the correct answers, it complicates the problem by making it iterative to converge on the pressure at the Tee where the main splits into branch 1 and branch 2.

 

Good luck,
Latexman

RE: Validity of using xxpansion factor Y for a branched system.

Quote (dbecker):

Now what should I use for my diameter in eq. 3-20 since the diameter changes throughout the line? Should I just use the smallest diameter in the line?
  No, no, no!  The problem must be split into 3 pipes and the correct diameter used for each one.

Good luck,
Latexman

RE: Validity of using xxpansion factor Y for a branched system.

(OP)
Latexman thank you for the insight!

That's what I expected, breaking it down into different parts and solving as an iterative solution.

I will probably end up writing a program to iterate for me and break up the system into individual components (just make the matrix bigger and break it up into more components to boost accuracy, that's all) and I should get a pretty accurate answer I suppose.

I was afraid I was going to have to do this! At least now I know what not to do.

  Thanks,

     P.S. Latexman,

Notice that equation 3-20 has Y to be found on page A-22 of crane's. This Y value is dependant on the deltaP across a single component if i want the flow through that single component. Since I do not know the deltaP across a single component (as that is what im solving for!) i have a big problem because now i have to make multiple assumptions, initial flow rate and Y.

What do you say to this?

    

RE: Validity of using xxpansion factor Y for a branched system.

You can also convert the branch with 2 different pipe diameters and lengths to one equivalent pipe diameter and length, if you like, but since you're writing simultaneous equations, its usually just easier to write all the equations down one time for each pipe, rather than performing spot substitutions using the equivalent pipe method.  Point simply being you have a choice.  

The matrix is not the problem, iterating the matrix to solution is the harder part.  Good initial guesses for flows in each branch helps.

**********************
"Pumping accounts for 20% of the world's energy used by electric motors and 25% to 50% of the total electrical energy usage in certain industrial facilities." - DOE statistic  (Note: Make that 99.99% for pipeline companies) http://virtualpipeline.spaces.live.com/

RE: Validity of using xxpansion factor Y for a branched system.

Sounds right to me.

To get a good initial guess, think of it like an electrical resistance problem.  For pipes in series, you add the K's.  For pipes in parallel, you use

1/Kave. = 1/K1 + 1/K1

Of course, all the K's in the equation above have to be based on the same diameter, so you have to deal with that too.

Good luck,
Latexman

RE: Validity of using xxpansion factor Y for a branched system.

1/Kave. = 1/K1 + 1/K2

Good luck,
Latexman

RE: Validity of using xxpansion factor Y for a branched system.

dbecker,
Above you said

Quote (dbecker):

and I should get a pretty accurate answer I suppose.

What are your expectations for "accuracy"?  If you are expecting to be +/- 5 psi over a 500 psi pressure drop, you may be disappointed.  If you are trying to determine if your pressure drop across 100 ft of pipe should be 5 psi or 10 psi you can probably have some confidence.  

All of the empirical flow equations derive from the Bernoulli Equation.  All of these (including Bernoulli) have a large number of simplifying assumptions that shade the precision toward a specific set of conditions.  For example, the AGA 3 gas measurement equations have a great deal of precision because they have extensive requirements for pipe orientation, roughness, and upstream/downstream fittings while going to great lengths to force v(max) into the center line of the pipe.  The other equations all have less precision.  I use the AGA compressible flow equation in situations where my ending density is within 50% of my starting density.  Outside of that constraint the equation can give you very wrong answers.  Same with the Crane equations.  Know the limitations and don't go outside of them.

David

RE: Validity of using xxpansion factor Y for a branched system.

(OP)
Thanks for the heads up again David and Latexman.

I wont be needing the solution to be 4 decimal places of accuracy. +/- 5 psi over a 70 psi drop should be 'ok'.

Crane's handbook does not really get into detail on the limitations of equation 3-20 and table A-22. Although I can make my own assumptions, and it is up to me to gauge the accuracy; that is just a judgement call I will have to make.

I will be using crane's for this project, but again, I don't know all of the limitations of 3-20. If someone can give me an example of a case when not to use 3-20, it would be most appreciated.

Also, what do I do about assuming a value for Y? As I stated in my previous post I have to assume both a Y and DeltaP. This will reduce accuracy further.

  Thank you.



 

RE: Validity of using xxpansion factor Y for a branched system.

Summarizing and extending what I said in your other post, thread378-234966: Limiting factors for sonic velocity with LOW K values. , for K < 1.2 try the method I outlined for orifices on A-21 and for K > 1.2 use A-22 as you discussed.  You should verify there is not a huge discontinuity when going from one method to the other.  If there is, you'll have to rethink this.

Good luck,
Latexman

RE: Validity of using xxpansion factor Y for a branched system.

Did you talk to anyone at Crane (www.cranevalve.com)?   

Patricia Lougheed

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