Parallel flow pipe network help
Parallel flow pipe network help
(OP)
Let's say I have a simple parallel flow problem as shown in the attachment. The flow is pressurized and the downstream of the return goes back to a piping system that is negligible. It does not vent to atmosphere.
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I've tried reading up on the subject, but I got stuck at a certain point. At point A, I know that the flow going in must equal the flow going out to the two pipes. Therefore, it will look like Q = Q1+Q2. Expanding Q1 and Q2 gives me V*A for each respective pipe.
I also know that the head loss of Pipe 1 must equal the head loss of Pipe 2. Expanding those equations, I find that I am faced with an unknown, which is the friction factor for each pipe. The friction factor can be explicitly calculated using the Swamee and Jain formula, but is dependent on the Reynolds Number, which is dependent on the flow velocity, which is ultimately dependent on the flow rate of each of the pipes. After getting the friction factor, everything else is easy. Simply plug the velocities from the head loss equations back into the Q formula shown above and solve for the unknown.
I know one can attain the correct friction factor value by many iterations, but is there a way without doing iterations by hand or by Excel and not fancy software?
Also, how would I find the total pressure loss of the system?
Thanks!
I've tried reading up on the subject, but I got stuck at a certain point. At point A, I know that the flow going in must equal the flow going out to the two pipes. Therefore, it will look like Q = Q1+Q2. Expanding Q1 and Q2 gives me V*A for each respective pipe.
I also know that the head loss of Pipe 1 must equal the head loss of Pipe 2. Expanding those equations, I find that I am faced with an unknown, which is the friction factor for each pipe. The friction factor can be explicitly calculated using the Swamee and Jain formula, but is dependent on the Reynolds Number, which is dependent on the flow velocity, which is ultimately dependent on the flow rate of each of the pipes. After getting the friction factor, everything else is easy. Simply plug the velocities from the head loss equations back into the Q formula shown above and solve for the unknown.
I know one can attain the correct friction factor value by many iterations, but is there a way without doing iterations by hand or by Excel and not fancy software?
Also, how would I find the total pressure loss of the system?
Thanks!





RE: Parallel flow pipe network help
RE: Parallel flow pipe network help
Sum all pressure drops in any path you can construct from source to sink.
Each path will have an equal pressure loss.
If it ain't broke, don't fix it. If it's not safe ... make it that way.
RE: Parallel flow pipe network help
RE: Parallel flow pipe network help
Using the Cvs, you can calculate the flow rates that will make both pipes have the same pressure drop.
Mike Halloran
Pembroke Pines, FL, USA
RE: Parallel flow pipe network help
RE: Parallel flow pipe network help
This problem is driving me crazy.
RE: Parallel flow pipe network help
I still think you have a assume a split between the two 'valves' until the pressure drop through the first 'valve' is the same as the pressure drop through the second 'valve'. Since Qt = Q1 + Q2 (Qt is the total flow and Q1, Q2 is the flow through each line) and dP is the same for a solved solution, you might be able to substitute into the two equations and come up with a single formula.
Mike, correct me if I'm wrong regarding your suggestion.
One thing this approach does not do is account for the change in friction factor as you adjust the split of the total flow through each 'valve'. That's why I prefer to use Excel to calculate the pressure drop through each line explicitly and then adjust the split until my pressure drops are equal.
RE: Parallel flow pipe network help
Do you mean to just treat each of the lines separate from each other first? (as if there was only that line in the system and not the other one). If so, I've already calculated the pressure drop for each of the individual lines in Excel already. I will try what you have mentioned and will report back.
Again, thanks all for the help!
RE: Parallel flow pipe network help
“The beautiful thing about learning is that no one can take it away from you.”
---B.B. King
http://waterhammer.hopout.com.au/
RE: Parallel flow pipe network help
I also use Excel.
After finding a Cv for each branch, I just use goal seek on the split to get the pressure drops equal.
Mike Halloran
Pembroke Pines, FL, USA
RE: Parallel flow pipe network help
Without using the Cv, can I just keep entering estimates for flow rates in each branch in my spreadsheet until the pressure drop of branch 1 and branch 2 are equal? I tried it just now and although they're not 100% exact, they are quite close. I understand that this takes a lot of trial and error, but with knowledge of these systems one could probably enter in a good estimate.
For the rest of the day, I will try to figure it out with using Cv. I just want some further clarification. Basically, I have two pressure drops (one for each branch) that have been calculated individually. I use the Cv equation by using each of those pressure drops and an estimate of the flow rate for each of the branch. Now I have two Cv values, one for each branch. How would you implement goal seek for this?
RE: Parallel flow pipe network help
I don't know what your Cv equals, but it must equal some valid expression for head loss as a function of flow.
Something like attached.
Could be better, but its my weekend already.
If it ain't broke, don't fix it. If it's not safe ... make it that way.
RE: Parallel flow pipe network help
RE: Parallel flow pipe network help
RE: Parallel flow pipe network help
Good luck,
Latexman
RE: Parallel flow pipe network help
In any case, for ( n pipes) in parallel, each pipe can have a DP vs W curve drawn , by assuming a cerain flow, calculating the DP and storing the resulting data in a file. For each calculated DP, you can vary the friction coeficient , as well as the heat transferred and the bouyancy or 2 phase flow effects.
Next, you assume a certain pressure drop across the circuit, and for each assumed DP, there is only one flow for each of the tubes. Add up the sumof these flows , for each assumed DP.
If the circuit is thermal-hydraulically stable ( static stability aka Ledinegg stability) then there will be only one unique total flowrate for each assumed DP. For the known total flowrate, select the DP that generates that total flowrate.
The above topic was widely discussed in the 1960's and was titled "multi channel flow instability"
RE: Parallel flow pipe network help
“The beautiful thing about learning is that no one can take it away from you.”
---B.B. King
http://waterhammer.hopout.com.au/
RE: Parallel flow pipe network help
I'm working on a parallel pipe scenario where there is one inlet and multiple outlets all exiting to free air. Do the constraints of the Hazen-Williams equation still apply (ie all hL values equal)? I've found solutions assuming so but in practice we have found that in a case where all pipes have identical ID, roughness, and length we will consistently see greater dispense volumes from the pipe farthest from the inlet.
a little background: inlet is horizontal, all dispense pipes are vertical exiting the bottom with all dispense inlets at same height. Prior to a timed dispense all pipes and inlet tube (manifold) have been primed and are assumed full of fluid (ie. no air volumes displaced at beginning of dispense).
Thanks in advance for any guidance,
Adam
RE: Parallel flow pipe network help
Patricia Lougheed
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RE: Parallel flow pipe network help
Nasa addressed this issue in the fuel distribution headers to their large rockets ( as you can view at the Houston space center or in the smithsonian A+S museum) by tapering down the header diameter as you proceed from center to end, to maintain a fixed header velocity , fixed velocity head, and constant static pressure at the inlet of each fuel discharge nozzle.
If there is only one flow case to contend with then you can address this by providing differential orificing at the inlet to each dispense pipes.