flow split in branch pipes from a main pipe

[nupin]

_______
: :
: :
: :

I have a main pipe that's divided into 2 branches. All 3 pipes have the same elevation. I have a manometer on each one of the smaller pipes, so I know the pressure there, plus I know the velocity of the fluid on the smaller pipes and on the main pipe. But I'd like to know the pressure on the main pipe just before the fluid splits in two.

I was comparing this system to an electrical circuit with 2 parallel resistors, where the voltage is kept constant throughout the system and the current is divided into the 2 resistors. I don't know if this system could be compared to an electrical circuit because the fluids do not rejoin, they're discharged on a vessel. But anyways, I considered the total energy of the fluid represented by the Bernoulli equation as the voltage on the electrical circuit and I did the following (ignoring friction losses):

(P3/density)+((V3^2)/2g)=(P2/density)+((V2^2)/2g)

3 for the main pipe
2 for the smaller pipe

The only thing I dont know in the equation is P3 so according to what I'm thinking I could calculate it. Am I right? Is it possible to use Hardy-Cross here, since I know the flow on each pipe to figure out the pressure on the main pipe just before the fluid splits in 2?

 

[BigInch]

One more thing. nupin & desertfox, You guys seem to be quite interested in the Electric to Water circuit analogy, so have a look at this site for the basis,

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/watcir2.html#c2

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[sailoday28]

Binginch-You are correct, I did not pay attention to the original statement
"I have a manometer on each one of the smaller pipes, so I know the pressure there, plus I know the velocity of the fluid on the smaller pipes and on the main pipe. But I'd like to know the pressure on the main pipe just before the fluid splits in two."
You are also correct in that the losses for the branch and run may also be determined BUT they are for "only those flow conditions"

Regards

 

[rcooper]

Would there be any merit in using the force/momentum equation at the branch to get some handle on the loses through the branch?

 

[sailoday28]

rcooper (Mechanical)Very good question, but how is it to be done?

Regards

 

[25362]

In practice there are energy "losses" in 90^o T-junctions as a result of flow separation.

 

[BigInch]

Most standard fittings and valve types have generally well known loss characteristics which can usually be found in the pipe and fitting reference texts.

Sailo, Frictional flow losses for pipe with standard flow conditons, as I'm sure you know, are well correlated to a number of equations which are not limited to one flow condition. In fact, having actual data with which to work, as the OP has above, should allow him to make further corrections if necessary and apply the general equations to virtually any hydraulically similar flow condition without suffering significant loss of accuracy. Generally large hydraulic systems are designed relying entirely on standard frictional loss equations, without any benefit of having the tiniest bit of actual data with which to work and the results are normally quite acceptable, so I don't think there will be much problem for the OP to extend the range of his equations to any practical limits he chooses.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[nupin]

Biginch, thanks for the website. You said in a previous post that if I were yo use the Hardy Cross method to solve this problem, I would have to create a virtual or pseudo loop. It was my understanding that you create pseudo loops to join two fixed grade nodes. I dont know if that would apply to my case because even though I know the pressure on the branches, they are supposed to be the same.

 

[BigInch]

No, you can include elevation differences. I'm not too keen on discussing the Hardy-Cross method where its not needed as in your case, but the typical textbook HC methods do not usually include elevation changes from one node to another, since all they are really concerned about is balancing flows and frictional head losses around the loops ([Σ] = 0) and the elevation changes are typically known values anyway, they prefer to discuss flat systems of loops subject only to differential heads created by friction, but you can include elevation heads if you want to and you're willing to do the extra math. And they also do not usually include any entry or exiting pipes with flows into or out of the looped circuits either, since those are determinate "free bodies", once the node pressures in the loops and the loop flows have been solved.

Hardy-Cross is only usefull for indeterminate system analysis with a looop or with flows across loops, so if you don't have any loop(s) (or if you have loops with flows in all segments are known), you must create some in order to have flows "to balance". What you have described is a "Y" pattern, so in order to make some loops, you would have to create 2 pipe connections, each beginning at an arm at the top of the Y and looping down to join at the bottom. But since you already know the flows at each arm, and also the leg Q0= Q1+Q2, you have no flows that remain for you to balance anyway. HC becomes only a method for distributing any errors you may have that could have resulted from the Darcy based analysis, but the frictional flow losses in HC are also based on similar Darcy equations, so what are you checking? Nothing, just doing the problem twice and ... including the hard way.

In any pipe segment, if you have any two of the 3 items, P1 inlet pressure (or head), P2 outlet pressure (or h) or the flow Q, and know the pipe parameters, roughness, diameter, length etc., such that friction loss can be calculated using a Darcy equation, the missing variable is solvable. That's why radials to/from the loops are ignored in the textbooks... the radial analysis is trival after loop analysis has determined the flow and pressure at the connection points to the loops are solved against the problem's boundary conditions, the total inlet and outlet flows =0 and at least one given reference head somewhere in the system.

Did I explain?



BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[nupin]

Hi, I understand what you are saying I was just curious as to how I would solve this if I did not have the data I have.

My system is not actually Y shaped, there is a main pipe that disctributes flow, to, lets say, an n number of pipes, which in turn discharge into a tank:

_______<--------- main pipe
: : :
: : :

It's more like a several squares. So if I had only the outlet pressures on all the branches, I could use the Hardy Cross method to solve this by creating a number of ficticious pipes that would join the branches, and then get on from there. right?

 

[BigInch]

Yes, as long as you had enough known variables to sufficiently specify the boundary conditions for the system, 1 reference pressure node somewhere in there and either a known flowrate or a known pressure at any other node that could allow fluid to enter or exit the system. (its assumed all pipe diameters, roughnesses and lengths are "known").

In your example, Let's say your reference pressure is at the "<" point of the main_line, a known inlet flowrate of 5 at the "e" point of the main_line, with branches (outlets?) "A", "B", and "C", with known outflow rates at A=-2 and B=-3 and C=0, you could tie B to both A and C to make virtual loops.

Typically it would go like this,

Start H-C by assuming flows in branch "A" of 1, "B"=3 and "C" = 1, looking at node "C", you would have an unbalanced flow of 1, which would be distributed around the "B-C" loop, and each time you sum the flows in that loop, any unbalance against "C" = 0 would always get pushed over towards "B" and enter the "B-A" loop to get distributed there. The same would happen when there was any unbalanced flows at "A", which would also redistribute over to "B-C". So you can see that whenever the flow in branch C was not 0, the redistribution to B-A would automatically handle that little problem for us, and likewise C to B-A, so they continuously fight eachother until the nodes balance. When flowrates at A, B & C finally balance, you would be left with 0 flows in the tie-overs B->A and B->C. If you didn't have 0 flows, you stopped the iterations too soon. You know you must have 0 flow in the virtual loops, because they obviously can't transport any fluid if they really don't exist. You also know that if there was 0 flow from the outlet at C, you would have zero flow in branch "C", and a balanced inflow on B = outflow at B must result in ZERO flow in the tie-overs B-C. Likewise B-A.

You might also see that if you just happened to make very good guesses, knowing that B->A and B->C really cannot carry any flow and in the end must = 0, and used that knowledge to assume a flow of 2 in branch "A", 3 in branch "B", 0 in branch "C" to start the H-C solution method, you would have arrived at the solution to all flowrates in the branches ... before you really ever started working on it. With known flowrates in each pipe and one reference pressure somewhere in the system, you can solve each for the differential pressure between their inlet's and outlets one by one with Darcy equations until all dPs for each pipe are known, then just start at the reference pressure node, chain the pipes together and algebraically add dP to get the pressure at the other end of each pipe.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[25362]

The subject of dividing and combining manifolds has been discussed in past threads, and is treated in textbooks on fluid mechanics.

 

[BigInch]

But probably not with Hardy-Cross and virtual tie-overs, for obvious reasons.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[nupin]

thanks for the advice BigInch

 

[ChristyBermen]

It sounds like your system is less than 5 pipelines. PIPE-FLO has a free downloadable demo which does fluid calculations of up to 5 pipelines for free. You could use it to easily check your calculations.

http://www.eng-software.com/demo/download/

Full Disclosure: I work for Engineered Software developing this tool.

Christy Bermensolo
Engineered Software

http://www.eng-software.com