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# Fluid Flow Problem

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## Fluid Flow Problem

(OP)
If I have a pump that is discharging say 500GPM into a 10" pipe and somewhere down the line the pipe splits in two and the other is a 6" and they are both open to atmosphere at the ends how does this affect the fluid flow? I know Q=AV plays a role here but does the GPM split evenly between the 2 different diameter pipes? Or does velocity remain constant throughout the whole system (which I don't think this is valid since a lower diameter should increase velocity due to A1V1 = A2V2). Most questions always give you almost all velocities and all flows and you have to solve for 1 variable but what if you dont know the velocities in discharge pipes or their flow rates?

### RE: Fluid Flow Problem

Why would velocity be the same?

It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)

### RE: Fluid Flow Problem

Check out the Poiseuille equation. It's has an analog in electrical circuits, with delta-p similar to voltage, Q similar to current and the other terms as an effective resistance.

https://en.wikipedia.org/wiki/Hagen%E2%80%93Poiseu...

Find the two resistances from each pipe after the split and then treat it like a voltage-division problem, solving for Q instead of current.
You'll find the volumetric flow splits as the ratio of the resistance of one pipe to the sum of the resistances of both pipes.

https://en.wikipedia.org/wiki/Voltage_divider

Between the volumetric flow rates and the pipe areas, you should be able to solve for the velocities.

### RE: Fluid Flow Problem

(OP)
Wouldn't I need to know how much GPM would flow into the pipe to know how much resistance that pipe is going to give me?

### RE: Fluid Flow Problem

Didn't you say there's 500gpm flowing into the pipe??

Did you make any attempt with the given equations?

### RE: Fluid Flow Problem

(OP)
oh no, I meant wouldn't I need to know the GPM flowing into the branches not the GPM of the initial discharge from the pump,

I did see the equation and it seemed pretty straight forward utilizing the difference in pressures to find the GPM but it made me question whether if a pipe branches out into 2 identical diameter pipes then unless the length of the both branches is the same then the flow rate would be different? Am I right? I guess it would make sense since the longer pipe would exhibit more friction.

### RE: Fluid Flow Problem

You have now introduced a variable, different lengths of the branches?
You need to define a definite condition, not ask open ended questions.

It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)

### RE: Fluid Flow Problem

This sounds a lot like the Three Reservoir Problem, with the fixed (?) head discharge at the pump being one "reservoir" and the atmospheric discharges of the two branches being the other two "reservoirs." I had to solve one of these in college and early in my career I had a real life version to solve. For the second one, I wrote a program for my HP-41CX calculator to solve it. Worked like a charm.

============
"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill

### RE: Fluid Flow Problem

(OP)
Yes that is exactly the type of problem that I am trying to understand, I can't find any help online that deals with 2 branches in the discharge, could you elaborate more in your experience, how does one begin to approach the problem if all you have is the gpm from the pump discharge?

### RE: Fluid Flow Problem

Thinking about this more, I doubt the flow would be able to fully develop in a 10" pipe to justify Poiseuille flow. Darcyâ€“Weisbach equation is also used, in conjunction with a moody chart. Theoretically, you'd still calculate resistance and split flow accordingly.

but seeing as the flow probably isn't fully developed (and almost certainly wouldn't be after the split - in fact it looks like you don't even give the diameter of the other branch?) the situation is more complicated.

If this already exists, I would just measure the flow.

### RE: Fluid Flow Problem

(OP)
Ok so would I split the problem in 2 in the sense that I would treat each discharge branch separately, So say calculate the friction losses of one branch as if it were a single 1 suction/ 1 discharge but utilizing the full flow of GPM that the pump is supplying and then do it again for branch 2?

### RE: Fluid Flow Problem

Ultganon...

A Google search for "three reservoir problem" turns up lots of hits, including YT videos, pdfs with solutions, an Excel spreadsheet that uses the goal seek feature, etc.

This is an iterative problem. In college, we solved it by hand (it's not terribly difficult). When I solved it for work, I wrote a calculator program. I like to automate common problems, but this one I haven't solved since.

Both times I solved this problem, I used Hazen-Williams for the pipe head losses. You can use Darcy-Weisbach just as easily, but only if you use an explicit approximation for the friction factor. If you use Colebrook-White for the friction factor, you introduce a second level of iteration and it's simply not worth it unless your prof makes you do it because he like torturing his students.

If you are not familiar with explicit approximations to the Colebrook-White equation, there is a good article here: https://en.wikipedia.org/wiki/Darcy_friction_facto...

I have attached pdf printouts of two Mathcad worksheets I prepared in 2014 that compare about two dozen friction factor formulas. The more recent ones in the Wikipedia article are, of course, not included.

============
"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill

### RE: Fluid Flow Problem

(OP)
Thanks, appreciate the help, I have been looking online but I've been searching for "multiple branches" or "2 discharge pipes" and nothing ever turned up.

### RE: Fluid Flow Problem

Nowadays, I think the main benefit that 40+ years of engineering experience brings to the table is knowing more online search terms to try than a student would think of.

============
"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill

### RE: Fluid Flow Problem

(OP)
What if, I now know the flow rates on each branch say branch 1 is 60 GPM and branch 2 is 200 GPM, would I need a pump that would discharge 260 GPM, is it that straightforward or is there a catch?

### RE: Fluid Flow Problem

What would you think, if 1 pipe flows is 60gpm and the other is 200gpm, what flow would you need from the pump at the appropriate head to achieve the condition you have described?

It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)

### RE: Fluid Flow Problem

#### Quote (Ultganon)

What if, I now know the flow rates on each branch say branch 1 is 60 GPM and branch 2 is 200 GPM, would I need a pump that would discharge 260 GPM, is it that straightforward or is there a catch?

There's a "catch":

#### Quote (Ultaganon)

If I have a pump that is discharging say 500GPM into a 10" pipe and somewhere down the line the pipe splits in two and the other is a 6"

What happens to the remaining 240 GPM... it does not just magically "vanish"?
Assuming that pump output is known to be 500 GPM (you told us it is) the sum of the two discharges has to equal 500 GPM.

www.SlideRuleEra.net

### RE: Fluid Flow Problem

Ultganon: back to what I posted sometime back, give a definite condition and stop asking pointless open ended questions.

It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)

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