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I'm designing a machine that uses water to boost fish in one phase of a process. My main concern is how to split the water flow that I get from a water pump in to $N$ outlets with same flow rate. The image below shows this graphically. I need to use PVC pipes. I posted same question on Physics but they redirect me to this page (https://physics.stackexchange.com/q/579522/274594)

enter image description here

Update 2020-09-17:

  • Flowrate from water pump is constant.
  • Diameters on the figure are not physically representative, it's a simple conexion diagram.
  • $D_{pump} > D_{outlets}$
  • $D_{outlets}$ are equals

I'm also concerned because I don't know too much about this and when I Google it I can't find anything related: equations.

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  • $\begingroup$ Start with matched orifices. $\endgroup$ – Solar Mike Sep 14 at 18:42
  • $\begingroup$ And continue with matched pipe diameters and lengths. $\endgroup$ – Transistor Sep 14 at 20:25
  • $\begingroup$ what total head are we talking about? is the flowrate constant? Is the resistant outside of the scope of your sketch (specifically A, B ,C ... N) constant (for a given flowrate)? What's the flowrate per branch? $\endgroup$ – mart Sep 16 at 6:04
  • $\begingroup$ @mart I update the information required, thanks for your help $\endgroup$ – Pablo Díaz Sep 18 at 18:42
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Even if you had matching orifices, you might have issues with the pressure drop inside the pipes and corners.

If you are really after matching flow rates, you could look into flow control valves/flow regulator.

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    $\begingroup$ It would be difficult to get exactly matching flow rates by just relying on tube lengths & bends because of slightly differing shock losses. Using a flow control value or regulator, as this answer states, particularly on each of the outlets would be easiest way to get matching outlet flows. $\endgroup$ – Fred Sep 15 at 13:23
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If the head pressure is any more than just adequate, the problem is very easy. Just ensure that the bottleneck is near the points of exit, that they are of equal diameter and approximately the same elevation. If those conditions are met the flow rate will be very nearly identical among the outlets, regardless of the configuration and lengths of pipe leading up to them.

Ex. If you have a manifold pipe with inside diameter D and there are n outlets coming off it, put a common reducer at the end of each, with inside diameter d such that nd2 < D2.

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    $\begingroup$ This is actually a decent idea and far simpler than my approach. The OP should calculate the headloss over the longest and shortest path (after the manifold, acounting for the other streams in manifold) to get an estimate how much difference there is, if that is close enough to equal. $\endgroup$ – mart Sep 17 at 6:18
  • $\begingroup$ (though your appraoch assumes that the pressure loss in the machine is equal for all branches or neglible compared to the pressure loss at d) $\endgroup$ – mart Sep 17 at 6:58
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This is a very easy problem to solve. Just do two things: 1) make the separate branches identical geometry, and 2) make the diameter of the main manifold pipe large enough so that there isn't too much pressure drop in the manifold. By too much, make it the same percent drop as the percent difference you can allow in the flow rate of the separate segments.

(1) is straight forward, and (2) can be confirmed by a simple pipe friction flow calculation with the most conservative result being to size the manifold diameter as large as needed to confine the pressure drop along its entire length - using the entire flow rate - to the tolerance of the specifications. This is ridiculously conservative, of course, but if you can provide such a manifold diameter, then so be it. A less conservative diameter can be calculated if you say, make the same calculation for the manifold diameter, but instead of the entire manifold length, use only the maximum length between segments.

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  • $\begingroup$ Same here, but there will be problem when discharge piping/hose is not equal in length or elbow quantity. But if that's not the case, this way is most simple. $\endgroup$ – RainerJ Sep 19 at 3:52
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You can support equal distribution by clever piping design (the manifil significantly larger thabn the individual pipes, short distances in the manifold between the branches, have the branches by highly similar) but ulimtely you will need some sort of flow control.

I assume the following:

  • flowrate is constant
  • medium is water without any fish (yet9
  • the flow resistance (system curve) of the machine is constant over time
  • the total head required is more than a few meters

Then, I see two possibilities:

One, each branch gets a regulating valve. You get a ultrasonic strap on flowmeter. The pump and the machine should be at the intended operating conditions or as close to them as possible. Then you go from branch to branch and adjust the valves until the flowmeter shows equal flow in each.

The other way, more comfortable IMO, is to install valves with integrated flowmeters as they are sometimes used in heating systems, like these. This would be more costly of course. Check if the sizes and flowrates available are ok for your application, and if the these valves are exact enough.

If you can't guarantee constant flow conditions there's really no way around having a flowmeter on each line, with an automatically actutated valve and a control system that regulates the flow.

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