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At datum height I have a pipe A (ID = 25mm) that discharges water at a volumetric flow rate of 10l/min, and unknown pressure. When this pipe is connected to a polyethylene pipe B (ID = 12mm), 50m long running to a height of 6m, then the end of this pipe B discharges water at 3l/min

Do I have enough information to calculate what the change in discharge rate at the end of pipe B would be if pipe B was of diameter 25mm instead of 12mm, and if so how could I? The equations I'm seeing seem to require a pressure measurement.

I've seen this answer, but it appears to ignore friction losses.

I'm guessing minor losses from the transition at the join of unlike pipe sizes can probably be ignored for an approximate answer.

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  • $\begingroup$ Yes, I think there is a pressure that partially offsets the 6m head differential to result in a reduced flow rate at the discharge point. I don't think the change in pipe diameter would change the flow rate, but discharge velocity. $\endgroup$
    – r13
    Apr 8, 2021 at 3:09
  • $\begingroup$ What Re are you operating at? You Colebrook equation may signify significantly. Check Cimbala and Çengel's textbook. $\endgroup$
    – WnGatRC456
    Apr 8, 2021 at 12:31
  • $\begingroup$ You can have a look at this question also. It describes the methodology for the pressure drop, which you can modify. $\endgroup$
    – NMech
    Apr 8, 2021 at 15:14

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Yes, you do have enough information. The equations you've seen that require a pressure measurement are the Colebrook-White equation (or its embodiment in the Moody chart) and the Darcy-Weisbach equation (as a definition of Darcy friction factor), right? Applying those equations three times to the situations described in your first paragraph (once to pipe A in isolation; once to pipe A when connected to pipe B; and once to pipe B when connected to pipe A) will give you three simultaneous equations, which you can use to compute the values of three unknowns: the pressure difference between entrance and discharge, the length of pipe A, and the pressure difference between the pipe junction and the discharge. The first two of those three unknowns can be expected to stay the same in the situation described in your second paragraph, so armed with their values, you can apply the equations to each pipe in that situation to get two simultaneous equations, from which you can compute values of two unknowns: the flow rate and the new value of the pressure difference between the pipe junction and the discharge.

(In case you're worried about the appearance of relative roughness in the Colebrook-White equation, I think "polyethylene" is intended to imply that the roughness can be safely treated as zero.)

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