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Two reservoirs are connected by two pipes with different diameters in series. The elevation of Reservoir A is 40m and Reservoir B is 35m to respective water surfaces. The first pipe is 500 m long with a diameter of 0.075m and the second pipe is 2000m long with a diameter of 0.1m. What is the flow between the two reservoirs? The absolute roughness is 0.01 for both pipes and teh pipe elevation is constant.

Schematic of the Problem Outlined

What I have tried so far is by trial and error in the Moody Diagram find a Friction Factor to use with the Darcy-Weisbach Equation. However, I cannot get a number matching my first guess of the Reynolds Number. The pipes have different diameters so that means I have to do a trial for each pipe. Also when calculating I cannot use the Head loss of 5m but of 1m since that is the correspondent Head Loss for that length of pipe? How do I go about solving for the problem above?

Thank you for your help.

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    $\begingroup$ What was your first guess of Re? Perhaps you need to revise it, if you show your working then we might be able to point out any error or omission. $\endgroup$
    – Solar Mike
    Jan 8 '20 at 10:00
  • $\begingroup$ The first Re I guessed ws 10^5 but it makes sense that the first pipe could be laminar and the second turbulent. $\endgroup$ Jan 8 '20 at 22:21
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Here's how I'd attack the question:

  • write down the Darcy Weisbach equation, with two terms on the right sides for the two different pipes. Head losses add up.

  • exchange flow velocity for a term dependent on volume flow and pipe diamter in both terms on the right side.

  • The pipe is really long and really thin and the head is really small. Start by using the laminar flow friction factor (64/Re)

  • Because of this you could solve this algebraically but I'd use any numerical tool (excel target value search is fine).

  • Check the actual resultant Re in both pipe segments, if the assumption (laminar flow) holds, if not take the friction factor from the moody chart and reiterate.

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  • $\begingroup$ Thank you for your response, for the second bullet point you wrote, what do you mean by it? So have everything instead of with V have it with Q/A? So Q would be the same for both but A changes and thus I can find my other values right? That bullet point is a bit unclear my apologies $\endgroup$ Jan 8 '20 at 22:23
  • $\begingroup$ You got it exactly right. $\endgroup$
    – mart
    Jan 9 '20 at 7:32

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