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Fred_Kohlhepp23-Emerald I
23-Emerald I
Jan 16, 2021 1:29 PM UTC
Solved

A water flow problem

Okay, here's the challenge:  measure the flow rate of a stream. 

  • Build a weir with a V-notch as shown below,
  • measure the water depth as shown.

What is the flow rate (liters/min) for a given height H?  A derivation and formula, please!

Fred_Kohlhepp_0-1610803649388.png

Fred_Kohlhepp_1-1610803694180.png

 

    AlanStevensAnswer
    19-Tanzanite
    Jan 18, 2021 3:36 PM UTC

    Here's my contribution

    FredsWeir.jpg

    Thought I should add a graph:

    FredsWeir2.jpg

    Alan

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    6 replies

    ValeryOchkov24-Ruby IV
    24-Ruby IV
    Jan 17, 2021 10:47 AM UTC

    I know very good handbook on this field of science. But in Russin.

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    BillWadsworth10-Marble
    10-Marble
    Jan 18, 2021 10:30 AM UTC

    Have a look at Ken Edward's stuff at LMNOeng.com  He seems to have solved this problem quite well.

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    AlanStevens19-TanzaniteAnswer
    19-Tanzanite
    Jan 18, 2021 3:36 PM UTC

    Here's my contribution

    FredsWeir.jpg

    Thought I should add a graph:

    FredsWeir2.jpg

    Alan

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      Fred_Kohlhepp23-Emerald IAuthor
      23-Emerald I
      Jan 19, 2021 1:50 PM UTC

      This is an interesting illustration of engineering adapting physics.

       

      Both Alan's solution (kudos, BTW) and the one attached below properly derive the physics of the problem from basic concepts: the gravity head creates a flow over the weir, and that times the area gives the flow rate.  But when the actual flow rate was measured it fell significantly short of what was calculated. 

       

      The old engineers, well used to having theory only approximate reality (because of the assumptions made to achieve a solution) merely created a "coefficient," to adjust theory to reality.  It would be interesting to see what ANSYS would do with this problem.

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        AlanStevens19-Tanzanite
        19-Tanzanite
        Jan 19, 2021 2:10 PM UTC

        "The old engineers, well used to having theory only approximate reality (because of the assumptions made to achieve a solution) merely created a "coefficient," to adjust theory to reality.  "

         

        Engineers regularly do this, of course.  They have discharge coefficients, friction factors, loss coefficients etc.  The nuclear reactor physicists I knew would never stoop to such common or garden terms.  When their theoretical rod positions didn’t quite match the measured ones, they modified their theory by an eigenvalue bias (a rose by any other name…!)

         

        Alan

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