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Transposing the hydraulic diameter formula

  1. Nov 1, 2011 #1
    Hi

    Is there a way of transposing the formula to calculate the width (W) from a known height (H) and hydraulic diameter (Dh)?

    Dh = (2xWxH)/(W+H)

    Many thanks

    Jon
     
  2. jcsd
  3. Nov 1, 2011 #2

    Doc Al

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    Staff: Mentor

    Multiply both sides by (W+H):
    (W+H)*Dh = 2*W*H

    Now just multiply out the left hand side. And so on.
     
  4. Nov 1, 2011 #3
    Thanks for the quick reply Doc Al.

    It's been a long time since I've needed to do this kind of thing, and at the moment I just can't see 'it' to isolate the width

    I have four pages of re-written equations, unfortunately none of them start W=

    Could you help a simpleton out, and finish the transposition through?

    Thanks again

    Jon
     
  5. Nov 1, 2011 #4

    Doc Al

    User Avatar

    Staff: Mentor

    Multiply both sides by (W+H):
    (W+H)*Dh = 2*W*H

    Now just multiply out the left hand side:
    W*Dh + H*Dh = 2*W*H

    Collect terms with W to one side:
    2*W*H - W*Dh = H*Dh

    W*(2*H - Dh) = H*Dh

    So:
    W = H*Dh/(2*H - Dh)

    There you go.
     
  6. Nov 1, 2011 #5
    W*(2*H - Dh) = H*Dh

    So simple when you can see it..

    Thanks for your help, that's been driving me crazy!
     
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