Transposing the hydraulic diameter formula

  • Thread starter Xpind
  • Start date
  • #1
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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
 

Answers and Replies

  • #2
Doc Al
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Dh = (2xWxH)/(W+H)
Multiply both sides by (W+H):
(W+H)*Dh = 2*W*H

Now just multiply out the left hand side. And so on.
 
  • #3
3
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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
 
  • #4
Doc Al
Mentor
45,029
1,329
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.
 
  • #5
3
0
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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