Transposing the hydraulic diameter formula

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Discussion Overview

The discussion revolves around the transposition of the hydraulic diameter formula to isolate the width (W) given a known height (H) and hydraulic diameter (Dh). The focus is on mathematical reasoning and manipulation of the formula.

Discussion Character

  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • Jon asks if it is possible to transpose the formula Dh = (2xWxH)/(W+H) to solve for width (W) given height (H) and hydraulic diameter (Dh).
  • Doc Al provides a step-by-step approach to manipulate the formula, suggesting to multiply both sides by (W+H) and then collect terms to isolate W.
  • Jon expresses difficulty in seeing the transposition and requests further assistance to arrive at the equation for W.
  • Doc Al completes the transposition, arriving at the formula W = H*Dh/(2*H - Dh) and confirms the solution.
  • Jon acknowledges the solution and expresses relief at having the problem resolved.

Areas of Agreement / Disagreement

Participants appear to agree on the steps taken to transpose the formula, with no significant disagreement noted in the mathematical approach presented.

Contextual Notes

None noted.

Who May Find This Useful

Individuals interested in hydraulic diameter calculations, mathematical transposition techniques, or those seeking assistance with similar mathematical problems.

Xpind
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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
 
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Xpind said:
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.
 
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
 
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.
 
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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