Transposing the hydraulic diameter formula

[Xpind]

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

 

[Doc Al]

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.

 

[Xpind]

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

 

[Doc Al]

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.

 

[Xpind]

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

So simple when you can see it..

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