Hydraulic diameter
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The hydraulic diameter, <math> D_h </math>, is a commonly used term when handling flow in noncircular tubes and channels. Using this term one can calculate many things in the same way as for a round tube.
Definition:
<math> D_h = \frac {4A}{U} </math>
where A is the cross sectional area and U is the wetted perimeter of the cross-section.
For a round tube, this checks as:
- <math> D_h = \frac{\frac {4 \pi D^2}{4}}{\pi D} = D </math>
The Manning formula contains a quantity called the hydraulic radius. Despite what the name may suggest, the hydraulic diameter is not twice the hydraulic radius.
For an annulus the hydraulic diameter is
- <math> D_h = \frac{4 \cdot 0.25 \pi (D_o^2 - D_i^2)} {\pi (D_o + D_i)} = D_o - D_i </math>
and for a rectangular duct
- <math> D_h = \frac {4 L W} {2 (L + W)} </math>
For the special case of a square duct, where <math> L = W </math>, then <math> D_h = L </math>
