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Hydraulic diameter

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The hydraulic diameter, $D h$ , 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.

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Definition:

$D_h = \frac {4A}{U}$

where A is the cross sectional area and U is the wetted perimeter of the cross-section.

For a round tube, this checks as:

$D_h = \frac{4 \frac {\pi D^2}{4}}{\pi D} = D$

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

$D_h = \frac{4 \cdot 0.25 \pi (D_o^2 - D_i^2)} {\pi (D_o + D_i)} = D_o - D_i$

and for a rectangular duct

$D_h = \frac {4 L W} {2 (L + W)} = \frac{2LW}{L+W}$

For the special case of a square duct, where $L = W$ , then $D h = L$ . For the other limiting case of a very wide duct, i.e. a slot of width $W$ where $L \gg W$ , then $D h = 2 W$ .