# Hydraulic diameter

Hydraulic diameter

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.

Definition:

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

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

For a round tube, this checks as:

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

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

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

and for a rectangular duct

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

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 $D_h = 2W$.

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