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:

$D\_h\; =\; frac\; \{4A\}\{U\}$

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 $D\_h\; =\; 2W$.

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