Hydraulic diameter

The hydraulic diameter, D_H, is a commonly used term when handling flow in non-circular tubes and channels. Using this term, one can calculate many things in the same way as for a round tube. It is defined as

${\displaystyle D_{\mathrm {H} }={\frac {4A}{P}},}$

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

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, but four times.

Hydraulic diameter is mainly used for calculations involving turbulent flow. Secondary flows can be observed in non-circular ducts as a result of turbulent shear stress in the turbulent flow.

Hydraulic diameter is also used in calculation of heat transfer in internal flow problems.

List of hydraulic diameters

Geometry	Hydraulic diameter	Comment
Circular tube	${\displaystyle D_{\mathrm {H} }={\frac {4\cdot {\frac {\pi D^{2}}{4}}}{\pi D}}=D}$	For a circular tube the hydraulic diameter is simply the diameter of the tube.
Annulus	${\displaystyle D_{\mathrm {H} }={\frac {4\cdot {\frac {\pi \left(D_{\mathrm {out} }^{2}-D_{\mathrm {in} }^{2}\right)}{4}}}{\pi \left(D_{\mathrm {out} }+D_{\mathrm {in} }\right)}}=D_{\mathrm {out} }-D_{\mathrm {in} }}$
Square duct	${\displaystyle D_{\mathrm {H} }={\frac {4a^{2}}{4a}}=a}$
Rectangular duct (fully filled)	${\displaystyle D_{\mathrm {H} }={\frac {4ab}{2(a+b)}}={\frac {2ab}{a+b}}}$
Channel of water or partial filled rectangular duct	${\displaystyle D_{\mathrm {H} }={\frac {4ab}{2a+b}}}$	For the limiting case of a very wide duct, i.e. a slot of width b where b ≫ a, then DH = 4b

For a fully filled duct or pipe whose cross section is a regular polygon, the hydraulic diameter is equivalent to the diameter of a circle inscribed within the wetted perimeter.

See also

• Equivalent spherical diameter
• Hydraulic radius
• Darcy friction factor