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. When the cross-section is uniform along the tube or channel length, it is defined as^[1][2]

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

where

A is the cross-sectional area of the flow,

P is the wetted perimeter of the cross-section.

More intuitively, the hydraulic diameter can be understood as a function of the hydraulic radius R_H, which is defined as the cross-sectional area of the channel divided by the wetted perimeter. Here, the wetted perimeter includes all surfaces acted upon by shear stress from the fluid.^[3]

${\displaystyle R_{\text{H}}={\frac {A}{P}},}$

${\displaystyle D_{\text{H}}=4R_{\text{H}},}$

Note that for the case of a circular pipe,

${\displaystyle D_{\text{H}}={\frac {4\pi R^{2}}{2\pi R}}=2R}$

The need for the hydraulic diameter arises due to the use of a single dimension in the case of a dimensionless quantity such as the Reynolds number, which prefers a single variable for flow analysis rather than the set of variables as listed in the table below. 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 larger.

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.^[4]