The hydraulic diameter, , 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
: is the cross-sectional
area of the flow,
: is the wetted perimeter
of the cross-section.
More intuitively, the hydraulic diameter can be understood as a function of the hydraulic radius , 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.
[Frank M. White. ''Fluid Mechanics''. Seventh Ed.]
Note that for the case of a circular pipe,
The need for the hydraulic diameter arises due to the use of a single dimension in case of dimensionless quantity
such as Reynolds number
, which prefer a single variable for flow analysis rather than the set of variables as listed in the table. 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 flow
s 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
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
This can be seen as follows: The
-sided regular polygon is a union of
triangles, each of height
Each such triangle contributes
to the total area and
to the total perimeter, giving
for the hydraulic diameter.
* Equivalent spherical diameter
* Hydraulic radius
* Darcy friction factor