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For a fully filled duct or pipe whose cross-section is a convex 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 N {\displaystyle N} -sided regular polygon is a union of N {\displaystyle N} triangles, each of height D / 2 {\displaystyle D/2 ...
In those cases, the characteristic length is the diameter of the pipe or, in case of non-circular tubes, its hydraulic diameter : = Where is the cross-sectional area of the pipe and is its wetted perimeter. It is defined such that it reduces to a circular diameter of D for circular pipes.
, the hydraulic diameter of the pipe (for a pipe of circular section, this equals D; otherwise D H = 4A/P for a pipe of cross-sectional area A and perimeter P) (m); , the mean flow velocity, experimentally measured as the volumetric flow rate Q per unit cross-sectional wetted area (m/s);
The wetted perimeter is the perimeter of the cross sectional area that is "wet". [1] The length of line of the intersection of channel wetted surface with a cross sectional plane normal to the flow direction.
The wetted perimeter for a channel is the total perimeter of all channel walls that are in contact with the flow. [10] This means that the length of the channel exposed to air is not included in the wetted perimeter. For a circular pipe, the hydraulic diameter is exactly equal to the inside pipe diameter: =.
P is the wetted perimeter (L). For channels of a given width, the hydraulic radius is greater for deeper channels. In wide rectangular channels, the hydraulic radius is approximated by the flow depth. The hydraulic radius is not half the hydraulic diameter as the name may suggest, but one quarter in the case of a full pipe. It is a function of ...
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The variations of Q/Q (full) and V/V (full) with H/D ratio is shown in figure(b).From the equation 5, maximum value of Q/Q (full) is found to be equal to 1.08 at H/D =0.94 which implies that maximum rate of discharge through a conduit is observed for a conduit partly full.