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
:$D\_\backslash text\; =\; \backslash frac,$
where
: 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.
:$R\_\backslash text\; =\; \backslash frac,$
:$D\_\backslash text\; =\; 4R\_\backslash text,$
Note that for the case of a circular pipe,
:$D\_\backslash text\; =\backslash frac=2R$
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 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

For a fully filled duct or pipe whose cross-section is a regular polygon, the hydraulic diameter is equivalent to the diameter $D$ of a circle inscribed within the wetted perimeter. This can be seen as follows: The $N$-sided regular polygon is a union of $N$ triangles, each of height $D/2$ and base $B\; =\; D\; \backslash tan(\backslash pi/N)$. Each such triangle contributes $BD/4$ to the total area and $B$ to the total perimeter, giving :$D\_\backslash text\; =\; 4\backslash frac\; =\; D$ for the hydraulic diameter.

** References **

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See also

* Equivalent spherical diameter * Hydraulic radius * Darcy friction factor Category:Fluid dynamics Category:Heat transfer Category:Hydrology Category:Hydraulics

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 $D$ of a circle inscribed within the wetted perimeter. This can be seen as follows: The $N$-sided regular polygon is a union of $N$ triangles, each of height $D/2$ and base $B\; =\; D\; \backslash tan(\backslash pi/N)$. Each such triangle contributes $BD/4$ to the total area and $B$ to the total perimeter, giving :$D\_\backslash text\; =\; 4\backslash frac\; =\; D$ for the hydraulic diameter.

See also

* Equivalent spherical diameter * Hydraulic radius * Darcy friction factor Category:Fluid dynamics Category:Heat transfer Category:Hydrology Category:Hydraulics