Hydraulic diameter

In the more general case, channels with non-uniform non-circular cross-sectional area, such as the Tesla valve, the hydraulic diameter is defined as: : D_\text{H} = \frac{4V}{S}, where : is the total wetted volume of the channel, : is the total wetted surface area. This definition is reduced to \frac{4A}{P} for uniform non-circular cross-section channels, and 2R for circular pipes. ==List of hydraulic diameters==

For a fully filled duct or pipe whose cross-section is a convex 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 \tan(\pi/N). Each such triangle contributes BD/4 to the total area and B to the total perimeter, giving : D_\text{H} = 4\frac{N BD/4}{NB} = D for the hydraulic diameter. ==See also==