Hydraulic diameter
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. When the cross-section is uniform along the tube or channel length, it is defined as where 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. 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 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. Non-uniform and non-circular cross-section channels. 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: where This definition is reduced to formula_6 for uniform non-circular cross-section channels, and formula_7 for circular pipes. 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 formula_8 of a circle inscribed within the wetted perimeter. This can be seen as follows: The formula_9-sided regular polygon is a union of formula_9 triangles, each of height formula_11 and base formula_12. Each such triangle contributes formula_13 to the total area and formula_14 to the total perimeter, giving for the hydraulic diameter.