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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 ...
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 the shape of the pipe, channel ...
It takes energy to push a fluid through a pipe, and Antoine de Chézy discovered that the hydraulic head loss was proportional to the velocity squared. [5] Consequently, the Chézy formula relates hydraulic slope S (head loss per unit length) to the fluid velocity V and hydraulic radius R: = =
is the hydraulic radius, which is the cross-sectional area of flow divided by the wetted perimeter (for a wide channel this is approximately equal to the water depth) [m]; is Manning's coefficient [time/length 1/3]; and; is a constant; k = 1 when using SI units and k = 1.49 when using BG units.
, 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);
Some texts then use a characteristic dimension that is four times the hydraulic radius, chosen because it gives the same value of Re for the onset of turbulence as in pipe flow, [17] while others use the hydraulic radius as the characteristic length-scale with consequently different values of Re for transition and turbulent flow.
The length of line of the intersection of channel wetted surface with a cross sectional plane normal to the flow direction. The term wetted perimeter is common in civil engineering, environmental engineering, hydrology, geomorphology, and heat transfer applications; it is associated with the hydraulic diameter or hydraulic radius. Engineers ...
R is the pipe radius, A is the cross-sectional area of pipe. The equation does not hold close to the pipe entrance. [8]: 3 The equation fails in the limit of low viscosity, wide and/or short pipe. Low viscosity or a wide pipe may result in turbulent flow, making it necessary to use more complex models, such as the Darcy–Weisbach equation.