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The need for the hydraulic diameter arises due to the use of a single dimension in the case of a dimensionless quantity such as the Reynolds number, which prefers 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.
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: = =
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 ...
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);
Similarly the maximum value of V/V (full) (which is equal to 1.14) is also observed at conduit partly full with H/D = 0.81.The physical explanation for these results are generally attributed to the typical variation of Chézy's coefficient with hydraulic radius R h in Manning’s formula. [1]
the permissible long term average depth of the water table (Dw) on the basis of agricultural drainage criteria; the soil's hydraulic conductivity (Ka and Kb) by measurements; the depth of the bottom of the aquifer (Di) the design drain spacing (L) can be found from the equation in dependence of the drain depth (Dd) and drain radius (r ...
For calculating the flow of liquid with a free surface, the hydraulic radius must be determined. This is the cross-sectional area of the channel divided by the wetted perimeter. For a semi-circular channel, it is a quarter of the diameter (in case of full pipe flow).