Hydraulic diameter

The hydraulic diameter has to be used if the pipe is only partly filled. In the case of flow in a partly filled cylindrical pipe, in non-cylindrical piping or in open channels the head losses can be calculated in principle in the same way as described in earlier sections. However, instead of the diameter of the filled cylindrical pipe, the hydraulic diameter d_h has to be used in those cases.

d_h = 4 A / O

where

d_h = hydraulic diameter (m)
A = cross sectional area of the liquid filled part of the circular section (m²)
O = the wetted perimeter (m)

For a completely full cylindrical pipe

i.e. in this case the hydraulic and geometric diameters coincide.

For a half filled cylindrical pipe

For a half filled rectangular section

with Reynolds number

and relative roughness k/d_h, Figure 8.6a and equation 8.6b and 8.6d apply with unchanged numerical values. Pipes whose flow is due entirely to gravitational head can operate filled. The degree of fullness depends, among other things, on the slope of the pipe and the operating conditions. For a cylindrical pipe the fullness is defined by the ratio d_depth /d_diameter where d_depth is the depth of liquid in the pipe and d_diameter is the diameter of the pipe. Figure 8.7d illustrates how various flow parameters change with the degree of fullness of the pipe. Both flow velocity and hydraulic diameter have their greatest value at a  filling coefficient of just below 1.

Figure 8.7d Flow in a partially-filled cylindrical pipe (with prime index = partly filled, without prime index = full).

In gravity flow pipes carrying contaminated liquids care must be taken with regard to sedimentation. The avoidance of  which can place certain conditions on the formation and operation of the pipe.