ABSTRACT
With a given roughness coefficient1 and longitudinal slope, the Mann ing formula may be expressed as Q = kA R 213, where k is a constant coefficient. Thus
KM)8
When the free surface just reaches the pipe soffit, Q = QF and <j> = 0 , so that
(7-33)
For the pipe operating half full:
(7.34)
The ratio QIQw is given by
The curve of QjQF against the proportionate flow depth is shown in Fig. 7.8. It will be noted that the maximum discharge occurs when the pipe is slightly less than full. This is because the addition of a relatively small area of flow at the top of the pipe entails a disproportionately large increase in the length of wetted perimeter. By differentiation of Eq. (7.32), the angle <j> corresponding to Qmax is found to be 57° 36' and Qme.xlQf is then 1*08. The relationship QF : Qm&x: Q1}2f is thus 1:1-08:0-5.
