A general equation is proposed for the determination of water-surface
slope of a steady, gradually varied open-channel flow at a critical se
ction. Thereupon the different types of singular points and water-surf
ace slopes are given at such a section caused by changes in (1) bed sl
ope, (2) channel width, (3) surface roughness of the channel, and (4)
discharge, or their combinations. Although these factors are very diff
erent they have similar hydraulic effects on the occurrence of a certa
in type of singular point and water-surface slope. It is shown that a
saddle type singular point is the only one which can become a control.
The water-surface slopes at a critical control are evaluated using th
e proposed equation and are verified by the experimental results of Wi
lkinson (1974) for cases (1) and (2).