Show that the most efficient trapezoidal channel section will have a hydraulic radius equal to one-half the depth. A rectangular flume is to be built to carry a discharge of 120 cfs on a slope of...

Show that the most efficient trapezoidal channel section will have a hydraulic radius equal to one-half the depth.

A rectangular flume is to be built to carry a discharge of 120 cfs on a slope of 0.001 ft/ft. If the flume is constructed of corrugated metal, what should be its dimensions to minimize the cost of the material?