Question three

A rectangular channel is being designed to carry a flow of $10\frac{m^3}{s}.$ At one particular point the channel must pass under a road, and there is a problem with the vertical clearance. Due to cost considerations, the width of the channel must be kept to a minimum, and because of physical restrictions a width of $2\mathrm{.}5$ m would be preferred. The channel is to be concrete lined $($Manning $n=0\mathrm{.}016).$ Calculate the dimensions and slope of a channel that will carry the required discharge most efficiently. $(20$ marks$)$