A rectangular channel of 5m width and 1.2m deep has a slope of 1 in 1000 and is lined with rubber for which the Manning's coefficient is 0.017. It is desired to increase the discharge to a maximum by changing the section so that the channel has same amount of lining. Find the new dimensions and probable increase in discharge.

Solution

Using Manning's formula, the discharge through the channel is given by,
Here,
Substituting the values,
Let be the width and depth of the flow for the new section of the channel. In order to have the same amount of lining,
For the discharge to be maximum in a rectangular channel, it can be proved that
Solving above two equation,
So, the area of cross-section and hydraulic radius for new channel cross-section becomes,

By Manning's formula, new discharge,
Percentage increase in discharge