Carrying capacity of a channel

[Emethyst]

Homework Statement

A drainage channel is to be made so that its cross section is an isosceles trapezoid. If the sides and bottom are all 1m in length, what angle, theta, will maximize the carrying capacity?

Homework Equations

Implicit differentation

The Attempt at a Solution

I got lost on this question when it said carrying capacity; I do not know what equation to differentiate here. I know it cannot be volume, because the actual length of the ditch is not given nor asked for, but I am not sure if it is either area or the perimeter I will have to use. Any help given will be greatly appreciated, thanks.

 

[Thaakisfox]

I think the question refers to the flux of the flow, i.e. volume of passing fluid in unit time. So you should maximize the area...

And you will most probably get 60 degrees for the angle i.e. 120 degrees for the lower angle.