Specific energy, $E,$ has been defined for a rectangular channel as

$E=y+\frac{u^2}{2g}$

Rewrite this equation for $E$ so that it is valid for channels of any cross$-$section geometry. In the cross section shown below $T$ is the top width, $dA$ and $dy$ are and depth increments, respectively.

Find the condition of minimum specific energy for channels of any cross$-$section geometry.