Problem $2$

Let the point velocity, $v,$ in the right trapezoidal channel in Problem $1$ be expressed as

$v=0\mathrm{.}5z^{\frac{1}{7}}$

where $v$ is in $\frac{m}{s}$;$z$ is the vertical distance $($in $m)$ measured from the channel bottom.

$($a$)$ Determine the rate of momentum transfer $($the density of water is $1000k\frac{g}{m^3})$

$($b$)$ Determine whether the flow is subcritical, supercritical or critical.