$5\mathrm{.}3\mathrm{.}11$ Consider a $5-m$ wide rectangular channel with a discharge of $12\mathrm{.}5\frac{m^3}{s}.$ The depth of flow upstream

of the step is $2\mathrm{.}5m.$ There is a step rise of $0\mathrm{.}25m$ in the bottom of the channel.

$(1)$ Determine the flow depth downstream of the step assuming no transition losses.

$(2)$ Compute Froude numbers for the upstream and downstream of the step.