b$)$ Determine the flow through a river section given the following information: Upstream maximum depth and width are $3\mathrm{.}5$ m and $10$ m respectively while the downstream maximum depth and width are $3\mathrm{.}4$ m and $11$ m respectively; the drop in elevation of the water surface between the upstream and downstream ends of the river section is $0\mathrm{.}5$ m ; the length of the section is $1$ km ; the roughness of the section is $\backslash ($ n$=0\mathrm{.}005\backslash ).$ Make one adjustment for velocity head and assume that the rivers cross$-$sectional profile is approximately triangular.

c$)$ A flood alleviation channel is being investigated using a $1$:$30$ scale model. The velocity of the design flood flow in the model is an average of $\backslash (0\mathrm{.}6\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ while the flow rate is $\backslash (0\mathrm{.}05\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash ).$ Determine the corresponding flood flow and velocity in the prototype. In addition, if the measured hydrostatic force produced by the flood on the model is $1\mathrm{.}5$ N determine the corresponding force in the prototype.