$($c$)$ A rectangular river channel is $5\mathrm{.}4m$ wide with manning's roughness $n=0\mathrm{.}04\frac{s}{m^{\frac{1}{3}}}$ and a bed slop $S_0=0\mathrm{.}0026.$ The flow in the river is $17\mathrm{.}4\frac{m^3}{s}$ when the normal depth is $2\mathrm{.}2m.$ A model investigation is to be undertaken in a rectangular laboratory flume that is $0\mathrm{.}54m$ wide. To reproduce the river hydraulic performance in the flume, what similitude needs to be considered? Outline how the model should be constructed to reproduce the largest flow in the river by specifying the slope, roughness, water depth and flow rate in the flume.

$\frac{10}{25}$