b$)$ An open channel model is constructed to a vertical scale of $1$:$100$ and a horizontal scale of $1$:$400.$ The model is used to investigate a flood alleviation scheme. At the design flood of $500m\frac{3}{s},$ the average depth of flow is $4\mathrm{.}8$ m for a channel width of $60$ m $.$ Determine the corresponding discharge in the model.