A $300$ mm diameter pipe is being designed for the following: maximum flow$-$rate $80$ l$/$s$,$ minimum allowable velocity $1\mathrm{.}0$ m$/$s$,$ roughness ks $0\mathrm{.}6$ mm$.$ Determine, using the Butler$$ Pinkerton chart: a$)$ the gradient required based on the pipe running full b$)$ the depth at which it will actually flow at that gradient c$)$ the minimum velocity that will be achieved if the working flow rate is $10$ l$/$s d$)$ the gradient at which the sewer would need to be constructed to just ensure that the minimum velocity is achieved at that flow$-$rate.