A $300mm$ diameter pipe is being designed for the following: maximum flow rate $80\frac{l}{s},$ minimum allowable velocity $1\frac{m}{s},$ roughness $ks0\mathrm{.}6mm.$ Determine the following, 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 $10\frac{l}{s},$

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.

answers: $[1$:$190,250mm,0\mathrm{.}78\frac{m}{s},1$:$95$