Consider a drainage pump with a tapered suction pipe that discharges water out of a

sump. It is given that the diameter of the inlet pipe is $1m$ and the tapering end of the

pipe is $0\mathrm{.}5m.$ The free water surface in the sump is $2\mathrm{.}5m$ above the centre of the inlet,

and the pipe is laid at a slope of $1($vertical$)$: $4($along pipeline$).$ The pressure at the top

end of the pipe is $0\mathrm{.}25m$ of mercury below atmosphere. It is known that the loss of

head due to friction between the two sections is $\frac{1}{5}$ of the velocity head at the top

section. Compute the discharge through the pipe if its length is $17\mathrm{.}5m.$