A drainage pump has a tapered suction pipe. The pipe is running full of water. The pipe diameters at the inlet and outlet ends are $1$m and $0\mathrm{.}5$m$,$ respectively. The free water surface is $2$ m above the centre of the inlet and the centre of upper end $($outlet end$)$ is $3$m above the top of the true water surface. The pressure at the top end of the pipe is $25$ cm of mercury and it is known that loss of head by friction between the top and the bottom sections is one tenth of the velocity at the top section. Compute the discharge. Neglect losses of heat at the entrance of the tapered pipe.