$(3)$ Water flows from a reservoir through a pipe of $0\mathrm{.}15$ m diameter and $180$ m long to a point $13\mathrm{.}5$ m below the open surface of the reservoir. Here it branches into two pipes, each of $0\mathrm{.}1$ m diameter, one of which is $48$ m long discharging to atmosphere at a point $18$ m below reservoir level, and the other $60$ m long discharging to atmosphere $24$ m below reservoir level. Assuming a constant friction coefficient of $0\mathrm{.}032,$ calculate the discharge from each pipe. Neglect any losses at the junction.

$(20$ Marks$)$