Q$\mathrm{.}2(40$p$)$ A pipeline is to be constructed to bring water from an upland storage reservoir to a town $30km$ away, at an elevation $150m$ below the water level of the reservoir. In summer the pipeline must be able to convey up to $5000m^3$ per day. If the pipe is fabricated from material of roughness $0\mathrm{.}3mm,$ find the required diameter.