A gravity distribution system is schematized into a $3000$ m long transmission main of $400$ mm diameter

$0\mathrm{.}2$ mm $).$ The water pressure at the end of the main should not drop below $35$ m above the datum. The

reservoir that feeds the transmission main has a constant water level of $43$ m above the datum.

i$)$ What is the maximum discharge that can be supplied from the reservoir while satisfying the pressure

condition?

ii$)$ What should be the diameter of an additional pipe $($in parallel to the existing one$)$ if the discharge is

increased to $600\frac{m^3}{h}r?(k=0\mathrm{.}2mm)$

iii$)$ Instead of laying a parallel main, a booster pump can be laid in the $400$ mm main to ensure that the

pressure is maintained at the required level. Calculate the head to be added by the pump for the flow of

$600\frac{m^3}{h}r.$

iv$)$ What is the pressure requirement of this pump in kW $,$ assuming a pump efficiency of $80\%?$