a$)$ A $50-$cm$-$diameter galvanized steel pipe carries $0\mathrm{.}15$ m $3/$s of water at $21$ C$.$ Find the head lost due

to friction $($m$)$ in the pipe over a distance of $5$ km$.$

b$)$ What diameter galvanized steel pipe would be required in the preceding example if a flow rate of

$0\mathrm{.}3$ m $3/$s was needed, while keeping the total frictional head loss at $<15$ m$?$

c$)$ Using the Colebrook equation, find the head lost due to friction $($m$)$ if the original $50-$cm$-$diameter

pipe in part A became heavily rusted.