b$.$ A horizontal sudden expansion in a pipe expends $4\mathrm{.}5$ kW of power when the pipe diameters are $200$ mm and $400$ mm before and after the expansions. Determine the discharge?

$(8$ marks$)$

a$.$ Explain the Hardy Cross method used for pipe network analysis in the water distribution system. Also derive the expression to apply correction to assumed flow successfully for each pipe loop in a network.

$(8$ marks$)$