$5\mathrm{.}9$ A water jet pump has an area $A_j=0\mathrm{.}06f{t}^2$ and a jet velocity $v_j=90fps,$ which entrains a secondary stream of water having a velocity $v_s=10fps$ in a constant$-$area pipe of total area $A=0\mathrm{.}6f{t}^2.$ At section $2,$ the water is thoroughly mixed. Assuming one$-$dimensional flow and neglecting wall shear

$($a$)$ find the average velocity of mixed flow at section $2$;

$($b$)$ find the pressure rise $(P_2-P_1),$ assuming the pressure of the jet and secondary stream to be the same at section $1.$