$2$

$($a$)$ Water $($density $1000kg{m}^{-3})$ is maintained at a gauge pressure of $4\mathrm{.}5$ MPa in a horizontal pipe of diameter $120$ mm $.$ It is passed through a nozzle of diameter $16$ mm which discharges a horizontal jet into the atmosphere. If the frictional losses reduce the theoretical discharge velocity by $7\%$ in this process, calculate the actual velocity of the jet and its flowrate in $kg{s}^{-1}.$

$($b$)$ This jet strikes an upward curved vane moving at $20m{s}^{-1}$ in a horizontal direction away from the jet, which deflects the water through an angle of $115.$ The impact is shockless. Calculate:

$($i$)$ the magnitude and direction of the velocity of the fluid leaving the vane;

$($ii$)$ the thrust on the vane in a horizontal direction;

$($iii$)$ the thrust on the vane in a vertical direction;

$($iv$)$ the power generated by the impact in the horizontal direction.