Problem $1.$ A centrifugal water pump is designed to operate at a speed of $N=1200rpm$ at a volume flow rate of $Q=35\frac{L}{s}.$ The impeller has the following dimensions:

$\backslash$table$[[$Parameter$,$Inlet,Outlet$],[$Radius$,r(cm),10,17\mathrm{.}5],[$Blade width, $b(cm),1\mathrm{.}0,0\mathrm{.}75],[$Blade angle, $(deg),30,40]]$

$($a$)$ Draw the inlet and outlet velocity diagrams to scale. $($b$)$ Determine the inlet and outlet absolute flow angles $($measured relative to the normal direction$).($c$)$ Calculate the head developed by the pump for swirl free entry and for the specified geometry. $($d$)$ For a pump efficiency of ${}_p=75\%,$ calculate the mechanical power delivered to the pump.