Q$\mathrm{.}3[$a$]$ A centrifugal pump impeller is $40$ cm in outer diameter and $2\mathrm{.}5$ cm wide at the exit. Its blade angle at the outlet is $30.$ When run at a speed of $1500$ rpm $,$ the flow rate though the pump is $80$ liters$/$s$.($i$)$ Calculate the radial, relative and absolute velocities at the impeller exit. $($ii$)$ If there is no inlet whirl, what would be the theoretical head added to the water by the impeller?

$($CO$4)$