Problem #$2$

A centrifugal pump is being designed to pump water at normal temperature and atmospheric pressure. The impeller has a uniform blade height of $b=2\mathrm{.}5$ in$.,$ with inlet and outlet radii of $r_1=6in.$ and $r_2=16\mathrm{.}0in.$ At the design conditions, the pump is to deliver $2500$ gpm of water with the impeller rotating at $1200$ rpm $.$ If the trailing edge angle ${}_2$ of the blade is $16,$ you are asked to do the following:

$(1)$ Determine the leading edge angle ${}_1$ of the blade.

$(2)$ Determine the pump head $H_p$ delivered at the given flow rate.

$(3)$ Determine the brake horse power required by the ideal pump, $W_{\text{s}\text{h}\text{a}\text{n}\text{f}}^{}.$