$14\mathrm{.}2$ The axial$-$flow pump in the figure has an impeller that is rotating at $1400$ rpm $.$ The mean radius is $50$ mm $.$ If the pump produces a flow of $1260$ gpm $,$ and there is an ideal most efficient performance axial pump, determine the shaft power in hp$.$ The average cross$-$sectional area of the open region within the impeller is $0\mathrm{.}04m^2$ and the angle between the relative velocity and the positive $U$ is $60$ at blade exit.