$5\mathrm{.}122$ Water is pumped from a tank, point $(1),$ to the top of a water plant aerator, point $(2),$ as shown in and Fig. P$5\mathrm{.}122$ at a rate of $0\mathrm{.}085\frac{m^3}{s}.($a$)$ Determine the power that the pump adds to the water if the head loss from $(1)$ to $(2)$ where $V_2=0$ is $1\mathrm{.}2$ m $.($b$)$ Determine the head loss from $(2)$ to the bottom of the aerator column, point $(3),$ if the average velocity at $(3)$ is $V_3=0\mathrm{.}6\frac{m}{s}.$

Figure P$5\mathrm{.}122$