(Solved): 1. A rectangular tank mounted on casters is filled with water (=1000kg/m3) to a depth of h=2 m ...

1. A rectangular tank mounted on casters is filled with water $\left(\rho =1000\mathrm{kg}/{\mathrm{m}}^3\right)$ to a depth of $h=2$ $\mathrm{m}$. On the right-hand side of the tank there is an open leak with area $0.005{\mathrm{m}}^2$ at a depth $0.3\mathrm{m}$ below the water surface. There is another leak with area $0.002{\mathrm{m}}^2$ at a depth of $0.5\mathrm{m}$ below the water surface on the opposite side of the tank. The water in the tank is replenished by an overhead supply such that the level remains constant. (a) What is the velocity of the replenished water by the overhead supply? [10 pts] (b) What is the horizontal force (magnitude $(\mathrm{N})$ and direction) required to keep the tank stationary? Neglect any friction effects and losses at the leaks. [15 pts]