HW$3-2$: In class, we solved an example where a tank was placed on a scale and water flowed through the system steadily. Our analysis

showed that force contributions were:

Weight of tank: $22\mathrm{.}2$ N

Weight of water: $511\mathrm{.}6$ N

Force due to momentum flux of incoming water: $80\mathrm{.}9$ N

Reconsider this example to determine what the incoming velocity would need to be in order for momentum flux contribution to provide the

same force as the weight of the water. You can imagine that if the velocity is increased, the system will no longer be in steady state, but will

reach a new steady state once the water level reaches a height that provides sufficient pressure at the bottom outlet ports to balance flow in

and flow out. For this determination, assume that the volumetric flow rate leaving scales linearly with pressure $($and that zero gauge pressure

results in zero flow$).$ What is the new steady$-$state height of the fluid? Make any assumptions necessary, but document them. You may

assume that the mass of the tank does not change.