Hydro-pneumatic pistons are very useful for a variety of engineering applications. Consider the following configuration of such a piston. At t=0, the vessel contains only mercury (pg=13620kg/m) with a height of ho=0.25m. At t=0, the piston stays at the bottom of the vessel. At t>0, a stream of nitrogen is directed towards the bottom part of the piston via a round duct with a constant mass flux of ma=2x10-3 kg/hr. The piston has a density of pp=7500kg/m and is moving without significant friction losses. t=0 P=0 ho ma P=0 1>0 d ho h(t) Part A) (40 Points) Starting from a general mass balance around a control volume, derive the differential equation that describes the rate of change of the height of mercury in the vessel.