[Mass Balance \& Math 60 points] A vertically oriented cylindrical tank with a base of area 1.0m2 is initially filled with water to a height of 2.0m. At a certain time, a pump is turned on to draw water from the tank at a volumetric flow rate proportional to the height of water in the tank. At the very same time, a stream is opened to begin filling the tank to make up for the water being pumped out. The mass flow rate of the entering stream is 5.0kg/s. For the purposes of this problem you may assume that the density () of water is 1,000kg/m3. The pump withdraws water from the tank according to the following relationship: V=4.0103sm2h where h is the height of water in the tank. a) What is the steady-state level of water in the tank? b) Determine an expression for the height of water in the tank as a function of time from the time at which the tank begins to drain and the fill stream is turned on