Problem 3. A mixing tank of height H and constant cross-sectional area A is used to combine two streams of water, one hot and one cold, to provide a lukewarm effluent water stream suitable for releasing into the environment without disrupting the temperature of a nearby lake (this is important so as not to do harm to the natural ecosystems present there!). Lets assume the flow rates of the hot water and cold water streams are maintained constant at qfh and 9fc, respectively. A controlled is in place to make the effluent volumetric flow rate linearly proportional to the height of the liquid in the mixing tank: in mathematical terms, qe = kh. (a) Write the differential equation version of the water mass balance that describes this above dh process, getting it into the form ... dt Then, manipulating your equation from part (a) as needed, address these three questions: (b) If the initial height of water in the tank is ho, determine the expression for the height in the tank as a function of time, h(t). (c) Assuming the tank cannot overflow, what is the height in the tank after a very long time? (d) Is it possible that the tank actually could overflow? If so, explain the relationship between H, k, and any other variables or constant that would have to be true for this to happen