Consider a tank with a shape of a cone standing on its base. The height (H) of the tank is 1 m and the radius of the base (R) is 50 cm. The tank is filled initially with water (density 1 g/cm3) up to 25% of its height (ho, measured from the base of the tank). At time t= 0 you deliver more water from the top of the tank with a volumetric flow (vin) of 1 L/s. Concurrently, you start emptying the tank at the bottom with a volumetric flow (v out) of 2 L/s. At some time (t empty) the tank is empty. Att= 5 min from the beginning of the whole process (i.e., starting to fill/drain the tank), you close the bottom valve (i.e., no water removal from the tank) and start filling the tank from the top again with the same volumetric flow as before (i.e., 1 L/s). The process stops when the tank is ompletely filled (t full). The figure below depicts schematically the entire process. e%3D Vn H R Vout Process time start process start filing a. (10 points) Derive a mass balance equation that describes the dependence of the height (h) of the liquid in the tank on time (t). b. (5 points) Using the result obtained in part a), write down the equation that enables you to relate the instantaneous level of water (h) in the tank to time (t). Do not solve anything. c. (5 points) Calculate the time it takes for the liquid present initially in the tank to empty the tank completely (tempty). d. (5 points) Calculate the time it takes for the liquid to fill the tank that is initially empty (tfill).