5. Water is added to in a 300 lt tank with variable flow rates. When the exit valve opens, the flow rate from there is proportional with the height of the liquid in the tank (or volume in the tank). The flow rate of the tank is slowly increased. At steady-state it (flow rate) reaches the value 60lt/min and the tank gets completely full, but there isn't an overflow. Then the flow rate of the feed is suddenly decreased to 20lt/min. a) Derive an equation between the exit flow rate q and water volume V, and using this relationship calculate the volume at steady-state when the inlet flow rate is 20lt/min. b) Derive a differential balance for water from the time that flow rate is decreased to the time passed for the volume reached to the steady-state value. (The equation must be in the form of dV/dt=) c) Integrate the equation which was derived for b ) to find the required relationship for V(t)