b) The dynamic model of the tank has to be written for the given process. The objective of mixing is to cool the hot water stream entering into the tank at a flow rate of q: and feed temperature of T, with a cooled water stream entering into the tank with a flow rate of q₁ and feed temperature of To. A stream is drawn from the tank. bottom at flow rate of q, by the pump and the level in the tank is proposed to be controlled by drawing another water stream at flow rate of q. Neglect evaporation losses from the tank.
The dynamic model of the tank is being observed with the help of material and energy balance as shown below: