Problem \#3 (35 points) Consider the stirred tank shown in the figure below. Suppose that the liquid entering from stream 1 comes from another unit and it has a mass flow rate of w1 and a temperature of T1, where this liquid is pre-heated prior to its transfer to another unit. The heating duty is given by Q. Stream 2 represents the outlet from the tank with a mass flow rate w2. Assume that the liquid is perfectly mixed and that the physical properties (density and specific heat capacity C ) are constant. In one day, due to corrosion phenomenon, a leak (denoted by stream 3) occurs at one side of the tank and its volumetric flow rate is approximated by F3=0.02h where h is the height of the liquid in the tank. The tank cross sectional area is given by A. Based on the given information, 1. Derive the dynamic model(s) of the process and simplify your resulting differential equation(s). Clearly state any additional assumptions. 2. Identify the input variable(s) and the output variable(s). Classify the inputs into either manipulated or disturbances. Use the following notations in your solution: Fi : volumetric flow rate, wi mass flow rate. 2 Figure 1: Stirred-tank for Problem\#3