A liquid storage tank is shown below in Figure 1. The initial inlet volumetric flow rate F1 is given by 0.05m3/min and the volume of the tank is 0.15m3. The cross sectional area of the tank is constant with the value of 0.20m2. The outlet valve resistance is assumed to be constant having a discharge coefficient CD=0.1m2/min. Assuming that the outlet flow rate is directly proportional to the liquid-level in the tank with the relationship F2=CDh Answer the following questions (clearly state any necessary assumptions) 1. Derive a dynamic model showing the differential of the liquid-level in the tankh(t) with respect to time, i.e. derive the differential equation for that model. Do not include any numerical value in this step. 2. Assuming the system is initially at steady state, what would be the steady state value of the liquid-level in the tankh ? 3. Derive the transfer function between the liquid-level variable H(s) and the inlet flow rate variable F(s); express the answer in the standard form. Be sure to work in deviation variables. Do not substitute numbers in the transfer function. 4. What would be the numerical values of the gain and time constant of the transfer function? Include the units. Figure 1: Liquid storage tank for Problem\#2