A tank containing a liquid is used as a storage system and is shown in the Figure 1. The following information is given: - The density of the liquid is constant. - The tank has a cross sectional area of A. - The inlet flow rate of the liquid is denoted by Fi - The exit flow rate is given by F. - The height of the liquid in the tank is denoted by h. - The exit flow of the tank has an orifice valve with a coefficient Cvk. 1. Develop a dynamic model for the liquid height h(t) in the tank. Express the outlet flow rate F in terms of the pressure difference and then simplify to eliminate any appearance of P. Note that both F&&P would not appear in the final equation. Useful equations: where Pa is the atmospheric pressure P=PPa=gcgh (1) F=CvPKCvgcg Find the transfer function between the height H(s) and the inlet flowrate Fi(s) and write it down in the standard form. Assume that the process is initially at steady state. Figure 1: Schematic diagram of the tank