A horizontal cylindrical tank shown in Fig. E4.13a is used to slow the propagation of liquid flow surges in a processing line. Figure E4.13b illustrates an end view of the tank and w_tis the width of the liquid surface, which is a function of its height, both of which can vary with time. Develop a model for the height of liquid h in the tank at any time with the inlet and out-let volumetric flow rates as model inputs. Linearize the model
assuming that the process initially is at steady state and that the liquid density ρ is constant.

di Figure E4.13a R - h R' w12 Figure E4.136