Q4/ A horizontal cylindrical tank shown in Figure 4.13a is used to slow the propagation of liquid flow surges in a processing line. Figure 4.13b illustrates an end view of the tank and w, is the width of the liquid surface, which is a function of its height, both of which can vary with time. Derive the transfer functions that relate the height of liquid in tank (output variable) to the inlet and outlet volumetric flowrates (input variables): H'(s)/Qi'(s) and H'(s)/Q'(s)? Also, draw the transfer function biock diagram model?

Q4/ A horizontal cylindrical tank shown in Figure 4.13a is used to slow the propagation of liquid flow surges in a processing line. Figure 4.13b illustrates an end view of the tank and w, is the width of the liquid surface, which is a function of its height, both of which can vary with time. Derive the transfer functions that relate the height of liquid in tank (output variable) to the inlet and outlet volumetric flowrates (input variables): H'(s)/Qi'(s) and H'(s)/Q'(s)? Also, draw the transfer function biock diagram model?