1. (3 points) The height of liquid in the tank below changes in response to the volumetric flowrates in and out of the tank, where the outlet flowrate, q, is controlled by a pump. The density of the liquid can be assumed to be constant. The tank has dimensions of 5 m in height a cross-sectional area of 3 m. 42 41 h m3 ; = 3 m The normal operating conditions are: 71 = 0.2; 7 = 0.25 A level alarm goes off when h = 0.5 m. min a. Derive the transfer functions H'(s)/Q'(s) and H'(s)/Q'(s) from the dynamic balance. Assume that q2 is constant. b. The outlet flowrate, q, abruptly increases to 0.65 m/min, and goes unnoticed for 20 , minutes, until q is returned to its initial value. During this time, the inlet flowrates remain constant. Write h'(t) using Laplace techniques. Write separate expressions for 0 20. What is the final height in the tank? Does the alarm go off during the disturbance? If so, when? c. Consider the process is at its normal operating conditions when the inlet flowrate, qi, decreases at a rate of 0.02 (m/min per minute (or -0.02*t) due to a clog. All other flowrates are constant. Write h'(t) using Laplace techniques. When does the alarm go off