# Question: figures 1 and 2 describe twotank water systems where r1...

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Figures 1 and 2 describe two-tank water systems where R1 and R2 are linearised coefficients of valve resistance, A1 and A2 are horizontal surface areas of the tanks, qi and qo are input and output volumetric flows respectively, while h2 is the water level in the second tank. The intermediate variables you may consider adding are the water level of the first tank h1 and flow between the tanks q1. (a) Derive the transfer function H2(s)/Qi(s) of the system in Figure 2. [Feel free to include intermediate variables if you find it useful.] (b) Assume R1 = R2 and A1 = A2. Using the location of the poles of the transfer function, or otherwise, show clearly that this system will never oscillate as long as a nonoscillatory input is applied. (c) If R1 = R2 = 1000 sm-2 and A1 = A2 = 1m2 , determine the time constants (if any) of the system. (d) What value of qi would ensure that h2 = 2m, if the whole system is in a state of equilibrium? (e) Assuming equilibrium conditions, derive h2(t) if the input flow qi is suddenly increased by 0.5 l/s (1m 1000l 3 = )? Part 2.2 (3 marks) Answer the same questions as in Part 2.1, this time for the system in Figure 3. Please see next page A1 qi qo R1 R2 A2 h2 Figure 2 Figure 3 A1 qi qo A2 h2 R1 R2 3 Part 2.3 (1 mark) Considering the time constants of both systems explain which system has a faster response. Part 2.4 (5 marks) [NOTE: No multiple choice questions are provided for this part. Your submitted work will be marked.] (a) Sketch block diagrams of the four components (two tanks and two valves) of the system in Figure 2 (b) Combine the four block diagrams into a single block diagram of the whole system using qi as the input and h2 as the output. (c) Using the rules for block diagram reduction only, obtain the transfer function of the system. Show clearly all steps