Question 1 A 250 litre tank used for liquid storage is configured as in figure below. Its mathematical model and its dynamic behaviour follow first order kinetics are as follows: General 1st order system: dy 1+ y = Ku(t) dt 1st order system: Ac dh + h = 1½ Fi cdt C Inlet flowrate is given by: F₁ = ch where c is outlet valve resistance; Ac is cross-sectional area; h is height of liquid in tank; Fi, F are inlet and outlet flowrates, respectively; and t is time. The transfer function is: H(s) = G(s)F₁(s) = The transfer function follows first order principles with a time constant Ac/c and steady-state gain of K 1/c. The cross-sectional area of the tank is 0.25 m2, and it may be assumed uniform. The outlet valve resistance, assumed to be linear, has a value c = 0.1 m2/min. = The entire system was initially at steady state with the inlet flowrate Fi at 37 litres/min (0.037 m³/min). Answer the following questions: 1.1 What is the initial value of the liquid level in the tank? Use dimensional analysis to determine hs if you are stuck. (3) 1.2 If the inlet flowrate was suddenly changed to 87 litres/min (0.087 m³ /min), obtain an expression for how the liquid level in the tank will vary with time. (15) 1.3 When will the liquid level in the tank be at the 0.86 m mark? (4) 1.4 To what final value will the liquid level ultimately settle? (3) [25 marks]