TEST 1 GROUP OPEN BOOK PIC : Due 6/03/23

Q1 [20mks]

Solve the following differential equation:

() + 5() + 6() = ()

by the method of Laplace transforms given the following conditions:

() = 1;(0) = 0;(0) = 1

Q2 [20mks]

A 250 liter tank used for liquid storage is configured as in Fig Q2. The cross-sectional area of the tank is 0.25 m2, and it may be assumed uniform.

The outlet valve resistance, which we shall assume to be linear for simplicity, has a value c = 0.1 m2/min.

The entire system was initially at steady state with the inlet flowrate F at 37 liters/min (0.037 m3/min). The following questions are now to be answered:

What is the initial value of the liquid level in the tank? [2mks]

If the inlet flowrate was suddenly changed to 87 liters/min (0.087 m3 /min), obtain an expression for how the liquid level in the tank will vary with time.[11mks]

When will the liquid level in the tank be at the 0.86 m mark? [5mks] And to what final value will the liquid level ultimately settle? [2mks]

: =

= 10 2 = 2.5

Fig Q2 Mixing tank with liquid level dynamics

Q3 [10mks]

Suppose now that for the system of Q2, the flowrate had been suddenly changed instead to 137 liters/min (0.137 m3 /min) from its initial value of 37 liters/min (0.037 m3 /min). An experienced plant operator says that such a change in the input flowrate will result in liquid spillage from the tank. Is this true? If so, when will the liquid begin to overflow? [10mks]

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