Question

QUESTION 8 Let Tank A, Tank B and Tank C be three connected mixing tanks. Figure 1 illustrates a three-tanks mixing system such that the directions of flows of liquid in and out of the tanks are indicated by the arrows. Initially, the three tanks contain 140 litres, 80 litres and 200 litres of pure water, respectively. Suppose a 0.4 kg/litre brine runs into the mixing system through Tank A at a rate of 3 litres/min. The well-stirred mixture exchanged between the three tanks at the indicated rates. The well-stirred mixture drains out of the system from Tank C at the rate of 3 litres/min. 0.4 kg/litre brine, 3 litres/min mixture, 5 litres/min Tank A Tank C mixture, 3 litres/min Tank B mixture, 4 litres/min mixture, 4 litres/min Figure 1 a) Calculate the volume of liquid in each tank at time t. b) Construct a system of linear differential equations representing a mathematical model to the above-mentioned mixture problem. (Do not solve the model.)

          QUESTION 8

Let Tank A, Tank B and Tank C be three connected mixing tanks. Figure 1 illustrates a three-tanks mixing system such that the directions of flows of liquid in and out of the tanks are indicated by the arrows. Initially, the three tanks contain 140 litres, 80 litres and 200 litres of pure water, respectively.

Suppose a 0.4 kg/litre brine runs into the mixing system through Tank A at a rate of 3 litres/min. The well-stirred mixture exchanged between the three tanks at the indicated rates. The well-stirred mixture drains out of the system from Tank C at the rate of 3 litres/min.

0.4 kg/litre brine, 3 litres/min
mixture, 5 litres/min
Tank A
Tank C
mixture, 3 litres/min
Tank B
mixture, 4 litres/min
mixture, 4 litres/min

Figure 1

a) Calculate the volume of liquid in each tank at time t.

b) Construct a system of linear differential equations representing a mathematical model to the above-mentioned mixture problem. (Do not solve the model.)

QUESTION 8

Let Tank A, Tank B and Tank C be three connected mixing tanks. Figure 1 illustrates a three-tanks mixing system such that the directions of flows of liquid in and out of the tanks are indicated by the arrows. Initially, the three tanks contain 140 litres, 80 litres and 200 litres of pure water, respectively.

Suppose a 0.4 kg/litre brine runs into the mixing system through Tank A at a rate of 3 litres/min. The well-stirred mixture exchanged between the three tanks at the indicated rates. The well-stirred mixture drains out of the system from Tank C at the rate of 3 litres/min.

0.4 kg/litre brine, 3 litres/min
mixture, 5 litres/min
Tank A
Tank C
mixture, 3 litres/min
Tank B
mixture, 4 litres/min
mixture, 4 litres/min

Figure 1

a) Calculate the volume of liquid in each tank at time t.

b) Construct a system of linear differential equations representing a mathematical model to the above-mentioned mixture problem. (Do not solve the model.)

Added by Michael R.

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