Question 3 Let brine tanks A, B, C be given of volumes 20, 40, 60, respectively, as in Figure Q3. 10 L/min A M25752 - Coursework 2 Engineering Mathematics and Numerical

Analysis 2023-2024 B Figure Q3 - Three brine tanks in cascade It is supposed that fluid enters tank A at rate of 10 L/min, drains from A to B, drains from B to C, and then drains from tank C at the same rate of 10 L/min. Hence the volumes of the tanks remain constant. Uniform 10 L/min Page | 2 stirring of each tank is assumed, which implies uniform salt concentration throughout each tank. Also, suppose added to tank A water containing no salt. Determine the amount of salt, XA(t), X(t), and xc(t) at time t in each tank where the initial conditions are XA(0) = D₁ kg, XB(0) = DB kg, and xc(0) = Dc kg. [12 marks]