(Solution) - Consider the cascading arrangement of tanks shown in Fig 2 4 10 -(2025 Original AI-Free Solution)

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Consider the cascading arrangement of tanks shown in Fig. 2.4.10, with Vi = 200 gal.

V2 = 200 gal, and V3 = 500 gal as the volumes of brine in the three tanks. Each tank initially contains 20 lb of salt. The inflow rates and outflow rates for tanks 1 and 2 are all 5 gal / sec, but the outflow rate for tank 3 is 10 gal / sec. The flow into tanks 1 and 2 is pure water.
(a) Let x(t), y(t), and z(t) be the amounts of salt in tanks 1 , 2, and 3, respectively. Set up the differential equation and the initial conditions that describe how the amounts of salt in tanks 1 and 2 are changing at any time t.
(b) Solve for x(r) and y (t).
(c) Using the results of part (b), solve for z(t).