Solution: 1318 Two-compartment mixing problems are similar to the mixing problems in

Chapter 10, Problem 15

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1318 Two-compartment mixing problems are similar to the mixing problems in Exercises 7.4.4548, except there are two connected tanks of fixed capacities filled with a well-mixed solution of some substance (for example, salt). Solution of a given concentration can enter each tank at a fixed rate, and solution also flows back and forth between the tanks. Solution can also leave each tank at a fixed rate. fc fc d d k k V V Using x1std and x2std to denote the amount of substance in each tank at time t, we obtain the following system of linear differential equations: dx1 dt f1c1 2 k12 x1 V1 1 k21 x2 V2 2 d1 x1 V1 dx2 dt f2c2 2 k21 x2 V2 1 k12 x1 V1 2 d2 x2 V4 Pulmonary air embolism In Exercise 10.3.11 wemodeled a pulmonary air embolism during surgery byviewing the lung as having two compartments: a deep and ashallow compartment, each of which removes CO2 from theblood. The system of differential equations wasdx1dt ac 1 a x2V 2 2a x1Vdx2dt ac 2 a x2V where x1 and x2 are the amounts of CO2 in the shallow anddeep compartments, respectively, a is the rate of absorptionof gas into each compartment from the blood, c is theconcentration of CO2 in this gas, and V is the volume ofeach compartment. Explain how these equations can beviewed as a special case of a general two-compartmentmixing problem.