Consider the two tanks shown in the figure below. Assume that tank A contains 50 gallons of water in which 25 pounds ofsalt is dissolved. Suppose tank B contains 50 gallons of pure water. Liquid is pumped into and out of the tanks as indicatedin the figure; the mixture exchanged between the two tanks and the liquid pumped out of tank B are assumed to be wellstirred. We wish to construct a mathematical model that describes the number of pounds x₁(t) and x₂(t) of salt in tanks Aand B, respectively, at time t.dx₁1dtdx1dtpure water3 gal/minmixture4 gal/minThis system is described by the system of equations150225dx2dt225225*11+-X2mixture1 gal/min-X2Bwith initial conditions x₁(0) = 25, x₂(0) = 0 (see (3) and the surrounding discussion on mixtures on page 107). What is thesystem of differential equations if, instead of pure water, a brine solution containing 3 pounds of salt per gallon is pumpedinto tank A?-225*1 + 50x2+6×dx22 - (25)*₁- (25)×₂2 -=x2dtmixture3 gal/min

Answered: Image /qna-images/answer/d139643e-dd22-45c0-974a-1315fd1f2591.jpg

Answered: Consider the two tanks shown in the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Fresh water flows into tank 1; mixed brine flows from tank 1 into tank 2, from tank 2 into tank 3, and out of tank 3; all at the given flow rater gallons per minute. The initial amounts x₁(0)=xo (lb), and x₂(0) = 0, and x3 (0) = 0 of salt in the three tanks are given, as are their volumes V₁, V₂, and V3. First solve for the amounts of salt in the three tanks at time t, then determine the maximal amount of salt that tank 3 ever contains. Finally, construct a figure showing the graphs of x₁ (t), x₂ (t), and x3 (t). r=60, x=60, V₁ = 15, V₂ = 12, V3 = 20 X₁ (t) = X₂ (t) = X3 (t)=
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The following problem deals with the open three-tank system. Fresh water flows into tank 1; mixed brine flows from tank 1 into tank 2, from tank 2 into tank 3, and out of tank 3; all at the given flow rate r gallons per minute. The initial amounts x1(0)= x0 (lb), x2(0) = 0, and x3(0) = 0 of salt in the three tanks are given, as are their volumes V1, V2, and V3 (in gallons). First solve for the amounts of salt in the three tanks at time t , then determine the maximal amount of salt that tank 3 ever contains. Finally, construct a figure showing the graphs of x1 (t) , x2(t) , and x3(t) r = 60, x0 = 45, V1 = 15, V2 = 10, V3 =30
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