6. Tanks A, B, and C (of volumes VẠ, VB, and Vc, respectively) containing a salt solution (initialmass concentrations cA.0, CB,0, and cc.o) are connected by pipes in that order. Pure waterflows into tank A at a volumetric rate r; liquid flows from A to B, from B to C, and from Cto waste at rate r.(a) Using a mass balance for salt on each tank, set up a system of differential equations todescribe the salt concentration in each tank (cA(t), cB(t), cc(t)) as a function of time.Also state the initial conditions needed to find a unique solution.(b) Without solving, predict limiting values of ca(t), câ(t), and cc(t) as t → o.

Answered: Image /qna-images/answer/55ebd42f-4b79-496b-970d-8a80f107b2b9.jpg

Answered: (a) Using a mass balance for salt on…

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter11: Systems Of Equations

Section11.CT: Test

Problem 24CT

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Consider the following tank-water system. Tank A holds 200 liters of water, initially pure. Brine with a concentration of 3 grams of salt per liter flows into tank A at 5 liters per minute. The solution flows out of tank A into tank B at a rate of 5 liters per minute. Tank B is a 125 liter tank of initially pure water which receives the outflow from tank A, and the well-mixed solution flows out of tank B at 5 liters per minute. Write down a system of differential equations that models the scenario.
20.Consider two interconnected tanks similar to those in Figure 7.1.6. Initially, Tank 1 contains 60 gal of water and Q01Q10 oz of salt, and Tank 2 contains 100 gal of water and Q02Q20 oz of salt. Water containing q1 oz/gal of salt flows into Tank 1 at a rate of 3 gal/min. The mixture in Tank 1 flows out at a rate of 4 gal/min, of which half flows into Tank 2, while the remainder leaves the system. Water containing q2 oz/gal of salt also flows into Tank 2 from the outside at the rate of 1 gal/min. The mixture in Tank 2 leaves it at a rate of 3 gal/min, of which some flows back into Tank 1 at a rate of 1 gal/min, while the rest leaves the system. a.Draw a diagram that depicts the flow process described above. Let Q1(t) and Q2(t), respectively, be the amount of salt in each tank at time t. Write down differential equations and initial conditions for Q1 and Q2 that model the flow process. b.Find the equilibrium values QE1Q1E and QE2Q2E in terms of the concentrations q1 and q2. c.Is it…
A container holds 200 gal of brine solution containing 50 lb of salt. Initially, fresh water is poured into the tank at a rate of 10 gal/min, while the well-stirred mixture leaves the tank at the same rate. Letting y as the amount of salt at any time t, the mass flow rate at output is maintained at 50. O True. O False. O Partially true. O Insufficient information to state its truth value.
A certain spring–mass system satisfies the initial value problem u′′+14u′+u=kg(t),u(0)=0,u′(0)=0,where g(t)=u3/2(t)−u5/2(t)g(t)=u3/2(t)−u5/2(t) and k > 0 is a parameter .Plot the solution for k = 1/2, k = 1, and k = 2. Describe the principal features of the solution and how they depend on k.
Two tanks are interconnected. Tank A contains 60 grams of salt in 50 liters of water, and Tank B contains 50 grams of salt in 40 liters of water.A solution of 1 gram/L flows into Tank A at a rate of 5 L/min, while a solution of 4 grams/L flows into Tank B at a rate of 7 L/min. The tanks are well mixed.The tanks are connected, so 8 L/min flows from Tank A to Tank B, while 3 L/min flows from Tank B to Tank A. An additional 12 L/min drains from Tank B.Letting xx represent the grams of salt in Tank A, and yy represent the grams of salt in Tank B, set up the system of differential equations for these two tanks.dxdtdxdt = −850x+340y+5Correct dydtdydt = 850x−12y+28Incorrect x(0)x(0) = Correct, y(0)y(0) = Correct Submit QuestionQuestion 1
Two tanks are interconnected. Tank A contains 60 grams of salt in 50 liters of water, and Tank B contains 50 grams of salt in 40 liters of water.A solution of 1 gram/L flows into Tank A at a rate of 5 L/min, while a solution of 4 grams/L flows into Tank B at a rate of 7 L/min. The tanks are well mixed.The tanks are connected, so 8 L/min flows from Tank A to Tank B, while 3 L/min flows from Tank B to Tank A. An additional 12 L/min drains from Tank B.Letting xx represent the grams of salt in Tank A, and yy represent the grams of salt in Tank B, set up the system of differential equations for these two tanks.dxdtdxdt = dydtdydt = x(0)x(0) = , y(0)y(0) =

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