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Tanks A, B, and C (of volumes VA, VgB, and Vc, respectively) containing a salt solution (in mass concentrations cAp, CB,0, and ec,o) are connected by pipes in that order. Pure w flows into tank A at a volumetric rate r; liquid flows from A to B, from B to C, and fro to waste at rate r. (a) Using a mass balance for salt on each tank, set up a system of differential equation describe the salt concentration in cach tank (ca(t), câ(t), cc(t)) as a function of t Also state the initial conditions needed to find a unique solution. (b) Without solving, predict limiting values of ca(t), cR(t), and cc(t) as t→ 0o.

Tanks A, B, and C (of volumes VA, VgB, and Vc, respectively) containing a salt solution (in mass concentrations cAp, CB,0, and ec,o) are connected by pipes in that order. Pure w flows into tank A at a volumetric rate r; liquid flows from A to B, from B to C, and fro to waste at rate r. (a) Using a mass balance for salt on each tank, set up a system of differential equation describe the salt concentration in cach tank (ca(t), câ(t), cc(t)) as a function of t Also state the initial conditions needed to find a unique solution. (b) Without solving, predict limiting values of ca(t), cR(t), and cc(t) as t→ 0o.

Advanced Engineering Mathematics
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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6. Tanks A, B, and C (of volumes VA, VB, and Ve, respectively) containing a salt solution (initial mass concentrations CA.0, CB.0, and cc.o) are connected by pipes in that order. Pure water flows into tank A at a volumetric rate r; liquid flows from A to B, from B to C, and from C to waste at rate r. (a) Using a mass balance for salt on each tank, set up a system of differential cquations to describe the salt concentration in cach 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), CB(t), and cc(t) as t → o.
Transcribed Image Text:6. Tanks A, B, and C (of volumes VA, VB, and Ve, respectively) containing a salt solution (initial mass concentrations CA.0, CB.0, and cc.o) are connected by pipes in that order. Pure water flows into tank A at a volumetric rate r; liquid flows from A to B, from B to C, and from C to waste at rate r. (a) Using a mass balance for salt on each tank, set up a system of differential cquations to describe the salt concentration in cach 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), CB(t), and cc(t) as t → o.
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