Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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QUESTION 1
Three 100 gallon fermentation tanks are connected in a closed fermentation
systtem. Tank 1 flows in to tank 2, tank 2 flows into tank 3, and tank 3 flows
back into tank 1. There are fans along the connecting pipes which keep the
alochol well mixed and the circulation flowing at a rate of 10 gal/min. Let
x,(t) be the amount of alcohol(in pounds) in tank T, at time t (i = 1,2,3). Derive the
following equations for this mixture problem. Do not solve.
10x'1= - X1+ X3
10x'2 = X1¬X2
10x'3 = X2-X3
Remember deriving means clearly explaining where these formulas come from and why
they are what they are. Not just stating them.
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Transcribed Image Text:QUESTION 1 Three 100 gallon fermentation tanks are connected in a closed fermentation systtem. Tank 1 flows in to tank 2, tank 2 flows into tank 3, and tank 3 flows back into tank 1. There are fans along the connecting pipes which keep the alochol well mixed and the circulation flowing at a rate of 10 gal/min. Let x,(t) be the amount of alcohol(in pounds) in tank T, at time t (i = 1,2,3). Derive the following equations for this mixture problem. Do not solve. 10x'1= - X1+ X3 10x'2 = X1¬X2 10x'3 = X2-X3 Remember deriving means clearly explaining where these formulas come from and why they are what they are. Not just stating them. Attach File Browse My Computer Browse Content Collection
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