Explanation Given: The condition for pure water entering into tank A is 4 gal/min . Mixture enter into tank A is 4 gal/min , and mixture outflows from tank A to tank B is 4 gal/min . Mixture enter into tank B from tank A is mixture outflows from tank B to tank C is 4 gal/min . Mixture enter into tank C from tank B is 4 gal/min and mixture outflows from tank C is 4 gal/min . Calculation: Consider the following equation for tank A to calculate the net rate of change, d x 1 d t = Input rate of mixture-output rate of mixture d x 1 d t = [ ( 4 gal/min ) ( 0 lb/min ) − ( − 4 gal/min ) ( x 1 200 lb/gal ) ] d x 1 d t = [ 0 − ( 4 gal/min ) ( x 1 200 lb/gal ) ] d x 1 d t = − x 1 50 lb/min Therefore, the net rate of change of x 1 ( t ) for tank A is, d x 1 d t = − x 1 50 lb/min Consider the following equation for tank B to calculate the net rate of change, d x 2 d t = Input rate of mixture-output rate of mixture d x 2 d t = [ ( 4 gal/min ) ( x 1 200 lb/min ) − ( 4 gal/min ) ( x 2 150 lb/gal ) ] d x 2 d t <

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 2.9, Problem 10E

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A mathematical model for the number of pounds of salt in all tanks and to predict the limiting values.

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Chapter 2.9, Problem 9E

Chapter 2.9, Problem 11E

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Chapter 2 Solutions

Advanced Engineering Mathematics

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