Explanation Given: The condition for pure water entering into tank A is 4 gal/min . Mixture enter into tank A from tank B is 2 gal/min , and mixture outflows from tank A is 6 gal/min . Mixture enter into tank B from tank A is 6 gal/min , mixture enter into tank B from tank C is 1 gal/min , mixture outflows from tank B to tank C is 5 gal/min and mixture outflows from tank B to tank A is 2 gal/min . Mixture enter into tank C from tank B is 5 gal/min and mixture outflows from tank C is 1 gal/min . 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 ) + ( 2 gal/min ) ( x 2 100 lb/gal ) ] − [ ( 6 gal/min ) ( x 1 d t lb/min ) ] d x 1 d t = [ 0 + ( 2 ) ( x 2 100 ) − ( 6 ) ( x 1 100 ) ] d x 1 d t = 0 + 2 100 x 2 − 6 100 x 1 d x 1 d t = x 2 50 − 3 x 1 50 Therefore, the net rate of change of x 1 ( t ) for tank A is, d x 1 d t = x 2 50 − 3 x 1 50 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 = [ ( 6 ) ( x 1 100 ) + ( 1 ) ( x 3 100 ) ] − [ ( 5 ) ( x 2 100 ) + ( 2 ) ( x 2 100 ) ] d x 2 d t = ( ( 6 ) ( x 1 100 ) + ( 1 ) (

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 2.9, Problem 8E

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A mathematical model for the number of pounds of salt at a given interval of time in all tanks.

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Chapter 2.9, Problem 7E

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Chapter 2 Solutions

Advanced Engineering Mathematics

Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

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A mathematical model for the number of pounds of salt at a given interval of time in all tanks.

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A mathematical model for the number of pounds of salt at a given interval of time in all tanks.

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Chapter 2 Solutions