Explanation Given: A tank is filled with 100 gallons of fluid initially and 10 pounds of salt is dissolved in it. Brine containing half pound of salt is pumped into the tank at the rate 6 gal/min. The mixed solution is pumped out at a rate 4 gal/min. Calculation: Calculate the rate of salt entering into the tank. R in = ( 1 2 lb gal ) ⋅ ( 6 gal min ) = 3 lb min The solution is pumped out at a slower rate of 4 gal / min . Calculate the rate of outflow of salt. R out = A 100 + ( 6 − 4 ) t = 2 A 50 + t lb / min Consider the equation for the mixing of two fluids. d A d t = R i n − R o u t d A d t = 3 − 2 A 50 + t d A d t + 2 A 50 + t = 3 (1) Compare equation (1) with d A d t + p ( t ) A = Q ( t ) . The value of p ( t ) is 2 50 + t and Q ( t ) is 3 . Calculate the integrating factor. I F = e ∫ p ( t ) d t = e ∫ 2 50 + t d t = e 2 ln | 50 + t | = ( 50 + t ) 2 Multiply the integrating factor ( 50 + t ) 2 in equation (1) and integrate

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 2.7, Problem 27E

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Calculate the number of pounds of salt in the tank after 30 min.

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Chapter 2.7, Problem 26E

Chapter 2.7, Problem 28E

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Chapter 2 Solutions

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Chapter 2 Solutions