Explanation Given: Tank contains 200 liters of fluid and 30 grams of salt initially then 1 gram / liter of salt is pumped at a rate of 4 L / min . Calculation: Calculate the rate of salt entering into the tank. R in = ( 4 L min ) ⋅ ( 1 gm L ) = 4 gm / min Let A be the number of grams of salt. Calculate the rate of outflow of salt. R out = ( A / 200 gm / L ) ⋅ ( 4 L / min ) = A 50 gm / 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 = 4 − A 50 d A d t + A 50 = 4 (1) Compare equation (1) with d A d t + p ( t ) A = Q ( t ) . The value of p ( t ) is 1 50 and Q ( t ) is 4 . Calculate the integrating factor. I F = e ∫ p ( t ) d t = e ∫ 1 50 d t = e t 50 Solve the differential equation using the integrating factor e t 50

6th Edition

ISBN: 9781284127003

Author: ZILL

Publisher: JONES+BARTLETT LEARNING,LLC (CC)

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Chapter 2.7, Problem 21E

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Calculate the number of grams of salt in the tank at time t.

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Chapter 2.7, Problem 20E

Chapter 2.7, Problem 22E

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