Explanation Use the equation formed by the given conditions to determine the integrating factor. Then multiply that factor with the equation and integrate to obtain the solution and use the given initial condition to obtain the particular solution. Then obtain the time at which the tank overflows to obtain the salt concentration at that time. Given: A 1000 L tank contains 500L of water with a salt concentration of 10g/L. Water with a salt concentration of 50 g/L flows into the tank at a rate of R i n = 80 L/minutes. The fluid mixes instantaneously and is pumped out at a specified rate R o u t . Let y ( t ) denote the quantity of salt in the tank at time t Calculation: The net flow of salt into the tank at time t is given by d y d t = ( 80 ) ( 50 ) − ( 60 ) ( y 500 + 20 t ) = 4000 − 6 y 50 + 20 t This can be rewritten as d y d t + 6 y 50 + 2 t = 4000 where A ( t ) = 6 50 + 2 t and B ( t ) = 4000 The integrating factor will hence be α ( t ) = ( 50 + 2 t ) 3 Therefore the above equation, when multiplied by the integrating factor becomes (

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 10.4, Problem 30E

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The salt concentration when the tank overflows, assuming that $R_{o u t} = 60 L / \min$

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The salt concentration when the tank overflows, assuming that R o u t = 60 L / min

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The salt concentration when the tank overflows, assuming that R o u t = 60 L / min

Solution Summary: The author explains how to determine the salt concentration when the tank overflows, assuming that R o u t = 60 L / min.

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The salt concentration when the tank overflows, assuming that Rout=60L/min

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Chapter 10 Solutions

The salt concentration when the tank overflows, assuming that $R_{o u t} = 60 L / \min$