4.12 A 200 L/min stream of freshwater is fed to and withdrawn from a well- mixed tank with a volume of 1000 L. Initially, the tank contains pure water. At timet=0, the feed is switched to a brine stream with a concen- tration of 180 g/L that is also fed at a rate of 200 L/min. a. Derive a differential equation for the salt concentration in the tank. b. Separate the variables and integrate to obtain an expression for the salt concentration as a function of time. c. At what time will the salt concentration in the tank reach a level of 100 g/L?

4.12 A 200 L/min stream of freshwater is fed to and withdrawn from a well- mixed tank with a volume of 1000 L. Initially, the tank contains pure water. At timet=0, the feed is switched to a brine stream with a concen- tration of 180 g/L that is also fed at a rate of 200 L/min. a. Derive a differential equation for the salt concentration in the tank. b. Separate the variables and integrate to obtain an expression for the salt concentration as a function of time. c. At what time will the salt concentration in the tank reach a level of 100 g/L?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

4.12 A 200 L/min stream of freshwater is fed to and withdrawn from a well-
mixed tank with a volume of 1000 L. Initially, the tank contains pure
water. At time t= 0, the feed is switched to a brine stream with a concen-
tration of 180 g/L that is also fed at a rate of 200 L/min.
a. Derive a differential equation for the salt concentration in the tank.
b. Separate the variables and integrate to obtain an expression for the salt
concentration as a function of time.
c. At what time will the salt concentration in the tank reach a level of 100 g/L?

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