Consider the mixing process shown in the figure. A mixing chamber initially contains 4 liters of a clear liquid. Clear liquid flows into the chamber at a rate of 10 liters per minute. A dye solution having a concentration of 0.6 kilograms per liter is injected into the mixing chamber at a constant rate of r liters per minute. When the mixing process is started, the well-stirred mixture is pumped from the chamber at a rate of 10 + r liters per minute. (a) Develop a mathematical model for the mixing process. Let Q represent the amount of dye in kilograms in the mixture. dQ kg/min dt (b) The objective is to obtain a dye concentration in the outflow mixture of 0.5 kilograms per liter. What injection rate r is required to achieve this equilibrium solution? T= L/min
Consider the mixing process shown in the figure. A mixing chamber initially contains 4 liters of a clear liquid. Clear liquid flows into the chamber at a rate of 10 liters per minute. A dye solution having a concentration of 0.6 kilograms per liter is injected into the mixing chamber at a constant rate of r liters per minute. When the mixing process is started, the well-stirred mixture is pumped from the chamber at a rate of 10 + r liters per minute. (a) Develop a mathematical model for the mixing process. Let Q represent the amount of dye in kilograms in the mixture. dQ kg/min dt (b) The objective is to obtain a dye concentration in the outflow mixture of 0.5 kilograms per liter. What injection rate r is required to achieve this equilibrium solution? T= L/min
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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Transcribed Image Text:Consider the mixing process shown in the figure. A mixing chamber initially contains 4 liters of a clear liquid. Clear liquid flows into the chamber at a
rate of 10 liters per minute. A dye solution having a concentration of 0.6 kilograms per liter is injected into the mixing chamber at a constant rate of
r liters per minute. When the mixing process is started, the well-stirred mixture is pumped from the chamber at a rate of 10 + r liters per minute.
(a) Develop a mathematical model for the mixing process. Let Q represent the amount of dye in kilograms in the mixture.
dQ
kg/min
dt
(b) The objective is to obtain a dye concentration in the outflow mixture of 0.5 kilograms per liter. What injection rate r is required to achieve this
equilibrium solution?
7 =
L/min
Would this equilibrium value of r be different if the fluid in the chamber at time t = 0 contained some dye? no
(c) Assume the mixing chamber contains 4 liters of clear liquid at time t = 0. How many minutes will it take for the outflow concentration to rise to
within 1% of the desired concentration of 0.5 kilograms per liter?
t =
min
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