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
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F262758b9-9596-4e59-a35a-387fe6558873%2Fa819bea0-937c-462a-b3eb-74115c1f0863%2Fuaifz9a.png&w=3840&q=75)
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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