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der the proce chamber at a rate of 10 liters per minute. A dye solution having a concentration of 0.4 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+ 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 0.4r-(Q/3)(10+) kg/min dr (b) The objective is to obtain a dye concentration in the outflow mixture of 0.25 kilograms per liter. What injection rater is required to achieve this equilibrium solution? L/min Would this equilibrium value of r be different if the fluid in the chamber at time=0 contained some dye? no (c) Assume the mixing chamber contains 3 liters of clear liquid at time t = 0. How many minutes will it take for the outflow concentration to rise to within 4% of the desired concentration of 0.25 kilograms per liter? min

der the proce chamber at a rate of 10 liters per minute. A dye solution having a concentration of 0.4 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+ 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 0.4r-(Q/3)(10+) kg/min dr (b) The objective is to obtain a dye concentration in the outflow mixture of 0.25 kilograms per liter. What injection rater is required to achieve this equilibrium solution? L/min Would this equilibrium value of r be different if the fluid in the chamber at time=0 contained some dye? no (c) Assume the mixing chamber contains 3 liters of clear liquid at time t = 0. How many minutes will it take for the outflow concentration to rise to within 4% of the desired concentration of 0.25 kilograms per liter? min

Advanced Engineering Mathematics
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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Consider the mixing process shown in the figure. A mixing chamber initially contains 3 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 0.4 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 0.4r-(Q/3)(10+) kg/min dr (b) The objective is to obtain a dye concentration in the outflow mixture of 0.25 kilograms per liter. What injection rate r is required to achieve this equilibrium solution? L/min Would this equilibrium value of r be different if the fluid in the chamber at time I = 0 contained some dye? no (c) Assume the mixing chamber contains 3 liters of clear liquid at time t = 0. How many minutes will it take for the outflow concentration to rise to within 4% of the desired concentration of 0.25 kilograms per liter? 1= min
Transcribed Image Text:Consider the mixing process shown in the figure. A mixing chamber initially contains 3 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 0.4 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 0.4r-(Q/3)(10+) kg/min dr (b) The objective is to obtain a dye concentration in the outflow mixture of 0.25 kilograms per liter. What injection rate r is required to achieve this equilibrium solution? L/min Would this equilibrium value of r be different if the fluid in the chamber at time I = 0 contained some dye? no (c) Assume the mixing chamber contains 3 liters of clear liquid at time t = 0. How many minutes will it take for the outflow concentration to rise to within 4% of the desired concentration of 0.25 kilograms per liter? 1= min
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