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for the mixing process. Let Q represent the amount of dye in kilograms in th

for the mixing process. Let Q represent the amount of dye in kilograms in th

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Dye r Umin solution Inflow Outflow Mixing chamber 10 Umin 10+r Umin
Transcribed Image Text:Dye r Umin solution Inflow Outflow Mixing chamber 10 Umin 10+r Umin
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 0.25 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 dt kg / min (b) The objective is to obtain a dye concentration in the outflow mixture of 0.1 kilograms per liter. What injection rate r is required to achieve this equilibrium solution? L/ min Would this eqilibrium 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 3 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 0.1 kilograms per liter? 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 0.25 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 dt kg / min (b) The objective is to obtain a dye concentration in the outflow mixture of 0.1 kilograms per liter. What injection rate r is required to achieve this equilibrium solution? L/ min Would this eqilibrium 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 3 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 0.1 kilograms per liter? min
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