To prove: That d Q d t + r 2 Q v 0 + ( r 1 − r 2 ) t = q 1 r 1 When the initial condition at time t = 0 with v 0 gallons of a solution in which, q o pounds is concentrate that is soluble in the tank. One more solution having q 1 pounds of the concentrate for each gallon gets run into the tank as per the rate of r 1 gallons/min . After it is kept well stirred, the solution gets withdrawn at the rate of r 2 gallons/min .

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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…

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Chapter 6.4, Problem 35E

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To prove: That dQdt+r2Qv0+(r1−r2)t=q1r1 When the initial condition at time t=0 with v0 gallons of a solution in which, qo pounds is concentrate that is soluble in the tank. One more solution having q1 pounds of the concentrate for each gallon gets run into the tank as per the rate of r1gallons/min. After it is kept well stirred, the solution gets withdrawn at the rate of r2gallons/min.

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