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Consider the mixing process shown in the figure. A mixing chamber initially contains 2 liters of...

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Advance Math

Consider the mixing process shown in the figure. A mixingchamber initially contains 2 liters of a clear liquid. Clear liquidflows into the chamber at a rate of 10 liters per minute. A dyesolution having a concentration of 0.75 kilograms per liter isinjected into the mixing chamber at a constant rate of rliters per minute. When the mixing process is started, thewell-stirred mixture is pumped from the chamber at a rate of10+r liters per minute.

Part A and B provided. Please solve part C...

(a) Develop a mathematical model for the mixing process. LetQ represent the amount of dye in kilograms in themixture.
dQ/dt = _______ kg / min

     3/4*r-Q/2(10+r)

(b) The objective is to obtain a dye concentration in the outflowmixture of 0.1 kilograms per liter. What injection rate ris required to achieve this equilibrium solution?
r =______ L / min

     20/13



Would this equilibrium value of r be different if thefluid in the chamber at time t=0 contained some dye?

(c) Assume the mixing chamber contains 2 liters of clear liquid attime t=0. How many minutes will it take for the outflowconcentration to rise to within 1% of the desired concentration of0.1 kilograms per liter?
t = ___________ min

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