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

Consider the mixing process shown in the figure. A mixing chamber initially contains 2 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 0.75 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.

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

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

3/4*r-Q/2(10+r)

(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?
r =______ L / min

20/13

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

(c) Assume the mixing chamber contains 2 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?
t = ___________ min

Expert Solution

Colby Messinger answered 2 years ago

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