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Question: consider a liquid blending tank shown below has two inlet...

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Consider a liquid blending tank shown below has two inlet streams with mass flow rates w1 and w2, and an exit stream with flow rate w3. The cylindrical tank is 2.5 m tall and 2 m in diameter, and the liquid has a density of 800 kg/m3 . Assume that the outlet stream is incorporated with a valve to establish flow rate w3, and the nominal inlet stream mass fractions of component A are x1=x2=0.5. The process has been operating for a very long time with constant flow rates and inlet concentrations, i.e., w1=120 kg/min and w2=100 kg/min. Under these conditions, it has come to a steady state with exit mass fraction x3=0.5 and level h=1.75 m. Based on the information above and the problem description below, answer the following questions. Assume the tank is perfected stirred.

(a) What is the value of w3 at the previously mentioned steady state? What is the constant Cv of flow w3, where w3= Cv√ℎ.

(b) If x1 is suddenly changed from 0.5 to 0.6 without changing the inlet flow rate, what is the final valve of x3? How long does it take to come within 1% of this final value? Hint: the new final value basically is the new steady state of x3.

(c) If w1 is changed from 120 kg/min to 100 kg/min without changing the inlet concentrations, what will be the final value of the tank level? How long will it take to come within 1% of this final value? Use built-in function to show a graph of the change of h after the changes in w1.

(d) Would it have made any difference in part (c) if the mass fraction of A had changed at the same time at which the flow rate was changed? Briefly explain your expectation.

W2 W1

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