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An open liquid surge system (p = constant) is designed
Chapter 6, Problem 6.16(choose chapter or problem)
An open liquid surge system (p = constant) is designed with a side tank that normally is isolated from the flowing material as shown in Fig. E6.16. Area =A1 Figure E6.16 Qo----,l Rl Valve 1 Area =A2 R2 Valve 2 Tl,~ E :I Figure E6.19 Exercises 111 (a) In normal operation, Valve 1 is closed (R1 ~ oo) and q1 = 0. What is the transfer function relating changes in q0 to changes in outflow rate q2 under these conditions? (b) Someone inadvertently leaves Valve 1 partially open (0 < R1 < oo ). What is the differential equation model for this system? (c) What do you know about the form of the transfer function Q2(s)/Q6(s) for Valve 1 partially open? Discuss but do not derive. (d) Is the response to changes in q0 faster or slower for Case (b) compared to Case (a)? Explain why but do not derive the response.
Questions & Answers
QUESTION:
An open liquid surge system (p = constant) is designed with a side tank that normally is isolated from the flowing material as shown in Fig. E6.16. Area =A1 Figure E6.16 Qo----,l Rl Valve 1 Area =A2 R2 Valve 2 Tl,~ E :I Figure E6.19 Exercises 111 (a) In normal operation, Valve 1 is closed (R1 ~ oo) and q1 = 0. What is the transfer function relating changes in q0 to changes in outflow rate q2 under these conditions? (b) Someone inadvertently leaves Valve 1 partially open (0 < R1 < oo ). What is the differential equation model for this system? (c) What do you know about the form of the transfer function Q2(s)/Q6(s) for Valve 1 partially open? Discuss but do not derive. (d) Is the response to changes in q0 faster or slower for Case (b) compared to Case (a)? Explain why but do not derive the response.
ANSWER:Step 1 of 3
The given system is,
(a)
If and
Therefore,
Now, by taking a Laplace transformation,
Since