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4. Consider a simple surge tank for water with a valve on the exit line. The inlet flow rate (q.) is a disturbance that varies with time. The exit flow rate (q) is proportional to the square root of the liquid level (h). a. Develop a dynamic mathematical model of the process that relates the liquid level (h) to the inlet flow rate (q). b. Linearize the model and obtain a transfer function in Laplace variables relating the liquid level with the inlet flow rate. c. Calculate the parameters of the transfer function based on the steady-state operational data given below: i. The tank has a diameter of 6 ft and a height of 10 ft. ii. At steady-state, the liquid level is 5 ft. iii. At steady-state, the inlet and outlet flow rates are 16 ft/h. d. If the inlet flow rate is increased to 24 ft3/h, what does the linearized model predict for the final liquid height at time o ? Is this a problem?

4. Consider a simple surge tank for water with a valve on the exit line. The inlet flow rate (q.) is a disturbance that varies with time. The exit flow rate (q) is proportional to the square root of the liquid level (h). a. Develop a dynamic mathematical model of the process that relates the liquid level (h) to the inlet flow rate (q). b. Linearize the model and obtain a transfer function in Laplace variables relating the liquid level with the inlet flow rate. c. Calculate the parameters of the transfer function based on the steady-state operational data given below: i. The tank has a diameter of 6 ft and a height of 10 ft. ii. At steady-state, the liquid level is 5 ft. iii. At steady-state, the inlet and outlet flow rates are 16 ft/h. d. If the inlet flow rate is increased to 24 ft3/h, what does the linearized model predict for the final liquid height at time o ? Is this a problem?

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Process Dynamics and Control, Third Edition or Fourth Edition, by D. E. Seborg, T. F. Edgar, D. A. Mellichamp, F. J. Doyle III, John Wiley & Sons, Inc, 2011

4. Consider a simple surge tank for water with a valve on the exit line. The inlet flow rate (q.) is a disturbance that varies with time. The exit flow rate (g) is proportional to the square root of the liquid level (h). h a. Develop a dynamic mathematical model of the process that relates the liquid level (h) to the inlet flow rate (q.). b. Linearize the model and obtain a transfer function in Laplace variables relating the liquid level with the inlet flow rate. c. Calculate the parameters of the transfer function based on the steady-state operational data given below: i. The tank has a diameter of 6 ft and a height of 10 ft. ii. At steady-state, the liquid level is 5 ft. ii. At steady-state, the inlet and outlet flow rates are 16 ft³/h. d. If the inlet flow rate is increased to 24 ft3/h, what does the linearized model predict for the final liquid height at time → * ? Is this a problem?
Transcribed Image Text:4. Consider a simple surge tank for water with a valve on the exit line. The inlet flow rate (q.) is a disturbance that varies with time. The exit flow rate (g) is proportional to the square root of the liquid level (h). h a. Develop a dynamic mathematical model of the process that relates the liquid level (h) to the inlet flow rate (q.). b. Linearize the model and obtain a transfer function in Laplace variables relating the liquid level with the inlet flow rate. c. Calculate the parameters of the transfer function based on the steady-state operational data given below: i. The tank has a diameter of 6 ft and a height of 10 ft. ii. At steady-state, the liquid level is 5 ft. ii. At steady-state, the inlet and outlet flow rates are 16 ft³/h. d. If the inlet flow rate is increased to 24 ft3/h, what does the linearized model predict for the final liquid height at time → * ? Is this a problem?
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