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Determine values for A and R from the step response

Determine values for A and R from the step response

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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Figure I shows a first order dynamic behavior of liquid level, h in Tank 1 after a step change of 10 m/min is being introduced to the inlet flow, F. The transfer function for the response is as follow: 1 As+1/R where A is the cross-section area of the tank and R is the valve resistance. The height of the cylindrical tank is 4.5 meter. The initial liquid level, h, is 1.5 meter and the final liquid level, he is 3.0 meter. Tank 1 h'(s) F(S) R h, m 3.500 3.228 3.132 2.868 2.500 5.05.7 6.5 7.0 Figure 1 t, min a) State the given transfer function to a standard transfer function of a first order system. Determine values for A and R from the step response in h given in Figure 1, and state the time-domain equation for the response in level. b) If the value of valve resistance, R, is increased to double of its value in 3(a), sketch and compare the new response with output response in Figure 1. c) If a step change of 25 m³/min in inlet flow occurred, is there any possibility for the tank to overflow? If yes, at what time it will overflow?
Transcribed Image Text:Figure I shows a first order dynamic behavior of liquid level, h in Tank 1 after a step change of 10 m/min is being introduced to the inlet flow, F. The transfer function for the response is as follow: 1 As+1/R where A is the cross-section area of the tank and R is the valve resistance. The height of the cylindrical tank is 4.5 meter. The initial liquid level, h, is 1.5 meter and the final liquid level, he is 3.0 meter. Tank 1 h'(s) F(S) R h, m 3.500 3.228 3.132 2.868 2.500 5.05.7 6.5 7.0 Figure 1 t, min a) State the given transfer function to a standard transfer function of a first order system. Determine values for A and R from the step response in h given in Figure 1, and state the time-domain equation for the response in level. b) If the value of valve resistance, R, is increased to double of its value in 3(a), sketch and compare the new response with output response in Figure 1. c) If a step change of 25 m³/min in inlet flow occurred, is there any possibility for the tank to overflow? If yes, at what time it will overflow?
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