Q.1 The dynamic behavior of a pressure sensor/transmitter can be expressed as a first-order differential equation that relates the measured value, Pm to the actual pressure, P: 20 dPm (t) dt Both Pm and P have units of psi, and the time has units of seconds. Suppose that an alarm will sound if Pm exceeds 50 psi. The process is initially at a steady-state (Pm = P = 40 psi). For performing an inspection of the sensor and the alarm system, P is suddenly increased to 60 psi and maintained at this value for 2 minutes before returning it to its initial value. (i) Deduce the transfer function for this 1st order process. (ii) Explain what type of input disturbance occurs in this process and express the disturbance in Laplace domain. (iii) Derive an expression for Pm (t). -= P(t)- Pm (t)
Q.1 The dynamic behavior of a pressure sensor/transmitter can be expressed as a first-order differential equation that relates the measured value, Pm to the actual pressure, P: 20 dPm (t) dt Both Pm and P have units of psi, and the time has units of seconds. Suppose that an alarm will sound if Pm exceeds 50 psi. The process is initially at a steady-state (Pm = P = 40 psi). For performing an inspection of the sensor and the alarm system, P is suddenly increased to 60 psi and maintained at this value for 2 minutes before returning it to its initial value. (i) Deduce the transfer function for this 1st order process. (ii) Explain what type of input disturbance occurs in this process and express the disturbance in Laplace domain. (iii) Derive an expression for Pm (t). -= P(t)- Pm (t)
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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Transcribed Image Text:Q.1 The dynamic behavior of a pressure sensor/transmitter can be expressed as a first-order differential
equation that relates the measured value, Pm to the actual pressure, P:
dPm (t)
20-
dt
Both Pm and P have units of psi, and the time has units of seconds. Suppose that an alarm will sound
if Pm exceeds 50 psi. The process is initially at a steady-state (Pm = P = 40 psi). For performing
an inspection of the sensor and the alarm system, P is suddenly increased to 60 psi and maintained at
this value for 2 minutes before returning it to its initial value.
(i) Deduce the transfer function for this 1st order process.
(ii) Explain what type of input disturbance occurs in this process and express the disturbance in
Laplace domain.
(iii) Derive an expression for Pm (t).
(iv) Graphically show the input disturbance and output response in a single plot. Use MICROSOFT
EXCEL in this purpose.
(v) If the alarm system works properly, compute how long it will sound.
= P(t)- Pm(t)
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