1. A gas detector is used to determine concentration of a flammablé gas ll Normally the gas concentration is 1% by volume which is below the alarm limit of 4% and the lower flammability limit of 5%. If the gas concentration is above the lower flammability limit it is flammable. The dynamic behavior of a particular gas detector can be expressed as a first-order transfer function (in deviation variables) that relates the measured concentration Ym to the actual concentration Y' Ym (s) Y'(s) 1 5s +1 where Ym and Y' are in volume percent and the time constant is in units of seconds. At a particular time the gas stream is flowing at a rate of q = 1.0 m³/s through a duct with a cross- sectional area of 1 m². a) If the flammable gas concentration suddenly increases from 1% to 7% by volume, how many cubic meters of the gas stream with the flammable gas component pass through the detector before the alarm is sounded? b) Is it possible for a plug of flammable gas to pass the detector without the alarm ever being sounded? Explain.
1. A gas detector is used to determine concentration of a flammablé gas ll Normally the gas concentration is 1% by volume which is below the alarm limit of 4% and the lower flammability limit of 5%. If the gas concentration is above the lower flammability limit it is flammable. The dynamic behavior of a particular gas detector can be expressed as a first-order transfer function (in deviation variables) that relates the measured concentration Ym to the actual concentration Y' Ym (s) Y'(s) 1 5s +1 where Ym and Y' are in volume percent and the time constant is in units of seconds. At a particular time the gas stream is flowing at a rate of q = 1.0 m³/s through a duct with a cross- sectional area of 1 m². a) If the flammable gas concentration suddenly increases from 1% to 7% by volume, how many cubic meters of the gas stream with the flammable gas component pass through the detector before the alarm is sounded? b) Is it possible for a plug of flammable gas to pass the detector without the alarm ever being sounded? Explain.
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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![1. **Gas Detector Dynamics**
A gas detector is used to determine the concentration of a flammable gas in a gas stream. Normally, the gas concentration is 1% by volume, which is below the alarm limit of 4% and the lower flammability limit of 5%. If the gas concentration is above the lower flammability limit, it is flammable. The dynamic behavior of a particular gas detector can be expressed as a first-order transfer function (in deviation variables) that relates the measured concentration \( Y'_m \) to the actual concentration \( Y' \).
\[
\frac{Y'_m(s)}{Y'(s)} = \frac{1}{5s + 1}
\]
where \( Y'_m \) and \( Y' \) are in volume percent, and the time constant is in units of seconds. At a particular time, the gas stream is flowing at a rate of \( q = 1.0 \, \text{m}^3/\text{s} \) through a duct with a cross-sectional area of \( 1 \, \text{m}^2 \).
a) If the flammable gas concentration suddenly increases from 1% to 7% by volume, how many cubic meters of the gas stream with the flammable gas component pass through the detector before the alarm is sounded?
b) Is it possible for a plug of flammable gas to pass the detector without the alarm ever being sounded? Explain.
**Explanation of Transfer Function:**
The transfer function provided relates the change in measured concentration to the change in actual concentration over time. It is a first-order system with a time constant of 5 seconds, indicating how quickly the detector responds to changes in gas concentration. This behavior impacts how quickly the alarm system can respond when the concentration exceeds safety thresholds.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8ed819a1-7cc7-4b35-b605-cdaaef8761fd%2F12f746a1-acf7-4d88-80db-4f59dfb1a231%2F50ez0n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. **Gas Detector Dynamics**
A gas detector is used to determine the concentration of a flammable gas in a gas stream. Normally, the gas concentration is 1% by volume, which is below the alarm limit of 4% and the lower flammability limit of 5%. If the gas concentration is above the lower flammability limit, it is flammable. The dynamic behavior of a particular gas detector can be expressed as a first-order transfer function (in deviation variables) that relates the measured concentration \( Y'_m \) to the actual concentration \( Y' \).
\[
\frac{Y'_m(s)}{Y'(s)} = \frac{1}{5s + 1}
\]
where \( Y'_m \) and \( Y' \) are in volume percent, and the time constant is in units of seconds. At a particular time, the gas stream is flowing at a rate of \( q = 1.0 \, \text{m}^3/\text{s} \) through a duct with a cross-sectional area of \( 1 \, \text{m}^2 \).
a) If the flammable gas concentration suddenly increases from 1% to 7% by volume, how many cubic meters of the gas stream with the flammable gas component pass through the detector before the alarm is sounded?
b) Is it possible for a plug of flammable gas to pass the detector without the alarm ever being sounded? Explain.
**Explanation of Transfer Function:**
The transfer function provided relates the change in measured concentration to the change in actual concentration over time. It is a first-order system with a time constant of 5 seconds, indicating how quickly the detector responds to changes in gas concentration. This behavior impacts how quickly the alarm system can respond when the concentration exceeds safety thresholds.
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