Working for an engineering consultancy firm, your knowledge of fluid dynamics is required to design a new safety feature for a high-pressure air line in a factory. The air line takes the form of a cylindrical pipe of diameter 150 mm, which is designed to operate between 0.45 MPa and 0.76 MPa. At the end of the pipe a bursting disk is placed so that, if the pressure exceeds the maximum operating pressure, the air is vented to atmosphere rather than over-pressuring the chemical reaction vessel (Figures 4a and 4b). In this question, you should treat the flow as quasi- one-dimensional and inviscid. The air in the surrounding atmosphere is at 101 kPa and 298 K. You have a choice of five disks which can withstand the following forces across them before bursting: 10.5 kN, 11.0 kN, 11.5 kN, 12.0 kN, 12.5 kN. Which of these bursting disks would you recommend, and why? Due to an over-pressurisation of the air line, the disk bursts at time t = 0. At what pressure in the air line will this occur? After the disk bursts, a shock wave travels in one direction while expansion waves travel in the other direction. At time t = t₁, the wave pattern in Figure 4c is observed. Plot the pressure distribution in the pipe from x = -6.0 m to x = 6.0 m corresponding to this wave pattern. You are given that a pressure tap at x = 0.0 m records the pressure at t = t₁ as 258 kPa. On your plot, annotate the pressure values in different regions of the air line. What is the Mach number of the shock wave that is travelling along the nine?
Working for an engineering consultancy firm, your knowledge of fluid dynamics is required to design a new safety feature for a high-pressure air line in a factory. The air line takes the form of a cylindrical pipe of diameter 150 mm, which is designed to operate between 0.45 MPa and 0.76 MPa. At the end of the pipe a bursting disk is placed so that, if the pressure exceeds the maximum operating pressure, the air is vented to atmosphere rather than over-pressuring the chemical reaction vessel (Figures 4a and 4b). In this question, you should treat the flow as quasi- one-dimensional and inviscid. The air in the surrounding atmosphere is at 101 kPa and 298 K. You have a choice of five disks which can withstand the following forces across them before bursting: 10.5 kN, 11.0 kN, 11.5 kN, 12.0 kN, 12.5 kN. Which of these bursting disks would you recommend, and why? Due to an over-pressurisation of the air line, the disk bursts at time t = 0. At what pressure in the air line will this occur? After the disk bursts, a shock wave travels in one direction while expansion waves travel in the other direction. At time t = t₁, the wave pattern in Figure 4c is observed. Plot the pressure distribution in the pipe from x = -6.0 m to x = 6.0 m corresponding to this wave pattern. You are given that a pressure tap at x = 0.0 m records the pressure at t = t₁ as 258 kPa. On your plot, annotate the pressure values in different regions of the air line. What is the Mach number of the shock wave that is travelling along the nine?
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
Transcribed Image Text:Working for an engineering consultancy firm, your knowledge of fluid
dynamics is required to design a new safety feature for a high-pressure
air line in a factory. The air line takes the form of a cylindrical pipe of
diameter 150 mm, which is designed to operate between 0.45 MPa and
0.76 MPa. At the end of the pipe a bursting disk is placed so that, if the
pressure exceeds the maximum operating pressure, the air is vented to
atmosphere rather than over-pressuring the chemical reaction vessel
(Figures 4a and 4b). In this question, you should treat the flow as quasi-
one-dimensional and inviscid. The air in the surrounding atmosphere is
at 101 kPa and 298 K.
a) You have a choice of five disks which can withstand the following forces
across them before bursting: 10.5 kN, 11.0 kN, 11.5 kN, 12.0 kN, 12.5
kN. Which of these bursting disks would you recommend, and why?
b) Due to an over-pressurisation of the air line, the disk bursts at time t =
0. At what pressure in the air line will this occur?
c) After the disk bursts, a shock wave travels in one direction while
expansion waves travel in the other direction. At time t = t₁, the wave
pattern in Figure 4c is observed. Plot the pressure distribution in the
pipe from x = -6.0 m to x = 6.0 m corresponding to this wave pattern.
You are given that a pressure tap at x = 0.0 m records the pressure at t =
t₁ as 258 kPa. On your plot, annotate the pressure values in different
regions of the air line.
d) What is the Mach number of the shock wave that is travelling along the
pipe?
Transcribed Image Text:aj
You have a cridice of five disks which can withstand the following forces
across them before bursting: 10.5 kN, 11.0 kN, 11.5 kN, 12.0 kN, 12.5
kN. Which of these bursting disks would you recommend, and why?
b) Due to an over-pressurisation of the air line, the disk bursts at time t =
0. At what pressure in the air line will this occur?
c) After the disk bursts, a shock wave travels in one direction while
expansion waves travel in the other direction. At time t = t₁, the wave
pattern in Figure 4c is observed. Plot the pressure distribution in the
pipe from x = -6.0 m to x = 6.0 m corresponding to this wave pattern.
You are given that a pressure tap at x = 0.0 m records the pressure at t =
t₁ as 258 kPa. On your plot, annotate the pressure values in different
regions of the air line.
d) What is the Mach number of the shock wave that is travelling along the
pipe?
e) In the frame of reference of the shock, what is the post-shock Mach
number? Also determine the post-shock temperature and explain
concisely in physical terms why the temperature has increased or
decreased through the shock.
f) Determine the value of t₁, i.e. how long after the disk burst was the
snapshot in Figure 4c captured?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY