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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
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
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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: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?
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?
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?
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