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 burs9ng disk is placed so that, if the pressure exceeds the maximum opera9ng pressure, the air is vented to atmosphere rather than over-pressuring the chemical reac9on vessel (Figures 4a and 4b). In this ques9on, you should treat the flow as quasione-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 burs9ng: 10.5 kN, 11.0 kN, 11.5 kN, 12.0 kN, 12.5 kN. Which of these burs9ng disks would you recommend, and why? b) Due to an over-pressurisa9on of the air line, the disk bursts at 9me t = 0. At what pressure in the air line will this occur? c) Aier the disk bursts, a shock wave travels in one direc9on while expansion waves travel in the other direc9on. At 9me t = t1, the wave pa\ern in Figure 4c is observed. Plot the pressure distribu9on in the pipe from x = -6.0 m to x = 6.0 m corresponding to this wave pa\ern. 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 aier the disk burst was the snapshot in Figure 4c captured?

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 burs9ng disk is placed so that, if the pressure exceeds the maximum opera9ng pressure, the air is vented to atmosphere rather than over-pressuring the chemical reac9on vessel (Figures 4a and 4b). In this ques9on, you should treat the flow as quasione-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 burs9ng: 10.5 kN, 11.0 kN, 11.5 kN, 12.0 kN, 12.5 kN. Which of these burs9ng disks would you recommend, and why? b) Due to an over-pressurisa9on of the air line, the disk bursts at 9me t = 0. At what pressure in the air line will this occur? c) Aier the disk bursts, a shock wave travels in one direc9on while expansion waves travel in the other direc9on. At 9me t = t1, the wave pa\ern in Figure 4c is observed. Plot the pressure distribu9on in the pipe from x = -6.0 m to x = 6.0 m corresponding to this wave pa\ern. 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 aier the disk burst was the snapshot in Figure 4c captured?

(a) chemical reaction vessel
pressurised air
reaction vessel
(b) bursting disk in normal operation
pressurised air
open to atmosphere
expansion waves
(x = -3.4 m to -0.4 m)
bursting disk
(x = 0.0 m)
(c) wave pattern at t = t₁, a short time after bursting at t = 0
normal shock
(x = 5.2 m)
Figure 4: Operation of a bursting disk
open to atmosphere

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