introduction

MEC3102

Fluid mechanicsFaculty of Engineering and Surveying

In t roduc to ry bookSemester 1 2013

Published by

University of Southern QueenslandToowoomba Queensland 4350Australia

http://www.usq.edu.au

© University of Southern Queensland, 2013.1.

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Table of contents

Page

Essential information 1

Introduction 2Course overview 2A suggested study strategy 3Direct lecturer contact 3Why use a discussion group? 4

Resources 4Textbook 4Video cassettes 5

Study schedule 7

Course assessment 8Relationship between course objectives and assessment 8Assessment 8Examination 9

Assignment 1 11

Assignment 2 15

Past examinations 17

MEC3102 – Fluid mechanics 1

Essential information

The topics in the following list provide important information that will assist you with your study. You can access a handout containing the information on your StudyDesk through the ‘Essential information (study materials)’ link <http://usqstudydesk.usq.edu.au/file.php/1/sitefiles/DeC/essential_info/essentialhandout.pdf>. You will need your UConnect username and password to access the file. Please make sure you read this information carefully before commencing your study.

• Getting started <http://usqstudydesk.usq.edu.au/file.php/1/sitefiles/DeC/essential_info/getting_started.pdf>

• Course specification <http://usqstudydesk.usq.edu.au/file.php/1/sitefiles/DeC/essential_info/course_specification.pdf>

• Support <http://usqstudydesk.usq.edu.au/file.php/1/sitefiles/DeC/essential_info/support.pdf>

• UConnect<http://usqstudydesk.usq.edu.au/file.php/1/sitefiles/DeC/essential_info/u_connect.pdf>

• Assignment submission<http://usqstudydesk.usq.edu.au/file.php/1/sitefiles/DeC/essential_info/assignment_submission.pdf>

• Grading levels<http://usqstudydesk.usq.edu.au/file.php/1/sitefiles/DeC/essential_info/grading_levels.pdf>

• Course evaluation <http://usqstudydesk.usq.edu.au/file.php/1/sitefiles/DeC/essential_info/course_evaluation.pdf>

• Residential schools<http://usqstudydesk.usq.edu.au/file.php/1/sitefiles/DeC/essential_info/residential_school.pdf>

• Library<http://usqstudydesk.usq.edu.au/file.php/1/sitefiles/DeC/essential_info/library.pdf>

• Referencing APA<http://usqstudydesk.usq.edu.au/file.php/1/sitefiles/DeC/essential_info/apa_referencing_guide.pdf>

• Referencing Harvard AGPS<http://usqstudydesk.usq.edu.au/file.php/1/sitefiles/DeC/essential_info/harvard_referencing_guide.pdf>

• Optional purchase of study materials<http://usqstudydesk.usq.edu.au/file.php/1/sitefiles/DeC/essential_info/optional_purchase.pdf>

• USQ policies and procedures<http://usqstudydesk.usq.edu.au/file.php/1/sitefiles/DeC/essential_info/policies_procedures.pdf>

2 MEC3102 – Fluid mechanics

Introduction

This introductory book is your guide to studying the course MEC3102 Fluid Mechanics. It contains the course specification and a study programme, documents you should examine closely, as well as general information about the course.

The presentation of this course takes the form of a guided study of prescribed text. You will need to purchase the prescribed textbook; Introduction to fluid mechanics, 8th edition, S1 version by Robert W Fox, Philip J Pritchard and Alan T McDonald, John Wiley & Sons, Inc. 2011.

In the study book you will find elaboration on some information and procedures presented in the text. To fulfil the aim of this course you need to have a good understanding of all the information presented in the text. There are some suggested problems after each section and at the end of each module. Attempt as many problems as are required to give you confidence in understanding the material.

Keep this book handy and refer to it at regular intervals throughout the course.

Relationship with other courses in the program

Knowledge of MAT1102 and MAT2100 Algebra and Calculus I and II are essential in handling the analysis involved in this course. Good grasp of Dynamics I would be of great help.

Course overview

Fluid Mechanics

Static Dynamic

Steady Unsteady

Density ρ Viscosity μ

Non-viscousμ = 0

Viscousμ > 0

Incompressibleρ = const.

Compressibleρ = ρ (P,T)


A suggested study strategy

In this course you will study many interesting topics. However, it requires your diligence and concentrated study to understand the different concepts outlined in each module, and to apply them in related engineering problems. You are advised to read the suggested textbook readings, without getting involved with the details, just to have an overall perspective of the topic. Then re-reading needs to be more thorough looking at the equations derived and the assumptions used in the derivation. Then go to the activities at the end of the section and see how many you can solve. You can check your answers with the answers given at the end of your textbook. If you have got them all right carry on to the next suggested reading otherwise look at the model solutions given at the end of each module in your study book then a third reading may seem necessary to clarify the points you may have missed. If you feel that you have grasped a reasonable amount after you have finished all the sections in the module, go to the self assessment problems I have suggested at the end of the module and try to solve them. Model solutions to these self assessment problems are also given in your answer book. It will be very helpful to you when solving problems if you follow the steps suggested in the text in section 1–1. They are closely followed in the model solutions given in your answer book.

For some of you the mathematics used in the derivation of the equations may look too complicated. Please do not get discouraged because you are not required to learn these derivations by heart. The main goal of going through them is only to see the physical meaning of each term and what assumptions were used to reach the final result. This will enable you to know which situations in engineering problems you can apply these equations to and which you cannot.

In your revision I suggest that you do not read the solution to the examples in the book or in the answer book before you actually try to solve them yourself. If things are not clear to you at any stage you are welcome to contact me.

My advice is to try to read other textbooks, as well, which are given as references in your course specification. Some books explain some parts better than others. They may also have an example which could clarify a point you are having a problem with.

Recommendation

I know that some of you have some experience with solving engineering problems in practice. If you feel that what you are learning in this course can help in improving the way you tackle these problems or if it clarifies some phenomenon, I encourage you to share these ideas with me or any of the other students enrolled in the course, either by sending an e-mail or by using the discussion group for this course. Information on the discussion group for this course follows.

Direct lecturer contact

All students wishing to contact the lecturer direct are welcome to do so during business hours on (07) 4631 2734. You are also encouraged to use the discussion group on USQStudyDesk or email direct at <[email protected]>. Once again, please be specific about the problem you wish to discuss and ensure that you have study materials at hand when you make the call. Such a detailed approach could save you time (and money). You should try to keep to the study schedule in this introductory book as it has been designed to provide you with a balanced study programme. If you find that you are having difficulty with the material, which is causing you to fall behind the study schedule, you should contact the lecturer immediately to seek assistance.


Why use a discussion group?

The aim of using the MEC3102 discussion group is to replicate, through electronic means, the types of interactions which would be available to you, the students, in an on-campus delivery of the course. I believe teacher and student interaction, through student participation, is an important factor in reinforcing the learning process. Every week I download all lecture PowerPoint presentations for that week on UConnect so if you would like to know what we have covered in class please make a regular check of this site.

Students are strongly encouraged to make a contribution to the discussion group. This contribution can take many forms:

• Ask questions.

• Share experiences related to the subject.

• Suggest improvement in any aspect of the printed materials, choice of text book, etc.

Even simple questions, experiences or suggestions may lead to a worthwhile discussion which may enhance your learning and the learning of the whole class. I encourage you all to make use of the discussion group for this course to raise queries, share ideas or just reflect on what you are studying. Many other students will benefit from your query and some may respond using practical applications that can help you to understand your problem better. I will also communicate with you regularly via the discussion group when needed. Hence a regular visit to the Study desk will keep you in touch with me and the other students in the course.

Students who are not able to access the discussion group on a regular basis are encouraged to either visit the nearest educational centre when possible to try to catch up on the discussion taking place or to send me, with your assignment, your contribution and I will try to put it on the discussion group and send you a copy or a summary of the discussions.

If you cannot access UConnect at all for any reason please inform me early in the semester so you don’t miss out on any important communication I may have with the class.

Resources

Textbook

The textbook required for this course (Introduction to fluid mechanics, 8th edition, by Robert W Fox, P J Pritchard and Alan T McDonald, John Wiley & Sons, Inc. 2011) was chosen because it is a good text for researchers and engineers and it was written mainly for students. It has many examples, practical problems to solve and the answers are given at the back of the book for the even number problems.

In this course we are going to cover most of the textbook except chapter ten, which is an application to many of the basics introduced in this subject and a few other sections that you will be told about in the study book. However, it makes an interesting independent reading.


Video cassettes

As a method of increasing your understanding of the phenomenon dealt with in the subject of fluid mechanics, a set of videos are available for you to borrow from the library of USQ. The Distance education student guide contains details of borrowing procedures. A list of these videos and a description of the topic covered in each and the call number is given below.

Flow visualization 1980–85, video recording, National Committee for Fluid Mechanics Films, Chicago. Distributed by Encyclopaedia Britannica Educational Corporation, Castle Hill NSW and narrated by Stephen Kline.

Demonstrates the use of flow visualisation involving boundary layer separation and transition: vortex generation and turbulence. Also illustrates the kinematic concepts linking visual observations to the velocity field in steady and unsteady flows: streamline, streakline, pathline and time.

Call Number: 532.051 Flo – 31 minutes

Cavitation 1980–85, video recording, National Committee for Fluid Mechanics Films, Chicago. Distributed by Encyclopaedia Britannica Educational Corporation, Castle Hill NSW and presented by Phillip Eisenborg.

Cavitation is seen on hydrofoils, marine propellers, pumps, turbines and dam spillways. Flow speed, hydrofoil incidence, ambient pressure and extent of the cavitating region.

Call Number: 532.0595 Cav – 31 minutes

Pressure fields and fluid acceleration 1963, video recording, National Committee for Fluid Mechanics Films, Chicago. Distributed by Encyclopaedia Britannica Educational Corporation, Castle Hill NSW and presented by Ascher Shapiro.

Experiments in a small water tunnel demonstrating the connection between velocity and pressure fields, primarily in diffusers, venturis and channel bends.

Call Number: 532.56 Pre – 30 minutes

The fluid dynamics of drag 1985, video recording, Educational Services. Distributed by Encyclopaedia Britannica Educational Corporation, Castle Hill NSW and narrated by Ascher Shapiro.

Introduces many of the major concepts of fluid mechanics, building up to similitude. Reynolds Number, laminar and turbulent boundary layers, pressure and friction drag and effects of geometric shape on total drag.

(1) Flow visualization (H-C)

(2) Cavitation (H-C-A)

(3) Pressure fields and fluid acceleration (C)

(4) The fluid dynamics of drag (H-C)


B/W

Call Number: 532.0533 Flu

Channel flow of a compressible fluid 1965, video recording, National Committee for Fluid Mechanics Films, Chicago. Distributed by Encyclopaedia Britannica Educational Corporation, Castle Hill NSW and presented by Donald Coles.

Schlieren flow visualisation and simultaneous display of the pressure distribution along a channel of varying area demonstrate the phenomena of choking, blocking and starting.

Call Number: 532.51 Cha – 29 minutes

Part 1 Some curious experiments – no. 21601 22 minutes

Part 2 Fundamental concepts – no. 21602 32 minutes

Part 3 The laws of drag in fluids of high and low viscosity– no. 21603 37 minutes

Part 4 How to reduce drag – no. 21604 29 minutes

(5) Channel flow of a compressible fluid


Study schedule

Week Module Activity/Reading(Study book) Assessment

1 Module 1: Introduction and fundamental concepts

1.1 – 1.5

2 Module 2: Fluid statics 2.1 – 2.2

3 Module 2: Fluid statics 2.3 – 2.4

4 Module 3: Control volume formulation

3.1 – 3.3

Reminder: End of week 4 is the last date to drop courses without academic or financial penalty.

5 Module 3: Control volume formulation

3.4 – 3.5

6 BREAK

7 BREAK

8 Module 4: Differential form formulation

4.1 – 4.3 Assignment 1 (15%)Due: 19 April 2013

Reminder: End of week 8 is the last date to drop courses without academic penalty.

9 Module 4: Differential form formulation

4.4 – 4.5

10 Module 5: Similitude and dimensional analysis

5.1 – 5.2

11 Module 6: Internal incompressible viscous flow

6.1 – 6.2

12 Module 6: Internal incompressible viscous flow

6.3

13 Module 7: External incompressible viscous flow

7.1 – 7.2 Assignment 2 (15%)Due: 24 May 2013

14Module 7: External incompressible viscous flow

Module 8: Compressible flow

7.3 – 7.4

8.1 – 8.4

15 Module 8: Compressible flow 8.5 – 8.6

16–17 EXAMINATION PERIOD(2 hour restricted examination – 70%)


Course assessment

Relationship between course objectives and assessment

Assessment

See the course specification for the details of the assessment of this course.

In broad terms I believe that students need continual assessment and immediate feedback while they are actually studying so that they can recognise any misunderstandings they might be developing. They also need to do exercises that will develop their self-confidence to handle real problems. This is the purpose of the many activities and self-assessment problems given in the study book. These do not carry any marks towards your final grade.

Two summative (i.e. counting towards your final grade) assignments are provided. These are intended primarily to keep you on schedule in your studies but also to let you gauge your progress and to build your self-confidence.

The project report is also summative, see the following section.

Summative assignments will be returned with mark achieved, appropriate diagnostic comments and model solutions.

Course objectives Assignment 1 Assignment 2 Examination

1. Estimate the forces on submerged bodies in static fluid situation

2. Analyse the transportation of different types of fluids in a variety of applications and be able to avoid unwanted phenomena such as cavitation and water hammer

3. Estimate the forces on moving, or stationary bodies caused by flowing fluids, either internally or externally such as forces on nozzles, elbows, blades and drag forces on chimneys, high rise buildings, different types of constructions, aircraft and ships

4. Analyse the behaviour of high speed flows ie compressible flow in ducts, nozzles and diffusers


Examination

The final exam will be a 2 hour restricted examination and will cover the whole of the course. Two sample examinations are given in this book.

Students may take into the final examination a handwritten A4 sheet (two sides) containing any information that they believe will be relevant for the examination. No other materials are permitted in the examination. Calculators which cannot textual information are permitted.

You need not worry about tables and charts for properties of fluids because these will be provided to you with your exam paper and any appropriate data or tables which are necessary for solving the exam problems.


Assignment 1

Note: Always outline your assumptions, draw a sketch of the problem, label important points and provide a detailed solution.

Question 1 (30 marks)

Approximate the torque and power necessary to rotate the inner 20 cm diameter cylinder shown in Figure 1. SAE 10W-30 oil at 20°C fills the gap. Assume a linear velocity profile.

Figure 1


Determine the pressure difference between the water pipe and the oil pipe shown in Figure 2

Figure 2

Due date: 19 April 2013

Weighting: 15% (150 marks)



A 4-m long curved gate is located in the side of a reservoir containing water as shown in Figure 3. Determine the magnitude of the horizontal and vertical components of the force of the water on the gate. (γw = 9810 N/m3)

Figure 3


A converging elbow (see Figure 4) turns water through an angle of 135° in a vertical plane. The flow cross-section diameter is 400 mm at the elbow inlet, section (1), and 200 mm at the elbow outlet, section (2). The elbow flow passage volume is 0.2 m3 between sections (1) and (2). The water volume flowrate is 0.4 m3/s, and the elbow inlet and outlet gauge pressures are 150 and 90 kPa, respectively. The elbow mass is 12 kg. Calculate the horizontal (x direction) and vertical (z direction) anchoring forces required to hold the elbow in place. Ignore viscous effects. (ρw = 1000 kg/m3, g = 9.81 m/s2)

Figure 4



Water flows into the sink shown in figure 5 at a flow rate of 8 L/min. If the drain is closed, the water will eventually flow through the overflow drain holes rather than over the edge of the sink. What is the minimum number of 1-cm diameter drain holes needed to ensure that the water does not overflow the sink? Neglect viscous effects.(ρw = 1000 kg/m3, g = 9.81 m/s2)

Figure 5


Assignment 2

Note: Always outline your assumptions, draw a sketch of the problem, label important points and provide a detailed solution.


If the velocity potential can be described by

where b is some constant, what is the formula for the stream function? Sketch the flow pattern.


The following measurements have been taken at sea level for a model aeroplane whose propeller had a diameter of 20 cm and was flying at 54 km/hr:

(a) Assume that viscous effects are negligible

(i) Plot this data using appropriate dimensionless groups

(ii) Determine the thrust of a similar aeroplane whose propeller has a 1.3 m diameter, spinning at 1500 rpm while flying at 300 km/hr at 3250 m altitude.

(b) Repeat part (a) assuming that viscous effects are dominant.

Due date: 24 May 2013

Weighting: 15% (150 marks)

Propeller speed (rpm) 2400 3000 4500

Thrust force (N) 4.2 5.4 8

φ b4--- x y–( ) x y+( )=

Byron

Highlight



A petrol tanker uses gravity to empty its 35 kL tank into an underground storage tank. The hose that is used has a roughness equivalent to galvanised iron, has an internal diameter of 10 cm and is 10 m long (see figure). The centreline of the square hose fitting on the tanker is mounted 50 cm off the ground, while the hose penetrates 2 m below ground level. All bends have a radius of curvature of 15 cm. It is claimed that the tank can be emptied within 30 min: verify whether this claim is correct.

Byron

Highlight


Past examinations

Any non-USQ copyright material used herein is reproduced under the provisions of Section 200(1)(b) of theCopyright Amendment Act 1980.

STUDENT NAME: ___________________________________ STUDENT NO.: __________________

UNIVERSITY OF SOUTHERN QUEENSLAND

FACULTY OF ENGINEERING AND SURVEYING

Course No: MEC3102 Course Name: FLUID MECHANICS

Assessment No: Internal

External

This examination carries 70% of the totalassessment for this course

Examiner: R. MOSSAD Moderator: D. BUTTSWORTH

Examination Date: JUNE/JULY, 2004

Time Allowed: Perusal – Ten (10) minutesWorking – Three (3) hours

Special Instructions:

This is a RESTRICTED examination.

Students may taken into the final examination, a handwritten A4 sheet (two sides) containing any informationthat they believe will be relevant for the examination. No other materials are permitted in the examination.

Students are permitted to use programmable and non-programmable calculators in the examination. Studentsmust note the make and model of the calculator used on the front answer book (or the examination paperwhere applicable). This may be subject to checking by the exam supervisor.

Students are permitted to write on the examination paper during perusal time.

Sketches and detailed answers are required.

All questions are of equal value.

Tables and Charts needed are attached.

All questions are to be attempted.

All examination question papers must be submitted to supervisors at the end of every examination andreturned to USQ.

X

X

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MEC3102 – FLUID MECHANICS JUNE/JULY 2004 Page 1

QUESTION 1

(a) A Newtonian fluid having a specific gravity of 0.92 and a kinematic viscosity of 4 × 10–4 m2/sflows past a fixed surface. The velocity profile near the surface is shown in Figure 1. Determinethe magnitude and direction of the shearing stress developed on the plate. Express your answer interms of U and δ, with U and δ expressed in units of metres per second and metres, respectively.Note that U and δ are constants.

(50 marks)

Figure 1

(b) A radio antenna on a car consists of a circular cylinder 6.5 mm diameter and 1200 mm long.Determine the bending moment at the base of the antenna if the car is driven 90 km/hr through stillair.

(50 marks)

QUESTION 2

A homogenous, 1.2 m wide, 2.4 m long, and 360 kg rectangular gate is held in place by a horizontalflexible cable as shown in Figure 2. Water acts against the gate which is hinged at point A. Friction inthe hinge is negligible. Determine the tension in the cable.

Figure 2

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QUESTION 3

Air discharges from a 5 cm diameter nozzle and strikes a curved vane, which is in a vertical plane asshown in Figure 3. A stagnation tube connected to a water U-tube manometer is located in the free airjet. Determine the horizontal and vertical components of the force that the air jet exerts on the vane.Neglect the weight of the air and all friction.

Figure 3

QUESTION 4

The stream function for a two-dimensional, incompressible flow field is given by the equation

where the stream function has the units m2/s with x and y in m.

(a) Sketch the streamlines for this flow field. Indicate the direction of flow along the streamlines.

(b) Is this an irrotational flow field?

(c) Determine the velocity and the acceleration of a fluid particle at the point x = 0.3 m, y = 0.6 m.

QUESTION 5

An orifice flowmeter uses a pressure drop measurement to determine the flow rate through a pipe. Aparticular orifice flowmeter, when tested in the laboratory, yielded a pressure drop of 50 kPa for a flowof 0.08 m3/s through a 15 cm diameter pipe. For a geometrically similar system using the same fluidwith a 60 cm diameter pipe, what is the required flow if similarity between the two systems is to bemaintained? What is the corresponding pressure drop?

ψ 2x 2y–=

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QUESTION 6

The three water-filled tanks shown in Figure 4 are connected by pipes as indicated. If minor losses areneglected:

(a) Write down the equations necessary to determine the flowrate in each pipe. (80 marks)

(b) Solve the set of equations derived in (a) to find the flowrates. (20 marks)

Figure 4

QUESTION 7

The stagnation temperature in an airflow is 149°C upstream and downstream from a normal shockwave. The absolute stagtnation pressure downstream from the shock wave is 229.5 kPa. Through thewave the absolute pressure rises from 103.7 to 140 kPa. Determine the velocities upstream anddownstream from the wave.

________________________________________________________________________________

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Any non-USQ copyright material used herein is reproduced under the provisions of Section 200(1)(b) of theCopyright Amendment Act 1980.

STUDENT NAME: ___________________________________ STUDENT NO.: __________________

UNIVERSITY OF SOUTHERN QUEENSLAND

FACULTY OF ENGINEERING AND SURVEYING

Course No: MEC3102 Course Name: FLUID MECHANICS

Assessment No: Internal

External

This examination carries 70% of the totalassessment for this course

Examiner: R. MOSSAD Moderator: D BUTTSWORTH

Examination Date: JUNE/JULY, 2005

Time Allowed: Perusal – Ten (10) minutesWorking – Three (3) hours

Special Instructions:

This is a RESTRICTED examination.

Students may taken into the final examination, a handwritten A4 sheet (two sides) containing any informationthat they believe will be relevant for the examination. No other materials are permitted in the examination.

Students are permitted to use programmable and non-programmable calculators in the examination. Studentsmust note the make and model of the calculator used on the front answer book (or the examination paperwhere applicable). This may be subject to checking by the exam supervisor.

Students are permitted to write on the examination paper during perusal time.

Sketches and detailed answers are required.

All questions are to be attempted. All questions are of equal value.

Tables and Charts needed are attached.

All examination question papers must be submitted to supervisors at the end of every examination andreturned to USQ.

X

X

of 4


QUESTION 1

(a) The pressure difference between an oil pipe and water pipe is measured by a double-fluidmanometer, as shown in Figure 1. For the given fluid heights and specific gravities, calculate thepressure difference .

(b) A steel sphere (s.g. 7.82) of 51 mm diameter is released in a large tank of oil (s.g. 0.82, viscosity0.95 Pa.s). Calculate the terminal velocity of this sphere.

Figure 1

QUESTION 2

Find the magnitude and point of application of the resultant force acting on the inclined 2 m diametercircular gate of figure 2. The tank is closed and has a layer of compressed air at 34 kPa gauge as shownin figure 2.

Figure 2

PΔ PB PA–=

A

B

60 cm

10 cm

15 cm

20 cm

WaterSG = 1.0

GlycerinSG = 1.26

OilSG = 0.88

MercurySG = 13.5

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QUESTION 3

Water flows into and discharges from a pipe U-section as shown in Figure 3. At flange (1), the totalabsolute pressure is 200 kPa, and 30 kg/s flows into the pipe. At flange (2), the total absolute pressure is150 kPa. At location (3), 8 kg/s of water discharges to the atmosphere, which is at 100 kPa.

Determine the x- and z-forces on the U-section.

Figure 3

QUESTION 4

A steady, two-dimensional, incompressible flow field in the xy-plane has the following stream function:

, where a, b and c are constants.

(a) Obtain expressions for velocity components u and v.

(b) Verify that the flow field satisfies the incompressible continuity equation.

(c) Is this an irrotational flow if a = 0.50 s–1, b = –1.3 s–1 and c = 0.50 s–1?

1

2

3

8 kg/s

3 cm

5 cm

10 cm

30 kg/s

22 kg/s

z

x

ψ ax2= bxy cy2+ +

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QUESTION 5

An explosion occurs in the atmosphere when an anti-aircraft missile meets its target (Figure 4). Ashock wave (also called a blast wave) spreads out radially from the explosion. The pressure differenceacross the blast wave ΔP and its radial distance r from the centre are functions of time t, speed of soundc, and the total amount of energy E released by the explosion.

(a) Generate dimensionless relationships between ΔP and the other parameters and between r and theother parameters.

(b) For a given explosion, if the time t since the explosion doubles, all else being equal, by what factorwill ΔP decrease?

Figure 4

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QUESTION 6

Water at 15°C is to be discharged from a reservoir at a rate of 18 L/s using two horizontal cast ironpipes connected in a series and a pump between them. The first pipe is 20 m long and has a 6 cmdiameter, while the second pipe is 35 m long and has a 4 cm diameter. The water level in the reservoir is30 m above the centreline of the pipe. The pipe entrance is sharp-edged, and losses associated with theconnection of the pump are negligible. Determine the required pumping head and the minimumpumping power to maintain the indicated flow rate.

Figure 5

QUESTION 7

A normal shock occurs at the inlet (diffuser) of a jet engine with the engine travelling at a Mach numberof 1.8 at an altitude where the ambient pressure is 30 kPa. Determine the Mach number, staticpressure, and stagnation pressure of the flow leaving the diffuser. The area ratio of the diffuser is3 to 1. Assume isentropic flow in the diffuser downstream of the shock.

Figure 6

________________________________________________________________________________

introduction

Documents

Transcript of introduction