INGM 321 PEC

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FLUID MECHANICS II

STUDY GUIDE FOR

INGM 321
P
E
C

*INGM321PEC*

FACULTY OF ENGINEERING





ii
























Study guide compiled by:

DR M VAN ELDIK




Edited

nn
.

=
Page layout by
Elsabe Strydom
,
g
raphikos
.

Printing arrangements and distribution by Dep
artment Logistics (Distribution Centre).

Printed by Nashua Digidoc Centre (018) 299 2827.

Copyright


20
1
2

edition. Date of revision 20
1
2
.

North
-
West University, Potchefstroom Campus.

No part of this book may be reproduced in any form or by any means witho
ut written
permission from the publisher.




iii

MODULE CONTENTS

Module information

................................
................................
................................
.....................
iv

Module code and name

................................
................................
................................
..............
iv

Prerequisites

................................
................................
................................
...............................
iv

Lecturer

................................
................................
................................
................................
.......
iv

Prescribed sources

................................
................................
................................
.....................
iv

Additional sources

................................
................................
................................
......................
iv

Contact times

................................
................................
................................
..............................
iv

Work prog
ram

................................
................................
................................
.............................
iv

How to use this study guide
................................
................................
................................
........

v

Introduction

................................
................................
................................
................................
.

v

What is fluid mechanics?

................................
................................
................................
............

v

Aims of module

................................
................................
................................
...........................
vi

Exit leve
l learning outcomes
................................
................................
................................
.......
vi

Teaching plan

................................
................................
................................
............................

vii

Lectures

................................
................................
................................
................................
.....

vii

Self study

................................
................................
................................
................................
...

vii

Practicals

................................
................................
................................
................................
..

viii

Tutorial classes

................................
................................
................................
.........................

viii

Tests

................................
................................
................................
................................
.........

viii

Work assignments

................................
................................
................................
......................
ix

Discussion classes

................................
................................
................................
.....................
ix

The use of calculators during evaluations
................................
................................
..................
ix

Evaluat
ion process

................................
................................
................................
.....................
ix

Evaluation opportunities

................................
................................
................................
.............
ix

Examination entrance requirements

................................
................................
..........................

x

Calculation of the final mark

................................
................................
................................
.......

x

Absence

................................
................................
................................
................................
......
xi

Module form

................................
................................
................................
...............................

xii

Warning against plagiarism

................................
................................
................................
......

xiv

Study unit 1

One
-
dimensional compressible flow
................................
.....................

1

Study unit 2

Boundary
-
layer theory

................................
................................
............

5

Study unit 3

Measuring techniques
................................
................................
.............

7

FORMULEBLAD / FORMULA SHEET

................................
................................
.....................

9



iv

MODULE
INFORMATION

M
ODULE CODE AND NAME

INGM321: Fluid Mechanics II

P
REREQUISITES

INGM312 Fluid mechanics I.

LECT
URER

Title and surname

Building and office number

Telephone number and e
-
mail

Lecturer:



Secretary:



PRESCRIBED SOURCES



Munson, B.R., Young, D.F., Okiishi, T.H., Fundamentals of Fluid Mechanics, Fifth
Edition, Wiley.

ADDITIONAL SOURCES



Shames, I H, Me
chanics of Fluids,
Third

Edition, McGraw
-
Hill
.

(out of print)



White, F M, Fluid Mechanics, Fourth Edition, McGraw
-
Hill.



Cengel, YA, Fluid Mechanics Fundamentals and applications, Second Edition in SI
edition, McGraw
-
Hill



Cenge
l
, YA, Fluid Mechanics Fundame
ntals and applications,
Tenth
Edi
tion, McGraw
-
Hill

CONTACT TIMES

During the first contact session the time schedule for the rest of the semester will be
discussed.

WORK PROGRAM

During the first contact session the work program for the rest of the semester
will discussed.



v

HOW TO USE THIS STUD
Y GUIDE

It is important to firstly understand the aim of this guide in order to exploit it best. The guide
does not include core notes on the subject content. The guide has a dual aim, namely (i) to
inform you on all
the necessary measures to ensure the smooth progression of this module,
and (ii) to establish a sound holistic structure for the module content in order to ensure your
overall impression of the content and the link between study units as well as provide
gu
idance to your learning process. The contents of this guide may change during the
semester, and in which case it will be clearly communicated in the class and e
-
fundi.

This guide has four main components, namely:



This introductory component in which you a
re introduced to the subject area and the
aims of the module. This part of the guide also includes information concerning the
teaching plan and study guidance on how to approach the learning process.



The module information component provides information
regarding the module code
and name, name and details of the lecturer, literature sources, contact times and
evaluation process.



A study component in which the structure of the module, as well as the study unit aims
and self
-
assessment exercises for each st
udy unit is provided.



An information page, which will be provided during evaluations. Information pages
must be brought along by the students themselves during class tests (which will be
discussed later on).



This guide is therefore an essential tool in
your learning process and must be brought
to each contact session. You will use this guide during each session.

INTRODUCTION

W
HAT IS FLUID MECHANI
CS?

Fluid mechanics is the engineering science in which the kinematics and dynamics of fluids
are studied. T
he term ‘fluids’ is the collective noun for fluids and gasses. Mechanics
involves the study of the physical characteristics, speed, accelerations, pressures, stresses
and the resulting forces. The mechanics of fluids is thus the engineering science in wh
ich
the physical characteristics, speed, accelerations, pressures, stresses and the resulting
forces associated with fluids are studied.

This second module concentrates more on the advanced aspects of this subject area. It
includes compressible flow, pote
ntial flow, boundary
-
layer theory and measuring techniques.

The practical applications of fluid mechanics is wide ranging and includes among others
aircraft propulsion, the stability and buoyancy of ships and submarines, numerical simulation
of flow fields
, physical model tests, wind resistance of cars, aircraft and projectiles, as well as
the flow through nozzles and pipe networks.


vi

AIMS OF MODULE

The aims of this module are as follows:



To equip the student with the basic knowledge of the subject field.



To

cultivate an understanding of the basic principles of the subject field.



To introduce the student to different practical applications of the subject content and to
enable him/her furthermore to apply their own knowledge in practise.



To enable the student
to analyse and solve both theoretical and practical problems in
the subject field.



To prepare the student to use the principles of the subject field in the design and
synthesis of practical flow systems.

EXIT LEVEL LEARNING
OUTCOMES

The aim of engineering

training is to equip learners with certain generic abilities, which they
will be able to use in practise. These abilities can also be described as the exit level
outcomes of this module. It is expected that learners will be able to do the following at th
e
end of his / her studies.

Outcome 1:

Identify, formulate and solve engineering problems both creatively and in
innovative ways;

Outcome 2:

apply fundamental and specialized knowledge;

Outcome 3:

design components and systems by means of structured and
unstructured
synthesis of knowledge and information;

Outcome 4:

apply methods of research in the planning of investigations and experiments,
as well as in the analysis and interpretation of data;

Outcome 5:

use appropriate engineering tools such as co
mputer software for calculations,
modelling, simulations and information systems as well as methods and
knowledge of the economy, business management, safety in the work place
and environmental conservation;

Outcome 6:

effectively communicate orally an
d in writing with technical as well as public
audiences;

Outcome 7:

have an awareness and appreciation for the impact of engineering activities
on society and the environment;

Outcome 8:

work effectively as part of a team in a multi
-
disciplinary envir
onment and take
the lead if necessary;

Outcome 9
:

be prepared to have a life long commitment to learning and being aware of
new developments in your area of learning;

Outcome 10:

realise the importance of professional and ethical conduct and be able to
take
responsibility in accordance with your knowledge and experience.


This module is structured in such a way that, although each of the above mentioned
outcomes aren’t dealt with in detail, it will have a direct impact on the actualisation of the
specifi
c module outcomes.



vii

At the completion of this module, students must be able to:



Apply the basic knowledge and principles of compressible flow, potential flow and
boundary
-
layer theory in order to solve fluid mechanics problems;



Make use of applicable e
ngineering tools such as the computer software Excel and
EES to solve flow problems and perform designs;



Analyse and interpret data obtained during practical sessions.

TEACHING PLAN

The planned learning process comprises the following components:

LECTU
RES



About
42

lectures will be presented during which the lecturer will introduce the practical
and theoretical aspects of the subject matter. Practical problems will also be
explained.



You, as the student, should see these opportunities as an open discu
ssion between
you and the lecturer during which you can use the knowledge and experience of the
lecturer to your full advantage.



You are invited to ask as many questions as possible to ensure that you understand
each point made during these sessions. Yo
ur questions are also the lecturer’s only
measure of your understanding of specific aspects of the discussion and will determine
whether the content must be dealt with again.



Taking hurried and unstructured notes in class will not be necessary. Copies o
f all
transparencies used during lectures will be made available
in advance
. You may make
copies of it and use it as core notes. Only additional notes can then be added during
contact sessions.

SELF STUDY



You will be expected to study new work further

in more detail and to master it on your
own time.



It is suggested that you use one evening per week per subject to master the new work
done in the previous week.



You may use your core notes, textbook and additional notes for this purpose.



You are al
so referred to specific, additional textbook exercises in the study component
of this study guide, which represent typical problems that you will have to solve during
evaluations. These exercises are chosen in such a manner that they cover all aspects
of
the module content. You should work through all of these problems.


viii

PRACTICALS



A maximum of two
practical
s

will be performed through the course of this semester to
illustrate certain aspects of the subject field.



One practical lecture presentation wil
l be held at the start of the semester.



The lecturer, as well as the practical assistants will be available throughout the
semester to provide further elucidation.



Your practical marks obtained for reports will form part of your participation mark (see
the

exposition of the formula for calculating your final mark in the module information
component of this guide).



It is every student’s own responsibility to ensure that all practical sessions are
attended. You must organise a repeat session with the demon
strator within 7 days of
being absent from any one of these sessions with a valid apology. No apologies will be
accepted at the end of the semester for earlier absences. Any problems concerning
the practical sessions can be discussed with the lecturer.

TUTORIAL CLASSES



E
xercise classes, of approximately 1

½ hour, will take place during the semester during
the scheduled classes.




You will get the opportunity to work on suggested problems in the presence of the
lecturer.



You should try to tackle as many

of these problems as possible during these classes
and immediately make use of and ask assistance of your lec
turer during tutorial
classes.



Potential tutorial test / exercises may be taken in during the tutorial class.

T
ESTS



Two

tests of approximately one

hour each will be written during the semester



It is important to note that all of the tests contribute to the calculation of the participation
mark as explained in the course information section.



These tests will test your basic comprehension of the work

done up till that point during
the semester. Your self
-
study and practise sessions will serve as preparation for these
tests.



These tests must also be seen as a method of feedback to yourself and your lecturer to
determine if the work done is really u
nderstood.



ix

WORK ASSIGNMENTS



You will receive
a maximum of
two assignments to complete through the course of this
learning area. These assignments must be completed on your own time.



Work assignments mainly consist of computer simulations and problems

addressing
the specific content of the learning unit.



You may work in groups (maximum of 3 members) in order to complete assignments
and your must preferably debate the content as much as possible.



Each group must submit their final attempt within the

time limit set on
day schedule or
e
-
fundi.



Marks achieved for these work assignments, will form part of your participation mark.
Please see the exposition of the calculation of the final mark in the course information
part of this guide.



Please Note: Gro
ups will receive a
zero

mark for the assignment if it bares any
resemblance with another group’s work!

DISCUSSION CLASSES



Two discussion classes will be held as final opportunity to discuss and attend to
problems in preparation of writing the final exa
m.

THE USE OF CALCULATO
RS DURING EVALUATION
S



The policy as set out in the yearbook of the Faculty of Engineering with regards to the
use of calculators will be strictly applied during all the tests and examinations

E
VALUATION PROCESS

EVALUATION OPPORTUNI
T
IES

Continuous evaluation of the student’s learning benefit will be done by means of the
following:



There will be
two

tests throughout the semester. Your test average for the semester
will be calculated as the average of
both
marks achieved.



A maximum o
f t
wo work assignments will be given during the semester.
Each of
these work assignments must be handed in, in order to receive acceptance to
write examination.

All the work assignments will count in order to determine your
work assignment average for th
e semester. You will receive a full memorandum for
each assignment with which you can assess your own progress. Dates for handing in
work assignments are not debatable.



A maximum of two practical experiments

will be conducted during the semester.

Eac
h
of these
practical experiments

must be handed in, in order to receive acceptance
to write examination.

All the
practicals
will count in order to determine your work
assignment average for the semester
.



Two final examination opportunities will be given d
uring the examination period.


x

EXAMINATION ENTRANCE

REQUIREMENTS

The following strict requirements apply to examination acceptance:



All work assignments

must be handed in.



All practical sessions

must be attended and all practicum reports (with no except
ion)
must be handed in. An average of at least 50 percent must be achieved for practical
assignments.



You must hand in
at least half

of the tu
t
orials which are asked during the semester



You must achieve a participation mark of at least 40 percent.

CALCU
LATION OF THE FINAL
MARK


Participation mark

/100

Exam mark

/100

Test average

/ 55

Work assignment average

/ 15

Practicu
m average

/ 15

Tutorials

/ 15


Final mark / 100

PP∙0.4+EP∙0.6




xi

ABSENCE



Class tests and the examinations will be written on the scheduled times as announced,
unless arranged otherwise.



If you are absent without a valid pre
-
arranged excuse, sick tests will only be p
ermitted
in exceptional cases, on the condition
as highlighted in the yearbook of the faculty of
engineering. You will receive a zero (0) mark if the faculty rules are not met.



Personal problems (death of next of kin
,

serious illness

or similar
) will be h
andled on an
individual basis. You must, however, make the necessary arrangements beforehand
and not assume that the excuse will be accepted.



Absence from scheduled classes without pre
-
arrangements will be at your own risk.



All tutorials and assignments
must still be handed in on time. For students with a
serious illness an exception could possibly be granted.
You must, however, make the
necessary arrangements beforehand and not assume that the excuse will be accepted.



Any work treated during your absen
ce will be considered completed and it remains
your responsibility to catch up. If certain information has been given in your absence
(including any announcements or arrangements made in class) it is your responsibility
if you are affected adversely.



A si
ngle sick test will be written in the last week of lectures by all who have missed one
of the semester tests due to valid reasons. It is your own responsibility to establish
with the lecturer the time of the sick

test. If you a valid accepted excuse and
you did
not write the sick test, you will receive zero (0) for the test.


xii

MODULE FORM

Module code:

INGM321

Prerequisites:
INGM312

Module name:
Fluidmechanics II

Co
-
requirements:
None

Module credits:
8

Lecturer:
Mr. W.H. Kaiser

CESM:
08.10


Module objec
tives:
To equip the student with the basic knowledge of compress
ible flow, boundary
layer flow
and measuring techniques in fluid mechanics. This module follows on MEGI 312 Fluid
Mechanics I and serves as further preparation for the modules in Heat Transfer

and Thermal Fluid
System Design.


Module outcomes:


One dimensional compressible flow; Potential
flow; Border layer theory; Measuring techniques.

Assessment criteria:

The student will be able to:

-

To apply the basic knowledge and principles of
compress
ible flow, potential flow and boundary
layer theory to solve problems.

-

Use the applicable engineering tools such as the
software package EES, and the specialist flow
network solver Flownex to solve problems.

-

Using the observed results of practical work

to
analyse and interpret data.

Assessment methods and weights:

Class tests
:
22
%

Assignments
:
6%

Practicum
:
6%

Tutorials
:
6%

Exam
:
60
%



ECSA Exit Level Outcomes:

This module contributes towards the development of the following ECSA ELOs:

(ELOs marked
* are assessed at Exit Level Outcome)

ELO1: Problem Solving

*
ELO2: Application of scientific and engineering knowledge





xiii

Detailed Content:

One dimensional compressible flow: The Mach cone; Isentropic compressible flow through orifices;
Stagnation charact
eristics; Subsonic and supersonic flow; True flow through orifices; Fanno and
Rayleigh lines; Normal shocks; Oblique shocks; Adiabatic flow through ducts with friction; Non
-
viscous flow through ducts with heat transfer.

Boundary layer theory: Conservation
equations for the maintaining of border layer flow; Border layer
thickness and displacement thickness; Blasius’ equation; Von Karman momentum integral equation;
Laminar border layers and wall friction; Transition to turbulent border layer for a flat plate;

Turbulent
border layers and wall friction; Flow around curved surfaces and separation; Drag effects on bodies.

Measuring techniques: Pressure measuring; Velocity measuring; Flow tempo; Measuring of free
surface flow; Measuring of viscosities.

Knowledge a
reas

Mathematics

Basic sciences

Engineering
sciences

Design and
synthesis

Computers
and IT

Complementary
studies

0

0

8

0

0

0


Prescribed textbook(s)
:

Munson, B R, Young, D F and Okiishi, T H, Fundamentals of Fluid Mechanics, Fifth

Edition, John Wiley &
Sons, USA, 2006.


Module Administration
:

Weeks per semester

14

Duration of lecture period

0.83

Number of lectures per week

2

Number of tutorials per week

1

Hours of practical

per semester

2

Other contact time per semester (h)

0

Other non
-
contact ti
me per semester (h)

8

Total number of hours per semester

82


xiv

WARNING AGAINST PLAG
IARISM


ASSIGNMENTS ARE INDIVIDUAL TASKS AND NOT GROUP ACTIVITIES
.
(UNLESS
EXPLICITLY INDICATED AS GROUP ACTIVITIES)

Copying
of t
ext from other learners or from other sources (for instance the study guide,
prescribed material or directly from the internet) is
not allowed



only brief quotations are
allowed and then only if indicated as such.

You should
reformulate

existing text and

use your
own words
to explain what you have
read. It is not acceptable to retype existing text and just acknowledge the source in a
footnote


you should be able to relate the idea or concept, without repeating the original
author to the letter.

The aim
of the assignments is not the reproduction of existing material, but to ascertain
whether you have the ability to integrate existing texts, add your own interpretation and/or
critique of the texts and offer a creative solution to existing problems.

Be warn
ed: students who submit copied text will obtain a mark of zero for the
assignment and disciplinary steps may be taken by the Faculty and/or University. It is
also unacceptable to do somebody else’s work, to lend your work to them or to make
your work avail
able to them to copy


be careful and do not make your work available
to anyone!




Study unit 1


1


1

ONE
-
DIMENSIONAL
COMPRESSIBLE FLOW




(9 lectures)

Aims:

To introduce the student to the properties of compressible flow and to the theory and
application of it to one
-
di
mensional flow.

Content:



Definitions and terms



Revision of the ideal gas relation equations



Propagation of an elastic wave



The Mach cone



Isentropic compressible flow through nozzles



Stagnation properties



The difference between subsonic and supersonic flow



Isentropic flow of a perfect gas in terms of the Mach number and stagnation properties



Actual flow through nozzles at design conditions



Fanno and Rayleigh lines



Normal
-
shock relations for a perfect gas



Oblique shocks



Actual flow through nozzles and dif
fusors



Adiabatic flow through a duct with friction



Nonviscous flow through a ducts with heat exchange

Study unit 1


2

OUTCOMES:

You should be able to do the following at the end of this study unit:



Know and reproduce (write down) the definitions of the speed of sound
, the Mach
number, subsonic, transonic, supersonic and hypersonic flow.



Know and reproduce the definitions of the specific heat capacities.



Understand and prove the relation between the specific heat capacities and specific
gas constant.



Understand and exp
lain the term isentropic flow.



Know and reproduce the relation between the speed of sound, the specific heat
capacities and the gas constant, as well as the temperature.



Understand and explain the difference between sound waves and shock waves.



Understan
d and explain by means of sketches how the Mach cone is formed.



Design a theoretical isentropic nozzle profile for compressible flow between two given
pressures.



Understand and explain what is meant by stagnation properties.



Understand and explain how th
e pressure and speed vary in subsonic and supersonic
nozzles and diffusors
.



Understand and explain the relation between the throat area and Mach number in a
nozzle.



Design isentropic nozzles using the one
-
dimensional isentropic relations in both the
equati
on and table format.



Understand what is meant by nozzle efficiency and use it in the analysis of the actual
nozzle flow at design conditions.



Understand and explain what is meant with the reheating factor.



Understand and explain the origin and form of

the Fanno and Rayleig lines.



Understand and explain the relation between the Fanno and Rayleigh lines and the
normal shock equations.



Analyse the conditions over normal and oblique shocks by using the normal shock
relations in both equation and table f
ormat.



Understand and explain the cause and shape of shocks at the front of supersonic
projectiles.



Understand and explain the functioning of converging as well as converging
-
diverging
nozzles.



Analyse flow problems in Fanno and Rayleigh flow by using

equations as well as the
Fanno en Rayleigh line tables.

Study unit 1


3

Evaluate your knowledge:

Can you:



Expl
ain how the Mach cone is formed



Design a nozzle by using one dimensional isentropic relations



Explain how and why a shock wave ap
pears



Use normal shock relation
s as well as one
-
dimensional isentropic relations to calculate
the conditions in
a convergent
-
divergent nozzle



Explain wha
t happens when a nozzle chokes



Solve the flow in a d
uct for Fanno and Rayleigh flow

Exercises:

The exercises will be published on e
-
fu
ndi.

Study unit 1


4



Study unit 2


5


2

BOUNDARY
-
LAYER THEORY






(4 lectures)

Aims:

To introduce the student to the fundamentals and practical application of boundary
-
layer
theory.

Content:



Introduction



Conservation equations for boundary
-
layer flow



Boundary
-
layer thickness and d
isplacement thickness



Blasius’ equation



Von K
á
rm
á
n momentum integral equations



Laminar boundary
-
layer and wall friction



Transition to turbulent flow for flow over a flat
-
plate



Turbulent boundary
-
layer and wall friction



Flow over curved surfaces and separ
ation



Drag force on bodies

Study unit 2


6

OUTCOMES:

You should be able to do the following at the end of this study unit:



Understand and explain the relation between potential flow and boundary
-
layer flow.



Understand and explain the relation between laminar and tur
bulent boundary
-
layer
flow.



Know and reproduce the assumptions under which the boundary
-
layer equations are
derived.



Conduct an order of magnitude analysis on the mass conservation and Navier Stokes
equations and explain how to derive the simplified mas
s and momentum conservation
equations for boundary
-
layer flow.



Understand and explain how potential flow and boundary
-
layer flow analysis can be
used together to analyse the complete flow field around a body.



Know and reproduce the definition of bound
ary
-
layer thickness and displacement
thickness.



Understand and explain the practical meaning of boundary
-
layer thickness and
displacement thickness.



Know and reproduce the conditions for which the Blasius equation is valid.



Apply the Blasius solutions for

boundary
-
layer thickness and displacement thickness in
practical problems.



Use the Von K
á
rm
á
n momentum integral equation to derive solutions for the boundary
-
layer thickness, displacement thickness, local wall friction coefficient and global wall
frictio
n coefficient in simple laminar and turbulent flow over a smooth plate.



Calculate the wall friction drag on simple bodies with the aid of the smooth plate
approach.



Understand and explain the cause of flow separation on a body as well as the
mathematica
l criteria indicating the flow separation point.



Calculate drag force on bodies by means of empirical values for the drag force
coefficient.

Evaluate your knowledge:

Can you:



Explain the difference between laminar and turbulent boundary
-
layer flow?



Ide
ntify and use the correct equations to solve laminar and turbulent boundary
-
layer
flow?



Calculate the wall friction on simple bodies?



Calculate the drag force on bodies?

Exercises:

The exercises will be published on e
-
fundi.


Study unit 3


7


3

MEASURING TECHNIQUES






(Self study)


Aims:

To equip the student with basic knowledge of the most important measuring techniques
being applied in fluid mechanics problems.

Content:



Measuring pressure



Measuring velocity



Measuring the flow rate



Measuring free surface flow



Mea
suring viscosity

OUTCOMES:

You should be able to do the following at the end of this study unit:



Know and explain the functioning of the piezometer, pitot tube, manometer and
Bourdon pressure meters as well as derive and apply all the relevant theory.



U
nderstand and explain the functioning of the anemometer and the static pitot tube for
measuring velocity. Students must also be able to derive and apply the related theory.



Understand and explain the functioning of nozzles, orifice plates and Venturi mete
rs in
the measurement of volume flow in incompressible and compressible flow as well as
derive and apply the relevant theory.



Understand and explain the functioning of a weir in the measurement of the volume
flow for free surface flow as well as derive and

apply the relevant theory.



Understand and explain the functioning of a concentric cylinder viscosity meter as well
as derive and apply the relevant theory.

Study unit 3


8

Evaluate your knowledge:

Can you:



Explain the functioning of the pitot tube, orifice plate or Vent
uri by me
ans of a
schematic presentation



Propose the correct measurement equipment for
a given measuring requirement

Exercises:

The exercises will be published on e
-
fundi.



Formula sheet


9

FORMULEBLAD / FORMUL
A SHEET

Algemeen / General:


Mach k
onus / Mach cone:


1D isentropiese verwantskappe / 1D isentropic relations:







1D normale skok
ke / 1D normal shock:






Fannovloei / Fanno flow:







F
ormula s
heet


10

Rayleighvloei / Rayleigh flow:








Grenslaagteorie / Boundary layer theory:

Von Karman momentum:




Kubiese snelheidsprofiel / Cubic velocity profile:







Laminêre vloei / Laminar flow:




Turbulente vloei / Turbulent flow:






Re
crit

320000

500000

10
6

3 x 10
6

A
BLT

1050

1700

3300

8700


Formula sheet


11

Vloeimeettegnieke / Flow measurement techniques:



F
ormula s
heet


12


Formula sheet


13

F
ormula s
heet


14


Formula sheet


15


F
ormula s
heet


16