College aantekeningen Advanced fluid dynamics (ME45042) Fluid Mechanics, ISBN: 9780124059351
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Course
Advanced fluid dynamics (ME45042)
Institution
Technische Universiteit Delft (TU Delft)
Book
Fluid Mechanics
Summary of the Advanced fluid dynamics (AFD) course from the TU Delft. Corresponds with the Fluid dynamics book from Kundu. Most of the first 5 chapters are covered.
College aantekeningen Advanced fluid dynamics (ME45042) Fluid Mechanics, ISBN: 9780124059351
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Technische Universiteit Delft (TU Delft)
Maritieme Techniek
Advanced fluid dynamics (ME45042)
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Advanced Huid dynamics
College 1
The Huid mechanica approach
a) Non Dimensionaal Numbers
-
(i) Physik Principles should be Independent of arbitrair Chosen dimensies
y
&
quantities.fm: h : :)
( II) Ome can be describe the behaviour of a physical system in terms of
parameters with no dimensies =
nondimensional parameter ( t )
(III ) Why are nondimensional parameters important in AFD ?
because they can quantify the
magnitude of computing physical
relativa
consider a
Physik System : we can describe Lexpress its behaviour in terms of :
number of
"
Physik parameters
''
•
a m
( µ f. l ,
,
u .
V. 9 .
. . .
)
these parameters include independent units
" "
•
m n
(M ,
S
, kg ,
K . . . . )
The behaviour of System can be described in terms of
''
m -
n
"
Independent
non -
dimensionaal Numbers IT , Th . .
_
Tm - n
Corolla : we ( alt Ip f (IT )
r D= m N Ir , Tip
- =
- . . - i
, , .
,
in particular If p =/
,
The I ,
=
corset .
Example :
maart
GL f?
l f 1-
Physik parameters :
-4 l f
9
m -
: M
, , ,
m.sk t Ig E '
2- Independent units
3-
Dynamics can be written in terms of a- 3 :
kg ,
M ,
S
M -
n = 4-3=1 non -
dimensionaal group
{
[m) :X = 0 D= -
x = É 8=0
I, =
ga .
f? mr fs .
[ s) : -
2x -
5=0 x =
-
E
( m.54.ms kg
' '
>
.
5 kg) : 8=0 S =
I
I, =
ff
from Corolla
r that
: I
,
-
_
cont .
→
FNV (f = # VE )
ijij
, Advanced Huid Dynamics
College 2
Sealing Analysis
• Determine the interdepandance of between physical parameters b
readning
based on
Physik intuition (
grounded in the
knowledge of
lans of
Physics relevant to the problem)
Etam
Warned : f
|
acceleratie
9h (
µ m mg
-
in ↳
°
Find a
scoding for the accelerator
↳• for er l
scoding
~
position
↳• f. f
scoring for
vetocity
-10 ~
↳*
sacting for acceleratie in f- ff
'
l f rent
µ g
-
- -
f n
#
Example
III. f ne viscose
I
→
Find dimensionaal for
a non -
scoring Law
drug
i) Dimensionaal
Analysis
1- Relevant physical parameters : U
,
A
,
µ P , ,
D
t t tegen
'
M = 5 ms m
2-
Independent units
in =3
Buckingham
dimensionale
3- I theoren : P =
5 -
3=2 non -
tof ÷ En ~
.
~ ND
,
=
↳ ←
Draag
COEFFICIENT
ijijij
, Tk t Re m'n
'
Reynolds
'
5 mi
in #
←
= =
m .
^ number
ft )
at tpg)
t ,
=
=
Co =
#Re)
Ii)
scoding Analysis
ASSUME sphere large vetocity U:
is Maring at
•
↳
assume effects of Velo
City
are
negligible
D Ps of ✓ via
t
N -
→ =
↳ ~
constant
/
↳ 42
Assume very smalt vetocity dominante
a
viscosity
•
D. ~
visgous
stress -
arr µ -
u -
a
µ I
M
- -
Troista
Cont
Re
from find that Red Co
soaling Analysis 1 ~
we :
,
constant
Red '
,
Co ~ Ee
(D= f (Re)
Co Ret
} for Large
=
a = 0 Re
× = -
I for smalt Re
109 ( Co )
=
109 (Ret )
109109 Plot t
log ↳ =
x
109 Re
÷
X X
1094 y
=
¥ "
IJ
, Advanced Huid Dynamics
College 3
Notaties and other mathematica reminders
.fi/: :
notaties fuII notatie index notaties
Nath notatie in Class (Kander)
Scot
Ranko
p µ PT P µ PT P µ PT PAPT
-
Vector
§)
U
→
Rank 1 U -4 U Ui ii. 2,3
Lto simpele
e-
÷:÷ ÷
dinge n '
Ranko div Ü
Ittf 3G I. k
JA
ta p
Ranko ⑦ 4)
die
Idiots IIY
t
dia
product À XE à tb-flb.br) a- b- aibj
nam
÷! :÷ :
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