chp02_aero fundamental and type of flow

8/8/2019 Chp02_aero Fundamental and Type of Flow

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CHAPTER 02

AERODYNAMIC FUNDAMENTAL

AND TYPE OF FLOW


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3/65

)()( dxdzdydy

dppdxdzp

+=

)(dxdydzdydp=

dxdydz)(=

!

0)()(=

dxdydzgdxdydzdy

d

!"#!"#

dyd = "#


4/65

$

=

2

1

2

1

h

h

P

P dygdp

hPP == )( 1212

% ' " !

1122ghPghP +=+

constant=+ gP

""

"(


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)*!

)1)()((12

PP = "+

$%""%"


6/65

,--!

===1

2

2

1

2

1

12

h

h

h

h

P

PgdygdydpPP

.-!

=

1

2)1(

h

h gdylF

/!,

&-

$ 0 $

"1


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&'(&'(

(2- -322-45

-

-$ &222"(66#' 6#278+"# $ -9(


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&2

[ ]3

21.46

slug/ft0.002377

)0(1071002377.0

=

=

)!

3

33

ft14,137

157

22

3

4

3

4

=

== r

,&-!

lb1082

137,14002377.02.32

=

== V


9/65

mW ==

2

ft/s11.4

8.24

282

)2.32/800(

8001082

=

=

=

=m

Wa

.!

:,&;& 322,&-$)--

3slug/ft00176.0137,142.32

800=

==

gV


10/65

;


11/65

''''''

/57

# ="

)$"

"$%"


12/65

*-


13/65

> !

cRA R toparallelofcomponentforceaxial tolarperpendicuofcomponentforcenormal

;-

sincos AL =

cossin AD +=

"8

"6


14/65

;!

surfaceupperonApointrandomatosurfacebodythealongmeasuredL.E.fromdistance=us

surfaceloweronBpointrandomatosurface

bodythealongmeasuredL.E.fromdistance=l

s

$)$%+,-%"


15/65

*-?- !

sincos'uuuuu

dsdspdN =

cossin'uuuuu

dsdspdA +=

"3

"@

"

$%"


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A!

sincos'lllll

dsdspdN =

cossin'lllll

dsdspdA +=

!

++=TE

LElll

TE

LEuuu

dspdspN )sincos()sincos('

+++=

TE

LElll

TE

LEuuu dspdspA )cossin()cossin('

"#2

"##

"#"

"#(


17/65

/


18/65

A!

lllllllydspxdspdM )cossin()sincos(' +++=

--!

++++

+=

TE

LElllll

uuu

TE

LEuuLE

dsypxp

dsypxpM

])cossin()sincos[(

])cossin()sincos[('


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SqC

N

=:tcoefficienforceNormal

Sq

A

CA

=:tcoefficienforceAxial

SlqC

M

=:tcoefficienMoment

."7D!

cq

Lc

l

'

cq

Dc

d

'

2

'

cq

Mc

m

;& #&


20/65

(.(.

'/ '.

--7

-


21/65


22/65

!"#$%!


23/65

&'( &'(

!


24/65

&)*&(''+&

!

"!#!

#!$%

%%%


25/65

!


26/65

(#,!#-"

-!#


27/65

)')&&)*).))')&&)*).)

'&

&

#$!""#


28/65

'

() *

("


29/65

()*


30/65

.).)

&+ ,

' +)

(-

AdVn

)(Volume =

.) +

,##$

!$)


31/65

(-

AdtVn

)(Mass =

.-

AVdt

AdtVm

n

n

==

)(

($+ -

areatheto velocityflowofcomponentdensityArea norma

/!0

/!1


32/65

"-

nV

A

m==

fluxMass

+ ",

22

#$!"#

/!3


33/65

+-

4*

)

5

65&

78$/!3* -

dSV =dSVn

(8$////-

=S

B dSV

//

//

//!


34/65

(8$//// ) -

= V dVtC

9-

= VS dV dSV

-0dSV =+

SV

dV

t

&$&$

///

///


35/65

6$-

0=+

)( V

t

7$-

S

dSV

- 0=)(

V

//

//:

//;

&&& .)&&& .)


36/65

&&&.)&&&.)

4


37/65

77",

6,

>? )

*,*

9-

+= V S viscouspdsfdV

((

22

))

//1


38/65

+8$//0,

SsurfaceacrossvolumeGcontrolofoutmomentumofflowNet

-

Vinsidepropertiesflowofnsfluctuatio

HunsteadytoduemomentumofchangeofrateTime

.-

=S

VG )( dSV

-

=

V

dVt

H V

//3

//3

/

/!


39/65

*-

HGmVdt

+=)(

+=

VSdVV VdSV )(

94


40/65

78$/-

++=+

V Vviscous

SV FpfdVpdVVdVt )( dSVV

8$/:$.$$-

kji wvuV ++=(,

viscousxx Ffx

puVt

u)()(

)(

++

=+

viscousyyFf

y

pvV

t

v)()(

)(++

=+

/:

/;

/;


41/65

viscouszzFf

pwV

t

w)()(

)(++

=+

' 7 55$,)( 0

=SS

pdSV)( dSV

-

x

puV

= )(

y

pvV

= )(

z

pwV

= )(

/;

/=

/0

/0

/0

'+ .)'+ .)


42/65

'+.)'+.)

22 8-

7-

dew=+

@-

gssurroundinfromvolumecontrolinsidefluidtoaddedheatofrate

1=B

volumecontrolinsidefluidondoneworkofrate2 =B

volumecontrolthroughflowsitasfluidofenergyofchangeofrate

3=B

/1


43/65

9-

321BBB =+

&-

dVqV

=heatingvolumetricofRate

+-

+=V

viscousQdVqB 1

/3

/:

/:!


44/65


45/65

7-

SpdSV

Sonforcepressuretodue

V)(insidefluidondoneworkofRate =

forcesbodytodueV)(insidefluidondoneworkofRate =

V

fdVV

'-

++=S viscousV

WdVVfdSpVB )(2

("6-

surfacecontrol2

)(acrossenergytotalflowofrateNet2

+=

S

VedSV

/:/

/:

/::

/:;


46/65

variablesfield-flowofvariationstransienttodueVinside

energytotalofchangeofrateTimedV

Ve

V

+

=

2t

2

++

+

= SV

VedV

VetB 2)dSV(2

22

3


47/65

++

+

=

+++

SV

V S V

viscousviscous

VedV

Ve

t

WdvpQdVq

2)dSV(

2

)Vf(dSV

22


48/65

!"#$#%&%"#%'%$(

) *+ %,-

*+ .-

!"#$#%#!&"'%"#%"&"

/ ,%##


49/65

0#"$"+%#%

1 %+$"##

),,,,( = acVfR

$2%&+$+

0),,,,,( = acVR

3#++(

timeofdimensions

lengthofdimensionsmassofdimensions

=

=

=

t

lm

4

15


50/65

6%78/7+"##++%"$%"

$%"+(

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11

1

3

2

=

=

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=

=

=

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lc

ltV

mlmltR

6%9 89 $$%"$%


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0),,(3212=f

3

),,,(

),,,(

),,,(

53

42

31

=

=

=

acVf

cVf

RcVf

*+1+(

RcV ebd

=1

1)

1

1"

1%

1/


52/65

3" :$"#

[ ] ( ) ( ) ( ) ( ) 02131

== mltlltml

ebd

*+

01=+d013 =+++ ebd

02 = b


53/65

3%$%% #%$#+#


54/65

= 8; ) 8)8)


55/65

& 85 8; )85


56/65

$#6%

),(Re,),(Re,

),(Re,

12

11

10

=

=

=

MfCMfC

MfC

M

D

L

/

1


57/65

!"#!!"#!


58/65

!

!$%


59/65

!

"

thenand TaT

24

1

1

1

2

1

2 ===T

T

T

T

21

2

1

2 ==T

T

a

a

1

1

1a

VM =

1

1

1

1

1

2

2

222 M

aV

aV

aVM ====

12 MM =


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"#$%

$

1

111

1Re

V=

1

111

2

222

22

)4)(2)(4(Re

VV==

1

1

111 Re==

dV

12ReRe =

!"#!!"#!


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&"'('$))*+*** (, -*#$.'('

(*

#&/$

!0

1%

2,1, LLCC =

2,1, DDCC =


62/65

2

12 ReRe =12 MM =

1

1

1

1

1T

V

a

VM =

2

2

2

2

2T

V

a

VM =

1

1

2

2

T

V

T

V=

mph5.577390

430550

1

2

12===

T

TVV

1

111

1

111

1Re

T

cVcV

=

2

222

2

222

2Re

T

cVcV

=


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2

2$343

2

222

1

111

TcV

TV =

1

2

2

1

2

1

1

2

T

T

c

c

V

V

=

2

1

2

1

T

T

V

V=

502

1

1

2 ==cc


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5647#8/9

2%

1.55390

43050

11

22

1

2 =

==

T

T

P

P

2

12lb/ft836,236.4321.551.55 === PP

! 4,%

atm26.112116

836,232

==P


65/65

!&'#!()!&'#!()

chp02_aero fundamental and type of flow

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