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ME2351 Gas Dynamics and Jet Propulsion -Lecture Notes
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m

A

. D

' . I ,

.

F , . H,

. I

.

M C

() A

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m ( F 1). I ,

M M ;

M = 1/M

F 1. M

I , ( ) //

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m

.

4.1F

I

. A

. T

: O,

. T,

.

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m

E '

. I , . I

. I

M . H,

%1 . F,

, . F

, . E

(4.16)

(4.17)

(4.18)

T ( )

(4.19)

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mF ,

(4.19)

.

T M M=1.

(4.20)

(4.21)

(4.22)

T

(4.23)

T

(4.24)

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C .

T . T

F (4.4). T

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' . T,

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D , ,

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m(4.26)

T

(4.27)

F (4.25) (4.27)

(4.28)

D ( ), ,

( )

(4.29)

O / (4.26)

(4.28)

(4.30)

R (4.30) , , ,

P/

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m(4.31)

R (4.31)

(4.32)

O

(4.33)

E (4.33)

. I (4.33)

(4.34)

B

(4.34). T (

). N,

M . T

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m . I

M . I M

. I M . F

F . A

(

). C, ( )

. N

.

F , . F

.

T .

F M=1 ( )

. S

.I M=1

. H, , M =1 . I

,

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m ' .

T

(4.28) .

(4.35)

F (4.35) (

). H .

F , , ,

( 4.36).

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I (4.354.36),

. T, (

).

T ( )

(4.37)

T, .

T M

. D

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m (4.9),

(4.38)

(4.38)

(4.39)

T (4.39), (4.37), (4.29), (4.26). N, (4.33) '

.

T

(4.37)

(4.33). F (4.39)

(4.37)

(4.40)

C (4.40) (4.33)

(4.41)

T ,

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m(4.42)

(4.42) (4.41)

(4.43)

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mT M

E (4.43) ()

(M ). I (4.43),

. T,

M . F

M . I M

. T M=

1 . T

. T

.''

A, M=1

. I , :

, M ,

, M

( F (4.5)).

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mT

. H

( ). F

, M . M

, . F,

.

I

F T (4.2) F (4.3) , PGDC,

1.4

/0 /0 /* /0 /*

0.886393 0.864201 0.694283 1.01155 0.6 0.606928 0.531054

.

T

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m M A (

. T, A

.

A ( ) 1.4

/0 /0 /* /0 /*

2 0.555556 0.230048 1.6875 0.127805 0.21567 0.593093

P B

T M 1.8137788

. T ''

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m

T M B . T

T (4.2) PGDC . T

: M = 1.6265306 M = 0.53884934

B . T

M=1.

/* 1.4

/0 /0 /* /0 /*

0.538865 0.945112 0.868378 1.27211 0.820715 1.04404 0.611863

1.62655 0.653965 0.345848 1.27211 0.226172 0.287717 0.563918

()

O

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m(4.44)T ,

. T M

,

. T

( ). I (4.44)

(4.45)

E M (4.45)

(4.46)

I (4.46)

. T . I

M=1

(.. , ) . H (4.46)

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m(4.47)S , (4.47)

(4.46)

(4.48)

E (4.48) M .

T

(4.47) M . C M=1 .

(4.49)

F ,

(4.50)

T ( ) ,

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m(4.51)E (4.51) F' F

. I F'

F' N.

(4.52)

T F' (F)

(4.53)

F' (4.47)

(4.54)

M=1

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m(4.55)

I , ,

(.. E ) . A

. S,

. T

( ). I

(4.76)

S (4.76)

(4.77)

I (4.77) B'

(4.78)

T, 2

(4.79)

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mT 2 , (4.80)

O

(4.81)

T (4.78)

(4.82)

S (4.82)

(4.83)

O (4.83)

(4.84)

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mA ( )

(4.85)

(4.86)

C (4.86) (4.84)

(4.87)

T

(4.88)

T , , ( M

) : M=1

. H M=1

. A

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m . T

.

T (4.84)

(4.89)

E (4.87)

(4.90)

S

(4.91)

F,

(4.92)

T

(4.93)

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mF , . I .O . A F (4.6).

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m 4.6 M N

F F 4.3 ' M=1 .

T

. I

.

T

(4.94)

E (4.94)

(4.95)

I . T

. T,

(4.96)

O , F

(4.7()).

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m

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mC

T

I . I

(

) . (4.89)

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m

(4.97)

N , , . I

. A,

(4.98)

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C

( )

F

. T '

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m . T

( (1)). I

( (1)) ( '

). I

20. T M

F (4.7()). I

3% ( ). A F

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B (4.100) F

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T,

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(4.7()).

T : . T

. T

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m

(4.101)

(1). T

(4.102)

:

(4.103)

. (4.88)

, .

F (4.8)

,

. T

.

O I . T

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mI ,

. T

F (4.9). T

(4.104)

T . T

(4.105)

C (4.104) (4.105)

(4.42)

(4.106)

R (4.106)

(4.107)

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m 4.S I

E (4.107) M

, . H,

M ,

. D M

. T, I

(4.108)

I I ( M=1 )

(4.109)

T I

(4.110)

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mT (4.107)

M . H,

(4.111)

T

S ()

(4.7)

P I . T

. A ,

I . T

(4.112)

(4.113)

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mS (4.86) (4.113)

(4.114)

A ( M=1 ) ( )

(4.115)

T

. T,

(3.19). D (3.19) (3.19)

(4.116)

A, G' (4.27)

. S

. T

,

(4.117)

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mT M

,

(4.118)

F,

(4.119)

E (4.27) (3.19)

(4.120)

T

(4.121)

A . T

. T

(4.122)

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mN, . (4.121)

(4.122)

(4.123)

S (3.19)

(4.124)

F

(4.125)

F

(4.126)

I . T

(4.127)

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m ( ) . T,

(4.128)

F

(4.129)

T M (3.34) M

(4.130)

I (4.120)

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m(4.131)T (4.131) B'

(4.132)

A

(4.133)

I C (3) (3.33)

(

).

(4.134)

(4.135)

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mT (4.136)

A

(4.137)

F'

(4.138)

F'

(4.139)

T

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m(4.140)

(4.141)

T , (4.131)

(4.142)

T 1. N

(4.143)

T M

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m(4.144)F M

(4.145)

T M

(4.146)

(4.147)

T

(4.148)

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m(4.149)

T M

(4.150)

F

(4.151)

PARTA

NITI BASIC CONCEPTS AND ISENTROPIC FLOS

1 S ?

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mC

, .., .

E: G,

I .

E: L

2 ? G .

T

= 0. T

.

1 + 12 = 2 + 22

3 E M M ?

M : T

M .

M : T M

(

) M

4 D .

T () = , C = C,

.

5 D M ?

T M .

M = I / E

I () ().

M = /

6 D * = 2 C (T T*)1/2

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mT M .

M = */*; * = * = 1

CT = CT* + *2

T, * = 2 C (T T*)1/2

7 M* M ?

I M M

8 D ?

N:

I .

D:

I

9 ?

T . T

. A

.T

. A M=1.

10 C .

T TS .

11 D M M ?

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m (M>1). T

3, 2, 1 S . T .

T S

M C

A M M .

=

12 M N ?

I , ()

B .

+. . .

13 D .

C

, .., .

E: G, 14 M ?

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mM

.

15 ?

T

.

16 D .

I

.

(SI )

17 A (=1.4, R=287 J/K) 420 K . D .

18 ?

19 .

I = 0. T

20 D .

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mM

.

21 E .

T

.

(..) F () .

22 D .

I ,

, .

23 D .

T

.

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m

1) D

/ 1 + = = / 1 =

.A ( =1.4, =287 J/ ) 400

.D:

1. 400 (2)

2. . (4)

3. . (4)

4. . (4)

5. . (2)

2) , 2.45 ,

26.5 C 1.4 . I 2.5

( =1.3, =0.469 J/ ). (16)

3) A ( =1.4,=287.43 J/ ) 300 ,3.45

150

/ 277 ,500 . A :

1. , (4)

2. , (4)

3. , , (4)

4. . (4)

4) A 800 / 10,000 (=223.15 ,=0.264 ).

. I

0.36 () () ,

. (16)

5) A (C =1.05 J/ , =1.38) 1 =3*10 5 / 1 =500

200 / 30 . C , ,

, ,

. (16)

6) ()

=1.4, / = 1 + + 1/40 + . (8)

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m()

( =1.4) 27.5 . (8)

7) A 300 / , 1.0 290 .

=1.4 =287J/ :

1) , (4)

2) , (6)

3) . (6)

8) A 15 30 .

T

P , 0.69,340 180 /

. D

1) , (4)

2) (6)

3) . (6)

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9) A 2.0 .A

0.69 310 .

1000.D

1) , , (4)

2) A , (4)

3) , (4)

4) . (4)

10) A =6.91 =325

0.98 .I 3600/ :

1) , , , (6)

2)E , , (6)

3) . (4)

11) A F21

10 4 .

500 /

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m A ,C =1.025 J/ , C =0.735 J/ , F 21 ,C =0.785

J/ , ,C= 0.675 J/ .

? (16)

12) D :

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*/ =(2/+1 +1 /+1) (8)

13) A 300 / , 1.0

290 K. T =1.4 R =287J/K K :

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2) (6)

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14) A 15 30 .

T

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2) (6)

3) . (6)

A , =1.4,C =1.00 KJ KK.

15) A 2.0 .A

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1), , (4)

2)A , (4)

3) , (4)

4) . (4)

16) A =6.91 =325

0.98 .I 3600K/ :

1) , , , (6)

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m2) , , (6)

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(16)

18) D :

A/A =/ (1 ) (8)

*/ =(2/+1 +1 /+1) (8)

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C ( F (9.1)). I

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(

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(9.2)

O

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I .

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I

(9.6)

O

(9.7)

I

.

(9.8)

I F

:

(9.9)

B (9.2) (9.10) (9.6)

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m(9.10)

D (9.11) ,

(9.11)

.

(9.12

B . B

(9.13)

(9.14)

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m (9.14) (9.11)

(9.15)

B (9.16)

(9.16)

I ( ) M

(9.17). D ((9.2))

(9.17)

(9.5)

(9.5)

(9.18)

D M (9.14) (9.14)

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E (9.17), (9.18), (9.19), (9.20), (9.21) .

(

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(9.24)

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mR (9.25) (9.25)

A

(9.26)

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(9.27) (9.18)

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(9.30)

.

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D,

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I (9.25)

(9.35)

A

(9.36)

B (9.36)

(9.37)

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(9.39)

I

(9.40)

(9.41)

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m(9.42)

(9.43)

(9.40) (9.44)

(9.44)

A (9.45)

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F (9.2)

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ME2351 Notes