prof. dr hab. in . Andrzej Prystaj dr hab. in . Krzysztof W. Ksi y ski IIiGW PK: Kraków 2010

!

"

#

$

%

&

'(

M → ∞ λmax = [(k + 1)/ (k − 1)]1/2

λmax = 61/2 → v max = 2,5 vk

+

,

&

# %

) *#

%

) %

'

'

d( x) d( x) x

+

,

-

'

.

(M2 − ) d v v d A 1

=

d x

A d x

/

0

,

M < 1:

v( x) ~ 1/ d) 0

M > 1

v( x) ~ d) v

0

d

M = 1

vk ≡ d min vk

&

0

&

d = const M = 1

v = const

1%

%

%

&

'

&

'

0

'

) &

' )

%

0 &

'

2 &

p

p

w = pa

o

v = 0

v

vo = 0)

%

v > vk

v < vk

'

"

-

$ p ≡

w

pa

0" 3

$

0

0

!

" 3

4

3

$

0

&

0

%

&

vo = 0 → po) ρ o To %

(

%

&

kp=1,4:

k

1,4

2

k −1

2

1,4−1

p = p

= p

= 0 5

, 28 p

k

o

o

o

k+ 1

14

, + 1

– pw > pk = 0,528 po 2 &

)

0

%

0 %

0

&

'( 0 %

0

0

)

%

3

%

0

– pw ≤ pk = 0,528 po 2 &

)

0

%

0 %

0

&

'( 0

)

%

3

'

&

'(

3

&

'(

.

)

k−1

k

2 k R T

p

vw =

g

o

1 −

w

k −1

po

5 &

Qm = ρ v Aw 2

k 1

+

k

k

2 k

p

p

p

o

w

w

Q = A

−

m

w

k − 1 R T

p

p

g

o

o

o

&

'(

)

& 0

- 0 &

&'

!

&

'(

% "

pk ≥ pw$

0

&

0

%

2 k Rg T

vk =

o

k +1

5 &

Qm = ρ v Ak k +1

k 1

po

2

−

Qm = Ak

k

Rg T

k − 1

o

%

0

-

.

&

v 2

T = T +

o

2 cp

%

v 2 k − 1

v 2

w

(

)

w

T = T −

= T −

w

o

o

2 k R

7 R

g

g

.

5

6

– po = 98 100

) To = 27 7) d = 5 %%) pw = pa = 981

– v = 8) Qm = 8

9

&

To = 273 + 27= 300 :) k = 1,4)

Rg = 287 %;<;<: 9

'

%

pw < pk = 0,528 po = 0,528 ⋅ 98 100 = 51 797

→

9

&

'

2 k Rg To

2 ⋅14

, ⋅ 287 ⋅ 300

vk =

=

= 316 9

, m/s

k +1

14

, +1

&

==

0

2

2

π d

π 0 0

, 05

−4

Aw =

=

= 01,963⋅10 [m2 ]

4

4

k +1

po

2

k −1

Qm = Aw

k

=

Rg T

k + 1

o

1,4+1

−

9 8

, 1⋅106

, −

4

2

1 4 1

= 01,963⋅10 ⋅

14

,

= 0 4

, 495 kg/s

287 ⋅ 300

14

, + 1

5

!

6

– po = 19 620

)

– To = 15 7)

– pw = pa = 981

– v = 8) Tw = 8

9

&

To = 273 + 15 = 288 :) k = 1,4)

Rg = 287 %;<;<: 9

'

%

pw < pk = 0,528 po = 0,528 ⋅ 19 620 = 10 360

→

&

'(

%

!

==

&

'(

k −1

2

k

k R T

p

vw =

g

o

1 −

w

=

k −1

po

1,4−1

2 ⋅14

, ⋅ 287 ⋅ 288

981

1,4

=

1 −

= 589 m/s

14

, −1

19620

%

2

vw

5892

T

T

w = o −

= 288 −

= 1155

, K = -157,7oC

7 Rg

7 ⋅ 287

0

!

6

– po = 49 100

) To = 15 7) Qm = 9,81

<)

pw = pa = 981

– dk = 8) dw = 8

9

&

To = 273 + 15 = 288 :) k = 1,4)

Rg = 287 %;<;<: 9

'

%

pw < pk = 0,528 po = 0,528 ⋅ 49 100 = 25 900

→

9

'

&

!

==

1

%

k +1

k 1

po

2

−

Qm = Ak

k

Rg T

k + 1

o

0

Qm

9 8

, 1

−4

2

Ak =

=

= 8 3

, 9 ⋅10 m

k +1

1,4+1

k −1

6

po

2

4 9

, 1⋅10

2

1,4−1

k

14

,

Rg T

k + 1

o

287 ⋅ 288

14

, + 1

>

Ak

8 3

, 9 ⋅10 4

−

dk = 2

= 2

= 0 0

, 327 m = 32 7

, mm

π

π

9

'

!

==

1

%

2

k 1

+

k

k

2 k

p

p

p

o

w

w

Q = A

−

m

w

k − 1 R T

p

p

g

o

o

o

0

A =

Qm

w

=

2

k 1

+

2

k

k

k

p

p

p

o

w

−

w

k − 1 R T

p

p

g

o

o

o

9 8

, 1

2

=

= 0 0

, 0443 m

2

1 4

. 1

+

2 ⋅14

,

4 9

, 1⋅106

981 1,4

981

1,4

−

14

, − 1 287 ⋅ 288

49100

49100

>

Aw

4 4

, 3⋅10 3

−

dw = 2

= 2

= 0 0

, 743 m = 74 3

, mm

π

π

9

-

%

%

/><

?71< %

%

/><

?71<

0

%

0

1

@

Qm=const)

ζ

M ≤ 0,8

%

5#AB< #CDEDC

'

k → n ∈ [0; ±∞]

T( y)

%

0

5#AB< #CDEDC

3 %

)

5#AB< #CDEDC

%

=

:

3

0

-

F

-

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'

%

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%

0

-

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0

-

%

&

%

F

-

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%

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