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
%
%
&
'
&
'
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
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
!
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
→
'
&
!
==
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
'
!
==
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
-
%
%
/><
?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
-
'
'
%
%
-
%
0
-
-
0
-
%
&
%
F
-
'
% -
%
%
%
'