Лекции по гидрогазодинамике
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•
v
p1
=
G
p
ρ
p
S
p1
; v
2
=
G
ρ S
2
; v
3
=
G
p
+ G
ρ S
3
,
•
p
3
= p
c
−
ρ v
2
3
2 ϕ
2
3
; p
2
= p −
ρ v
2
2
2 ϕ
2
4
; p
p1
= p
p
−
ρ
p
v
2
p1
2 ϕ
2
1
.
v
p1
, v
2
, v
3
,
G
p
, G
p
p
, p , p , p
p1
, p
2
, p
3
S
p1
, S
2
, S
3
S
2
= S
3
−S
1
ρ
p
, ρ , ρ
c
ϕ
1
, ϕ
2
, ϕ
3
, ϕ
4
•
∆ p
c
∆ p
p
= ϕ
2
1
S
p1
S
3
"
2 ϕ
2
+
2 ϕ
2
−
1
ϕ
2
4
!
ρ
ρ
S
p1
S
2
n
2
− (2 − ϕ
2
3
)×
×
ρ
ρ
c
S
p1
S
3
(1 + n)
2
#
ϕ
1
= 0.95;
ϕ
2
= 0.975; ϕ
3
= 0.9; ϕ
4
= 0.925
∆ p
c
∆ p
p
=
S
p1
S
3
"
1.76 + 0.7
ρ
p
ρ
S
p1
S
2
n
2
− 1.07
ρ
p
ρ
c
S
p1
S
3
(1 + n)
2
#
ρ
p
= ρ = ρ
c
∆ p
c
∆ p
p
= ϕ
2
1
S
p1
S
3
"
2 ϕ
2
+
2 ϕ
2
−
1
ϕ
4
!
S
p1
S
2
n
2
− (2 − ϕ
2
3
)×
×
S
p1
S
3
(1 + n
2
)
#
n
∆ p
c
= p
c
−p
∆ p
p
= p
p
− p
•
•
•
90%
~v
0
x ~v
0
~
R
x, y, z
~
R =
~
F
x
+
~
F
y
+
~
F
z
.
~
F
x
~
F
y
~
F
z
~v
0
y
~
F
z
= 0
~
R =
~
F
x
+
~
F
y
F
x
F
x
= C
x
S
ρ v
2
0
2
,
G = ρ v S; K
x
= G v = ρ v S v;
C
x
S
C
x
Re
~
F
~
F
x
F
y
= C
y
S
ρ v
2
0
2
,
C
y
F
x
= γ K
x
= γ ρ v
2
S,
γ
a = ~v V
0
S
0
−→
Q
~v
= 0
S
0
Q
i
=
I
S
3
X
k=1
(−σ
ik
+ ρ · v
i
· v
k
) · n
k
· ds.
S
0
S
0
S
S
S
0
= S + S
Q
m
S
(~v ·~n)|
S
= 0
Q
m
|
S
=
Z
S
ρ~v ·~n · dS = 0.
S
−→
~
Q
~v
S
=
Z
S
ρ~v · (~v~n) · dS = 0.
R
i
=
Z
S
3
X
k=1
(−σ
ik
· n
k
) · ds.
R
i
= −
Z
S
3
X
k=1
(−σ
ik
+ ρ · v
i
· v
k
) · n
k
· ds.
S
~
R = −
Z
S
.
[ ·~n + ρ~v · (~v~n)] · dS,
~
R
~
M
~
R
= −
Z
S
.
([~r × ·~n ] + [~r × ρ~v ] · (~v vecn)) · dS,
~n
V
0
v
∞
p
∞
v
u
p
u
S
1
= S
2
S
1
S
2
~
R =
−
Z
S
1
+
Z
S
2
[ ~n + ρ ~v(~v ·~n)] · dS,
S
S
S
1
− S S
2
− S
S
1
S
2
R = (p
∞
+ρ
∞
v
2
∞
) [S +(S
1
−S )]−(p
u
+ρ
u
v
2
u
) S +(p
∞
+ρ
∞
v
2
∞
)(S
2
−S ).
G = ρ v S
S
G G
G = G + G
R = (p
∞
− p
u
) S + G (v
∞
− v
u
) − G v
u
.
p
∞
= p
u
2 ÷3 %
R = G (v
∞
− v
u
).
l =
~
M ·
~
Ω
G
,
~
M, [ · ]
~
Ω, [1/c]
G, [ /c] z
~
Ω = |Ω| ·
~
k,
~
M ·
~
Ω = M
z
· |Ω|,