Лекции по гидрогазодинамике
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ρ /ρ
ρ > ρ
ρ /ρ
z
ψ = g z
ψ = −C
g
/R R
p
ρ
−
g
R
−
ω
2
r
2
2
= onst.
R
0
g = g
0
p|
(
R=R
0
r=0
)
= 0, const = −
C
g
R
0
,
C
g
= g
0
R
2
0
p|
S
= 0
g
0
R
2
0
R
+
ω
2
r
2
2
= g
0
R
0
,
R
0
R
= 1 −
ω
2
R
2
sin
2
θ
g
0
R
0
,
R ≈ R
0
1 +
ω
2
R
0
2 g
0
sin
2
θ
r = R sin θ
R − R
0
R
0
=
ω
2
R
0
2 g
0
≈
1
600
.
ρ = ρ(p) z
(p = ρ R T )
p
ρ
n
= ; ρ =
p
!
1/n
.
z = 0)
p|
z=0
= p
0
, ρ|
z=0
= ρ
0
.
p
Z
p
0
dp
ρ
=
p
0
ρ
0
n
n − 1
p
p
0
!
n − 1
n
− 1
.
ψ = g z
p
0
ρ
0
n
n − 1
p
p
0
!
n − 1
n
− 1
+ g z = .
p = p
0
"
1 −
n − 1
n
ρ
0
g z
p
0
#
n
n − 1
.
n
12 − 16
80%
ρ = , n → ∞
p = p
0
− ρ
0
g z,
z
max
p = 0
z
max
=
p
0
ρ
0
z
.
p
0
= 0.1 ; ρ
0
= 1.2 /
3
z
max
≈ 8
∼ 10
2
H
p p
p
p = p − ρ · g · H;
p = p − ρ · g · H,
p − p = ∆ p
∆ p = (ρ − ρ ) · g · H,
ρ , ρ
T
0
= , n = 1
p = p
0
exp
−
ρ
0
g z
p
0
!
= p
0
exp
−
g z
R T
0
!
.
p = 0
z
max
→ ∞
∼ 10
3
T
T
0
=
p
p
0
!
n − 1
n
,
T
T
0
=
"
1 −
n − 1
n
ρ
0
g z
p
0
#
,
T = T
0
−
(n − 1)
n
g z
R
.
z
max
=
n
(n − 1)
R T
0
g
.
n = k = 1.4; T
0
= 288 K;
R = 287 / K ∼ 35
∼ 11 )
∆T = 0.65 K
0.0065
n
R = 287 / K
(n − 1)
n
g
R
= 0.0065, n ≈ 1.235.
ω
ψ
ψ = g z −
ω
2
r
2
2
.
ψ = g z
p = p
0
exp
−
ρ
0
(g z − ω
2
r
2
/2)
p
0
= p
0
exp
−
g z − ω
2
r
2
/2)
R T
0
.
T = const
ω
2
r
2
/2 g z
p
(i)
= p
(i)
0
exp
ω
2
r
2
/2
R · T
0
= p
(i)
0
exp
µ
m
ω
2
r
2
/2
R
0
T
0
.
R = R
0
/µ
m
R
0
= 8.314 / K
µ
m
p
(i)
N 1 − N
p
(1)
/ (p
(1)
+ p
(2)
) ∼ N; p
(2)
/ (p
(1)
+ p
(2)
) ∼ (1 − N).
q
0
=
p
(2)
/p
(1)
p
(2)
0
/p
(1)
0
= exp
ω
2
r
2
(µ
m2
− µ
m1
)
2 R
0
T
0
.
(UF
6
)
235
UF
6
µ
m1
= 349
238
UF
6
µ
m2
= 352
238
UF
6
ω r, / q
0
, −
−d
v
2
2
+
p
ρ
+ g z
= dL .
E = v
2
/2+p/ρ+ g z
dS
dQ
E
= ρ v E dS.