Лекции по гидрогазодинамике
Подождите немного. Документ загружается.
e =
Z
V
ρ v
2
r
2
dV =
∞
Z
R
ρ v
2
r
2
4 π r
2
dr = 4 π R
3
ρ v
2
R
2
.
(p
∞
− p
k
) p
∞
= const, p
k
= p
(p
∞
− p
k
) = const
A =
V
Z
V
(p
∞
− p ) dV,
V = 4 π R
3
/3
A = (p
∞
− p )
4 π (R
3
− R
3
)
3
.
e A
v
R
=
v
u
u
u
u
u
u
t
2
3
(p
∞
− p )
R
R
!
3
− 1
ρ
.
p p
∞
R R
(R
3
/R
3
) 1
v
R
=
v
u
u
u
t
2
3
p
∞
ρ
R
R
!
3
(R → 0)
∆p =
v
u
u
t
2 E
3
p
∞
R
R
!
3
(E ≈ 20 · 10
8
)
(R /R ∼ 10
2
)
p
∞
= 0.1
∆p ≈
v
u
u
t
2 · 20 · 10
8
3
· 10
5
· 10
6
= 12.11 · 10
9
≈ 12 · 10
3
.
4−18
0.4−1.8
H
z
= H
0
− H −
α v
2
2 g
− ∆H ,
H
z
H
0
= p
0
/(ρ g)
H = p /(ρ g)
∆H
H =
p
ρ g
p
∆H = H − H +
α v
2
2 g
= H
0
− H − H
z
− ∆H .
∆H
∆H
∆H
(I)
∆H
(I)
= 10
n
√
Q
C
4/3
.
C
C
n
s
n
s
50 − 70 70 − 80 80 − 150 150 − 200
C 600 − 750 800 800 − 1000 1000 − 1200
n
s
= 3.65 n
√
Q
H
3/4
,
H
Q
3
/c
n /
H
z
H
z
> 0
H
z
< 0
20
C
Q = 20 /c n = 2900 / n
s
= 70.
C = 800 ∆H
(I)
∆H
(I)
= 10 ·
2900 ·
√
0.020
800
4/3
= 4.1 .
H
0
= 10 .
20
C H =
0.24 .
H
z
= H
0
− ∆H
(I)
− H − ∆H = 10 − 4.1 − 0.24 − ∆H =
= 5.66 − ∆H .
h < 5.66
100
C H = 10
∆H
(I)
∆H
(I)
= 4.1 .
H
z
= H
0
− ∆H
(I)
− H − ∆H = 10 − 4.1 − 10 − ∆H =
= −4.1 − ∆H .
p
0
, T
0
, ρ
0
p, T, ρ
∆p = p − p
0
; ∆T = T − T
0
; ∆ρ = ρ − ρ
0
.
•
∆p
p
0
1;
∆T
T
0
1;
∆ρ
ρ
0
1.
•
∆p
p
0
' 1;
∆T
T
0
' 1;
∆ρ
ρ
0
' 1.
x τ
x dτ
dx x + dx
c = dx/dτ
x x + dx
dp, dT, dρ
dx
dv S
dK = m dv = ρ dV dv = ρ S dx dv
dx, dv, dτ
dp S
m dv = ρ S dx dv = dp S dτ.
dv
dx dρ
dV = S dx dm = dρ dV
dQ dV
S dv
dτ dQ = ρ dv S dτ dm = dQ
dρ S dx = ρ dv S dτ.
c = dx/dτ
c
2
=
∂p
∂ρ
.
c
2
=
∂p
∂ρ
=
1
β ρ
=
E
ρ
.
c = c
S
=
v
u
u
t
k p
ρ
=
√
k R T .
k = 1.4, R = 287 /( · K)
c =
√
1.4 287 T ≈ 20
√
T .
ρ = const c = ∞
E = 20 · 10
8
, ρ = 1000 /
3
)
c = 1414 /c E = 20·10
10
, ρ = 7.8·10
3
/
3
), c = 5060 /c
c = 340 /c
~c
~c
~c
~v
~c = ~c + ~v.
c v
~c
~v ~c ~v+c ~e
~e
~v
c
~c
v < c ~v + c ~e
v = c
v > c ~v+c ~e
~v
sin α =
c
v
; α = arcsin
c
v
!
= arcsin
1
M
!
.