Сягло И.С. Теоретическая механика
Подождите немного. Документ загружается.
ρ = ρ(p)
~
Φ =
1
ρ
∇p.
~
Φ = ∇
Z
dp
ρ(p)
.
~
Φ = −∇u
u +
Z
dp
ρ(p)
=
oz
u = gz, p = − ρgz.
d~v
dt
=
∂~v
∂t
+ (~v∇)~v =
∂~v
∂t
+ ∇
v
2
2
+ 2~ω ×~v.
~ω = 0
~v = ∇ϕ
∇(
∂ϕ
∂t
+
v
2
2
+ u +
Z
dp
ρ
) = 0.
∂ϕ
∂t
+
v
2
2
+ u +
Z
dp
ρ
= f(t).
f(t)
v
2
2
+ u +
Z
dp
ρ
= .
ρ
v
2
2
+ ρgz + p = .
p
0
ρ
0
p
o
ρ
o
p = p
o
+ p
0
, ρ(p
o
+ p
0
) ≈ ρ
o
+
1
c
2
p
0
.
ρ(p)
p
0
1
c
2
=
dp
dρ
¯
¯
¯
¯
¯
¯
p
o
.
~
Φ
vp
0
∂~v
∂t
= −
1
ρ
o
∇p
0
,
∂ρ
0
∂t
=
1
c
2
∂p
0
∂t
= −ρ
o
∇~v.
ρ
o
∇
∆p
0
−
1
c
2
∂
2
p
0
∂t
2
= 0,
∆
c
~u = ( x −z)
~
i + (y + z)
~
j − xy
~
k.
x = x
o
(1 + t), y = y
o
(1 + t)
2
, z = z
o
(1 + t)
3
.
~v = (x
2
y + y
3
)
~
i − (x
3
+ xy
2
)
~
j.
v
x
= −yF (r), v
y
= xF (r), v
z
= 0, r =
r
x
2
+ y
2
.
α
p = kρ
γ
v
1
S
1
S
2
S
2
S
1
H
r ϕ
x = r cos ϕ, y = r sin ϕ.
r ϕ
ϕ r
A
r = r
o
ϕ = ϕ
o
-
6
*
K
¸
~e
r
~e
ϕ
~v
v
r
v
ϕ
ϕ
o
r
o
A
-
6
ª
R
µ
O
~e
ϕ
~e
θ
~e
r
µ
^
θ
r
ϕ
~v A
~r = x
~
i + y
~
j = r cos ϕ
~
i + r sin ϕ
~
j.