242 55 2MB
Russian Pages 226 [229] Year 2002
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34.32 24 669.04:533:662.9(07)
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№ 14/18.2-86
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ISBN 000-000-000-0
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1. 1.
.
1.1. ,
(
),
[ /
2
=
]. , T [ ].
,
-
P⋅V = M⋅R⋅T, 3
(1.1)
, V; R = Rμ / μ [ /( ⋅ )] – /( ⋅ )– 1 ; Rμ = 8314 ;μ[ / ]– 1 .
V [ ]– ;M[ ]– ,
-
. = 273
P
– P . = 10333
: 101325 = 760 . , : 1 = 98000 = 735,6 =Δ =
-
(
.
. = 10333
/ 2. –
.
/ 2.
. = 10000 ,
. "
, (
=0° .
.
"( . ,
=
)
"
"(
).
< 0, ,
.
. 1.1 ), P ,
)
=
, (
. .
), h
h
, , : 12
h
= ρ⋅g⋅h.
P
h
.
-
. (
. 1.1 ),
-
. / 3
/
2
=
⋅ /
3
= -
. 1.1.
:
;
-
ρ [ / 3]. ,
, 1
3
.
, , /ρ [ ⋅ / ]
. 1
. "z"
z
= ρ⋅g⋅z. ,
-
,
,
-
= ρ⋅g⋅z.
(1.2) ,
,
-
.
0
. z, z 0
=
0
- ρ ⋅g⋅z,
– 13
;ρ –
(1.3) .
,
(1.2)
(1.3) 1
+
=
1
+
2
2
=
0,
(1.4)
. .
-
. ,
(1.4)
1
+ ρ ⋅g⋅z1 =
2
+ ρ ⋅g⋅z2 = const.
, 2
+ ρ ⋅g⋅z2. = =
, , . .
1
z1 = z2,
1
, ,
2 1
(1.5)
>
+ ρ ⋅g⋅z1 > . -
2
,
,
.
"
-
-
-
":
.
1.2.
,
r W
r r , . . W = ∂L / ∂τ ,
r L –
. [1], v
F
=
v
V [ 3] τ.
dV
dτ
, ⎡ 3⎤ ⎢ ⎥, ⎣ c ⎦
(1.6)
, T
-
F
" " T.
V
v -
.
r W
-
v
F
, .
:
14
-
W=
[ ], m=
d2V dv = [ / ]. dF ⋅ dτ dF
(1.7)
dM dV ⋅ ρ = = v ⋅ ρ [ / ]. dτ dτ r qm , F .
m
τ
m F
(1.8)
, -
: qm =
d2M = W ⋅ ρ [ /( 2⋅ )]. dF ⋅ dτ
1.3.
(1.9)
. ,
, :
=
.
ρ ⋅ W2 . 2
(1.10) ,
.
U-
, 1
(
3
V ,
ρ.
. 1.2). W2/2.
1
L ( P = 760 t =0° .
-
)V , , .
. . 1.2.
U–
v0 15
-
t= 0°
,
W0, . . P = 760 . . m [ / ].
-
. v0
v0 = m / ρ0,
ρ0 –
(1.11) .
V = V0 ⋅
T P0 ⋅ T0 P
: v = v0 ⋅
T P0 ⋅ . T0 P
(1.12) (
W W = W0 ⋅
) W0
T P0 ⋅ . T0 P
(1.13)
(1.13) , P = 3-4
-
. v ,
W
(1.13) W = W0 ⋅
α = 1 / 273 K–1 –
T = W0 ⋅ (1 + α ⋅ t ) , T0
(1.14) .
.
-
,
P
=
W02 ⋅ ρ0 P0 T ⋅ ⋅ . 2 P T0
(1.15) -
, P
=
W02 ⋅ ρ0 T W02 ⋅ ρ0 ⋅ = ⋅ (1 + α ⋅ t ) . 2 T0 2
16
(1.16)
.
-
. W=
v [ / ], F
(1.17)
v– t.
.
,
),
(
F1 ⋅ ρ1 ⋅ W1 = F2 ⋅ ρ 2 ⋅ W2 = const = m .
(1.18)
T ≈ const
,
P ≈ const,
F1 ⋅ W1 = F2 ⋅ W2 = const = v . .
(1.19)
, t
1.4.
-
. .
v0
(
-
)
, . . ,
, . , . .
. P
1
+P
1
+
1
>P
2
17
+P
2
+P
2,
1–1 ΔP
2–2 ΔP
.
,
.
. " +
P
1
12
–
ΔP
ρ ⋅ W12 + ρ ⋅ g ⋅ z1 = P 2
2
ρ ⋅ W22 + ρ ⋅ g ⋅ z 2 + ΔP 2
+
,
3
1
12
"
(ρ1 = ρ2)
,
(1.20)
.
(1.20) ΔP
.
12
= 0,
(
2
> P 1,
2
2300
.
, . (
,
) . . -
.
. , , dW /dy=const.
,
, ,
, . 26
,
-
,
, ,
-
, τ =η ⋅ η [
⋅ ]–
,
η
.
dW [ dy
(2.5)
η
η
. η
. [8] .
(
],
)
η
,
τ = (η + η ) ⋅
η = 0.
η,
η
-
η
dWx [ dy
.
].
(2.6)
2.4.
.
, . , . "
-
,
"
.
,
, ( (
),
. 2.7).
,
, , . .
, 1 %.
( =δ)
δ
27
, . . Wδ
-
δ (
,
-
, . 2.7).
-
-
δ ,
, (
. 2.4). :
. 2.7.
, :
13-
; 2; 4-
-
,
;
-
. -
;5-
. . , (
dF . 2.8).
,
,
, .
, , .
,
L ,
=L
– -L ,
L
L –
,–
( ,
– -
. 2.8). – -
, –
.
28
δ max < R δ =R
( . 2.9). L=L , . . .
L= L
. 2.8. L= L .
= -
L L
-L
. (
)
-
, . W0⋅x/ν > 5⋅105
. 2.9.
Re = -
.
, (
)
, .
,
-
, .
,
, . 2.5.
–
-
. . 29
2.5.1.
: . ( [6]). f1, f2 f3 z0, τ); z = f3( 0, 0, z0, τ).
= f1( 0, 0, z0, τ); τ = 0: 0,
.
, . . = f2( 0, z0 0
f5
(
)
⎡ ∂ (ρ ⋅ Wx ) ∂ ρ ⋅ Wy ∂ (ρ ⋅ Wz ) ⎤ ∂ρ = −⎢ + + ⎥ ∂τ ∂y ∂z ⎦ ⎣ ∂x
(2.8)
Dρ ∂ρ ∂Wx ∂Wy ∂Wz = + + + ∂x ∂y ∂z dτ ∂τ
(2.9) .
∂ρ / ∂τ = −div (ρW )
(2.8)
(2.10)
Dρ / dτ = −ρ ⋅ div (W ) ,
div (ρW ) =
-
(2.7)
∂Wy ∂Wz ⎤ ⎡ ∂W Dρ = −ρ ⋅ ⎢ x + + ⎥, dτ ∂y ∂z ⎦ ⎣ ∂x
(2.7)
0,
Wx = f4( , , z, τ); Wy = f5( , , z, τ); Wz = , . -
, f3, f4 f6( , , z, τ).
-
,
(
(2.11)
)
∂ (ρ ⋅ Wx ) ∂ ρ ⋅ Wy ∂ (ρ ⋅ Wz ) + + ∂y ∂x ∂z
(2.12) ,
30
divW =
∂Wx ∂Wy ∂Wz + + ∂y ∂x ∂z
(2.13)
. (2.10)
(2.7)
-
:
. dV ( (
. dV dτ -
, 3
1
),
1
) . "
"
-
. , . . ,
"
z
.
,
"
,
[9].
(2.8)
,
, (
) [10]. :
(
) (
)
(2.7)
.
(2.10), (2.8)
(2.11).
ρ = const
.
∂Wx ∂Wy ∂Wz + =0. + ∂x ∂z ∂y
(2.14)
(2.14) :
.
, "
"
"
. (Wy =Wz = 0) 31
(2.10)
"
∂ (ρ ⋅ Wx ) ∂ρ =− . ∂x ∂τ
(2.15)
∂ (ρ ⋅ Wx ) =0. ∂x
(2.15) (2.16)
Э
2.5.2.
, -
M– M⋅Wx –
d(M⋅Wx) = GΣx⋅dτ [ ⋅ ],
(2.17)
; Wx –
(
; GΣx – M; GΣxxdτ –
); ,
. , . .
, .
-
, :
I = m⋅W = ρ⋅F ⋅W⋅W [ ].
(2.18) -
(2.17) m = dM/dτ m⋅(Wx2 - Wx1) = GΣx,
(2.19)
. .
, ,
-
,
, , , .
, .
GΣx, ,
,
(2.19)
. .
32
-
2.5.3.
( (
-
)
)
(
-
) .
(
,
)
-
,
:
⎡ ∂ (ρWx Wx ) ∂ ρWy Wx ∂ (ρWz Wx ) ⎤ ∂ (ρWx ) ∂P = −⎢ + + η Δ2 Wx , + ⎥ + ρg x − ∂τ ∂ ∂ ∂ x y z ∂ x ⎦ ⎣
(
∂ ρWy ∂τ
) = −⎡ ∂(ρW W ) + ∂(ρW W ) + ∂(ρW W )⎤ + ρg ⎢ ⎣
∂x x
y
∂y y
(
∂z
y
z
)
y
⎥ ⎦
y
−
∂P + η Δ2 Wy , ∂y
⎡ ∂ (ρWx Wz ) ∂ ρWy Wz ∂ (ρWz Wz ) ⎤ ∂ (ρWz ) ∂P + = −⎢ + + η Δ2 Wz , ⎥ + ρg z − ∂ ∂ z ∂τ ∂ x y z ∂ ⎣ ⎦
Δ2 Wx = Δ2 Wy =
Δ2 Wz =
∂ 2 Wx ∂ 2 Wx ∂ 2 Wx , + + ∂z 2 ∂y 2 ∂x 2 ∂ 2 Wy ∂x 2
+
∂ 2 Wy ∂y 2
+
∂ 2 Wy ∂z 2
(2.20)
(2.21)
(2.22)
(2.23)
,
(2.24)
∂ 2 Wz ∂ 2 Wz ∂ 2 Wz + + . ∂x 2 ∂y 2 ∂z 2
(2.25)
(2.20-2.22) 0L,
-
: " ."
"
-
" .
dV = dxxdyxdz 1
1
3
dτ
. 33
(2.20-2.22), ,
:
ρ⋅
∂P DWx = ρ ⋅ gx − + η ⋅ Δ2 Wx , ∂x dτ
ρ⋅
DWy
∂P + η ⋅ Δ2 Wy , ∂y
(2.27)
ρ⋅
DWz ∂P = ρ ⋅ gz − + η ⋅ Δ2 Wz , dτ ∂z
(2.28)
dτ
= ρ ⋅ gy −
(2.26)
DWx ∂Wx ∂Wx ∂Wx ∂Wx , + Wz ⋅ + Wy ⋅ + Wx ⋅ ⋅ = dτ ∂z ∂y ∂x ∂τ
DWy dτ
=
∂Wy ∂τ
+ Wx ⋅ ⋅
∂Wy ∂x
+ Wy ⋅
∂Wy ∂y
+ Wz ⋅
∂Wy ∂z
(2.29)
,
(2.30)
DWz ∂Wz ∂Wz ∂Wz ∂Wz + Wz ⋅ + Wy ⋅ + Wx ⋅ ⋅ = dτ ∂z ∂y ∂x ∂τ
(
)
(2.31)
. (2.26-2.28) ( –
.
-
2.5.1) :
-
0L, 0L. .
-
, -
(2.26-2.28) ,
(
, )
( ,
-
,
. .).
34
. . , -
.
-
. 4
.
-
, ∂Wx ∂Wy ∂Wz + + =0. ∂y ∂x ∂z
(2.32)
(2.26-2.28)
(2.32)
-
. – ( )
. ( ,
123-
20
-
), A + B⋅y + C⋅y' = 0:
( = 0): A + B⋅y = 0; ( = 0): A + C⋅y' = 0; : A + B⋅y + C⋅y' = 0. '–
, ;
. " W = 0) –
, ,
–
,
-
,
, "
( 12-
: . ,
, ,
∂W/∂ = 0,
. ,
. ,
.
,
,
,
.
,
.
, ) dW τ = η⋅ , dL
( . .
35
,
-
2.6.
(
.
. ,
)
,
-
Wz = 0,
: -
. : Wx = f1( , ), Wy = f2( , ). ( ) m = ρ⋅W0⋅δx⋅z, δx.
, ,
: W = f(r). ∂P/∂y
. ,
. . -
: ∂P/∂x=0.
Wx ⋅
Wx ⋅
∂Wy ∂x
+ Wy ⋅
⎛ ∂ 2 Wx ∂ 2 Wx ⋅ ⎜⎜ + 2 ∂y 2 ⎝ ∂x
⎞ ⎟, ⎟ ⎠
(2.33)
⎛ ∂ 2 Wy ∂ 2 Wy ⎞ ⎟, = ν ⋅⎜ + ⎜ ∂x 2 ∂y ∂y 2 ⎟⎠ ⎝
(2.34)
∂Wx ∂Wx =ν + Wy ⋅ ∂y ∂x
∂Wy
∂Wx ∂Wy + =0. ∂x ∂y
(2.33)
(2.35)
(2.34)
. (2.34)
,
. .
, -
(2.33) . . ,
, : ∂Wx/∂y >> ∂Wx/∂x.
36
∂P/∂x = ∂P/∂y = 0
-
-
:
Wx ⋅
∂ 2 Wx ∂Wx ∂Wx , =η ⋅ + Wy ⋅ ∂y ∂x ∂y 2
(2.36)
∂Wx ∂Wy + =0. ∂x ∂y
(2.37)
(2.36-2.37)
.
,
.
-
. (2.36-2.37)
[9, 11]. .
,
-
. :
δ x = 5 / Re 0x,5 ,
Rex = W0⋅x/ν –
(2.38)
; τ = 0,6642 ⋅
:
1 Wo2 ⋅ ρ ⋅ . 2 Re0x,5
(2.39)
δ W.
(
)
W
W=
2 I 1 = ⋅ ∫ 2 ⋅ π ⋅ r ⋅ ρ ⋅ Wr2 dr = W 3 m ρ⋅W⋅F 0 R
. . 2
. .
W = K2⋅W , = 2/3 = 0,667.
⎛ ⎞ E = m ⋅ ⎜⎜ W ⎟⎟ / 2 [ ⎝ ⎠ 2
],
(2.79)
W –
( (
).
)
49
W > W > W.
W
. R ⎛ 2 2 W2 ⎞ ⋅E = ⋅ ∫ ⎜⎜ 2 ⋅ π ⋅ r ⋅ ρ ⋅ Wr ⋅ r ⎟⎟dr = m 2 ⎠ ρ⋅W⋅F 0 ⎝
W=
.
:
3
W = K3⋅W ,
W
W
1 ⋅W 2
(2.80)
=
12 =
0,707. P
1
,
3
E m⋅W ρ⋅W ρ ⋅ (K 3 ⋅ W = = = = v 2⋅v 2 2 2
P
2
W.
=
P
)2
[
/ 3].
=
(2.81)
W,
W
K 32 ⋅ W ⋅ ρ . K12 ⋅ 2 2
(2.82) α.
K 32 / K12
α =
-
0,5 =2, . . 0,52 2
2
, W.
( )
, I = m ⋅ W = m ⋅ K2 ⋅ W 2/
,
= m ⋅ K 2 W / K1 = F ⋅ ρ ⋅ W ⋅ K 2 / K1 [ ]. 2
1
W.
50
α,
(2.83) -
Э
2.12.2.
(1.20)
(2.19)
,
-
. ,
(1.20)
(2.19)
.
-
, ,
–
( . .
)
.
(
)
:
m ⋅ α 2 ⋅ W2 − α 1 ⋅ W1 = G Σ [ ],
P1 + α 1 ⋅
(2.84)
W12 ⋅ ρ W2 ⋅ ρ + ρgz1 = P2 + α 2 ⋅ 2 + ρgz 2 + ΔP 2 2
12
[
].
(2.85)
2.12.3.
2.10, . τ
(2.73),
: ,
-
. , τ =τ
. .
,
,
. –
-
[9]. . , "
"
-
. R = 4⋅103 - 3⋅106
. W ⋅y Wx + 5,5 , = 2,5 ⋅ ln W ν
= R - r, R –
,r–
(2.86) .
51
. 2.13
"
" -
. ,
, .
.
. .
-
, τ =τ ⋅
y . R
(2.87) .
. . ,
.
, -
, W.
. , . -
. ,
. . . -
. 2.13. .
Re
.
, , ,
,
,
.
-
. , .
52
-
–
:"
.
[15] ,
,
".
2.13. 2.13.1.
-
L12 :
ΔP
12
=η ⋅
32 ⋅ L12 ⋅W , D2
(2.88)
. . .
W
,
-
. , ΔP = μ ⋅ μ –
L W2 ⋅ ρ , ⋅ D 2
(2.89)
,
. (2.88)
μ
=
-
(2.89)
64 . Re
(2.90)
Wy = 0,
(2.72)
R
,
–
. (2.89)
D
F [ 2] – "
"
4⋅F
=
;
,
[ ]–
53
-
(2.91) .
2.13.2.
, . Re = 106 Δ–
ε = Δ/R,
,
-
. 2.14 ε ,
.
. μ .
"
-
" . μ
μ
,
-
.
. 2.14. .
Δ/R
,
), ,
( . .
. 2.15 μ = f(Re, Δ/R) 0,0667. μ = f(Re)
"
"
, ).
ε = Δ/R (Δ/R < 0,00197) . μ ( -
μ
Re1,
. .
-
Re2,
Re Δ
. . δ, ,
Δ/R,
μ ,
. ,
(
) .
54
.
Re Δ/R
. 2.15.
2.14.
( W1
W2)
, .
-
-
, . . (
. 2.16).
. 2.16. -
: ;
-
; -
55
900
2-2 Δ
,
12.
α = 180° : ΔP
(
1-1 c 2,
>Δ
ΔP
12
" "
2 = ρ ⋅ W1 / 2 − ρ ⋅ W22 / 2 1
12.
.
(W − W ) ⋅ ρ .
=
)
-
2
1
2
(2.92)
2
. ϕ
ϕ = 6-8°
.
, ϕ
. : ΔP
.
=K
⋅
= (ϕ, D2 /D1)
-
W1 ⋅ ρ . 2 2
⎡ ⎛D ⎞ = ⎢1 − ⎜⎜ 1 ⎟⎟ ⎢ ⎝ D2 ⎠ ⎣ 1.
ϕ = 180°
(2.93)
2
⎤ ⎥ . ⎥ ⎦
.
2
D2 >> D1,
-
( ), ( . 2.16 , 2.16 )
. Wx ΔP Wx (2.93),
=
(W
W2:
)
− W22 ⋅ ρ . 2
2 x
(2.94)
, ,
.
56
. -
. .
-
:
⎡
4 ⎞ ⎤ ⎛ ϕ ⎥ ⋅ ⎜1 − cos ⎞⎟ . 2⎠ ⎝ D 2 ⎠ ⎥⎦ ⎝
(ϕ, D2 / D1 ) = 0,5 ⋅ ⎢1 − ⎜⎜ D1 ⎟⎟ ⎛
⎢ ⎣
K
ϕ = 360°.
K
:Δ
=
.
1 ⎛ R⎞ , ⎜ ϕ , ⎟ = (1 − cos ϕ ) R ⎝ D⎠ 1+ 3 D
R–
(2.95)
. . (2.96)
. ,
(2.95-2.96) . ϕ = 90° (R = 0) W2 ⋅ ρ , . . =α 2
P
=α.
,
. ,
(
.
. 2.17 - ).
-
, – .
,
. 2.17.
,
: .
-
1-
[16]. 57
; 2-
2.15. Э
-
( )
(
,
)
. ,
. -
, , ),
, ( (
,
).
. (
)
,
-
, . ,
,
-
,
,
.
, ,
.
,
,
.
2.15.1.
-
. [5]
X = x / L0; Y = y / L0; Z = z / L0, L0 –
(
(2.97)
,
,
,
), W
/
=
Wy Wx W ; Wy / = ; Wz / = z , W0 W0 W0
W0 –
(2.98)
(
,
,
-
). Wx (2.26, 2.29) ,
gx = 0 (2.26, 2.29)
W0 L0 (∂Wx/∂τ = 0) :
58
W02 L0
⎡ ∂Wx / ⎤ ∂Wx / ∂Wx / + Wz / ⋅ + Wy / ⋅ ⋅ ⎢ Wx / ⋅ ⎥= ∂Z ⎦ ∂Y ∂X ⎣
=−
1 ∂P ν ⋅ W0 + 2 ⋅ ρ ⋅ L 0 ∂X L0
⎛ ∂ 2 Wx / ∂ 2 Wx / ∂ 2 Wx / + + ⋅ ⎜⎜ 2 2 ∂Z 2 ∂Y ⎝ ∂X
⎛W ⎞ ∂⎜⎜ x ⋅ W0 ⎟⎟ 2 / W ∂Wx W ⎠ = W0 ⋅ W / ⋅ ∂Wx = W0 ⋅ x ⋅ ⎝ 0 Wx ⋅ x ∂X ∂x L0 W0 ⎛ x ⎞ ∂⎜⎜ ⋅ L0 ⎟⎟ ⎝ L0 ⎠
⎞ ⎟ ⎟ ⎠
(2.99)
. .
⎡ ⎛ Wx ⎞⎤ W0 ⎟⎟ ⎥ ⎢ ∂ ⎜⎜ 2 / ∂ W ∂ ⎛ ∂Wx ⎞ ∂ ⎠ ⎥ = W0 ⋅ ∂ Wx ⎢ ⎝ W0 = ⎜ ⎟= 2 2 2 ∂ x ⎝ ∂x ⎠ ⎞ ⎥ L0 ⎞⎢ ⎛ x ⎛ x ∂x ∂X L 0 ⎟⎟ ⎢ ∂ ⎜⎜ L 0 ⎟⎟ ⎥ ∂ ⎜⎜ ⎠ ⎥⎦ ⎠ ⎢⎣ ⎝ L 0 ⎝ L0 2
(2.99)
Wx / ⋅ =−
Eu =
(2.101)
W02 / L0,
⎛ ∂ 2 Wx / ∂ 2 Wx / ∂ 2 Wx / + + ⋅ ⎜⎜ 2 2 ∂Z 2 ∂Y ⎝ ∂X
∂2W / ∂2W / ∂Eu 1 ⎛ ∂ 2 W / + + + ⋅ ⎜⎜ ∂X Re ⎝ ∂X 2 ∂Z 2 ∂Y 2
; Re =
P – ρ ⋅ W02
Wx / ⋅
. .
∂Wx / ∂Wx / ∂Wx / = + Wz / ⋅ + Wy / ⋅ ∂Z ∂Y ∂X
1 ν ∂P + ⋅ 2 X L ∂ ρ ⋅ W0 0 ⋅ W0 =−
(2.100)
∂Wy / ∂X
+ Wy / ⋅
W0 ⋅ L 0 – ν
∂Wy / ∂Y
59
+ Wz / ⋅
⎞ ⎟= ⎟ ⎠
⎞ ⎟, ⎟ ⎠
(2.102)
. ∂Wy / ∂Z
Wy =
gy = 0
=−
2 / ∂ 2 Wy / ∂ 2 Wy / ∂Eu 1 ⎛⎜ ∂ Wy + ⋅ + + ∂Y Re ⎜⎝ ∂X 2 ∂Y 2 ∂Z 2
,
⎞ ⎟. ⎟ ⎠
(2.103)
z
, gz = g:
Wz Wx / ⋅
∂ 2 Wz / ∂ 2 Wz / 1 ∂Eu 1 ⎛ ∂ 2 Wz / + + + ⋅ ⎜⎜ − 2 2 Fr ∂Z Re ⎝ ∂X ∂Z 2 ∂Y
= Fr =
∂Wz / ∂Wz / ∂Wz / = + Wz / ⋅ + Wy / ⋅ ∂Z ∂Y ∂X
W02 – g ⋅ L0
⎞ ⎟, ⎟ ⎠
(2.104)
. (2.102) - (2.104) : 1)
–
-
, ,
: X, Y, Z, Re, Fr; 2)
–
, Wx / , Wy / , Wz / , Eu.
. ,
Re, Eu (
-
Fr
). (2.102) - (2.104)
-
:
Wx / = fx(X, Y, Z, Re, Fr);
(2.105)
Wy / = fy(X, Y, Z, Re, Fr);
(2.106)
Wz / = fz(X, Y, Z, Re, Fr);
(2.107)
Eu = fEu(X, Y, Z, Re, Fr).
(2.108)
,
(2.26) - (2.31) Wx, Wy Wz : W = f( , , z, ρ, ν, g, W0, L0). (2.102) - (2.104) , , 60
8
-
∂Wy / ∂Wz / ∂W / = 0, + + ∂Z ∂Y ∂X
(2.109) (
. . 35)
. (
)
.
-
W02 L 0 , . .
1
). Gp
G,
G (
G . G
-
G: Fr =
GP
G: Eu =
G W02 W2 L . = 0 0 ~ G L0 ⋅ g g
(2.110)
(P / ρ) / L0 ~ G . P = 2 G W02 L0 ρ ⋅ W0
(2.111) G
G : Re =
G W0 ⋅ L0 W02 / L0 . ~ = ν ν ⋅ ( W0 / L 0 ) / L 0 G
(2.112)
, ,
( )
,
.
, "
-
". . 1.
, . . . ,
,
, .
61
-
2. . 3. . ,
, -
Wx / , Wy / , Wz /
= 1 / L01 = 2 / L02; Y = y1 / L01 = y2 / L02; Z = Re = W01⋅L01/ν1 = W02⋅L02/ν2 :
z1 / L01 = z2 / L02 Wx / =
Eu
Wy1 Wy 2 Wx1 Wx 2 W W = ; Wz / = z1 = z 2 , ; Wy / = = W01 W02 W01 W02 W01 W02
(2.113) . -
-
. .
:
. – .
–
μ
Re . (
.
-
5)
. 2.15.2.
[1]
: 1.
, ,
. .
,
-
. . 2.
, . .
-
. .
-
. , . ,
. 62
,
,
(
)
. , .
,
.
,
, . -
(Re
= Re )
, ν
(Fr ,
,
. -
10
, (W0
)
10
> Fr ). =ν
-
103
, .
. ,
, .
. Re .
-
. < Re ;
63
3. 3.1.
,
. . . (
, -
< 0,1⋅
), . . 3.1. (
. )
.
Fmin -
. , , . . . ,
,
-
, .
. 3.1.
:
)
; ) ; )
P
1
+
W12 ⋅ ρ1 + z1 ⋅ g ⋅ ρ1 = P 2
; )
1-1
2
+
2-2
W22 ⋅ ρ 2 + z 2 ⋅ g ⋅ ρ 2 + ΔP 2 64
; ) -
12
,
(3.1)
1
= 0, ρ1 = ρ2 = ρ, z1 = z2, Δ W2 = W
2 ⋅ (P
=
−P ρ
1
).
= 0,
12 2
(3.2)
, , . ,
2
(
). , ( " "),
ΔP
12
=
⋅
⋅ ρ2 , 2
W22
W2 = W
ϕ–
( W2 < W
), -
.
(3.1)
2 ⋅ (P
= ϕ⋅
ϕ = 1 / (1 +
−P ρ
1
2
),
(3.3)
).
(3.4) ,
( (
" "). " ")
.
v
= W ⋅F ,
F ε,
.
F
v
= ϕ⋅ε⋅F
2 ⋅ (P
65
−P ρ
1
/F
2
).
-
(3.5)
ϕ⋅ε
μ. . 3.1. 3.1 ϕ 0,98 0,82
,
ε 0,63 1
μ 0,62 0,82 , ,
(3.3)
(3.5) ( )
.
P =P
-
- ρ ⋅g⋅H,
–
(3.6) ,
-
. P =P
- ρ ⋅g⋅H.
(3.7)
P1 - P2 = P - P = g⋅H⋅(ρ - ρ )
v
2 ⋅ g ⋅ H ⋅ (ρ − ρ ρ
= ϕ⋅
W
= μ⋅F
⋅
(3.8)
),
2 ⋅ g ⋅ H ⋅ (ρ − ρ ρ
(3.9)
).
(3.10)
3.2.
,
,
.
, , . . dq 66
= 0.
, (H = q = 0), [Δs = (Δq + Δq ) / T = 0]
.
, -
/ ρ = const, =
p
/
v
–
;
p,
v
(3.11)
/( ⋅ )] – 3
[
.
, ⎛ P ρ = ρ ⋅ ⎜⎜ ⎝P
,ρ –
⎞ ⎟⎟ ⎠
1
K
,
(3.12) .
Δq
.
(1.22), + Δq = 0,
.
L
= ⋅dV
-
,
. (3.12) -
: W=
=
(1.22)
⎡ 2⋅ K P ⎢ ⎛ P ⋅ ⋅ 1 − ⎜⎜ K −1 ρ ⎢ ⎝ P ⎣
⎞ ⎟⎟ ⎠
K −1
K⎤
–
⎥, ⎥ ⎦
(3.13)
.
⎡⎛ ⎞ 2 K ⎛ P P 2⋅K ⋅ P ⋅ ρ ⋅ ⎢⎜⎜ ⎟⎟ − ⎜⎜ m = F ⋅ρ ⋅ W = F ⋅ ⎢⎝ P ⎠ P K −1 ⎝ ⎣
⎞ ⎟⎟ ⎠
K +1
K⎤
⎥. ⎥ ⎦
(3.14)
= const =
. .
67
(3.13), .
-
( = 0) =
W
2
P ⋅ = −1 ρ
2
−1
⋅ R ⋅T .
(3.15) , (3.14) ,
-
, (
. 3.2),
. ,
. 3.2.
, ( ) ( ):
–––––––––––– – –⋅–⋅–⋅–⋅– –
= . ρ = ρ m → 0.
; (3.14)
,
, . . = 0. P =P
, c
c
⎛ 2 ⎞ =P ⎜ ⎟ ⎝ +1⎠
K
−1
.
W,
: , -
(3.16)
.
-
. ,
(
) (
, . ≈ 0,5⋅
3.17
3.20). = const
W ρ
-
,
. 3.3.
(
( (
-
. 3.3). –
), 69
)
,
-
.
. -
. 3.3. : 1-
(3.13).
;2-
m
(3.14), .
70
4.
"
4.1. -
"
(
. 4.1), -
, =
⋅ρ ⋅g,
+
2
(4.1)
= 0). t > t, – ρ = – ρ = ρ0 /(1+α⋅t ), . . ρ0 ≈ ρ0 .
( ρ0 /(1+α⋅t )
>
2
⋅ρ ⋅g.
+
(4.2) , -
-
, 2
>
.
2
, Δ
. 4.1. ; 2-
; 3; 5-
, ; 4-
; 6-
;
7-
1
t. (
ρ –
) G .
, ρ 6)
(
(5.3) .
. 5.2). ,
(5.3) dL = b⋅L.
(5.4)
(
m0 –
)
L m , = 0,316 ⋅ d0 m0
(5.5)
⎞ ⎛ L m = ⎜⎜ 0,316 ⋅ − 1⎟⎟ . d m0 0 ⎠ ⎝
(5.6)
,
[ / ]. ,
–W ,
-
. W
>W ,
, . ,
83
-
. ,
, W =
W
m1 ⋅ W1 + m 2 ⋅ W2 . m1 + m 2
(5.7) , – I0,
(5.7) -
. (5.2)
I
= I0.
(5.4)
. . -
. (5.2), (5.5), . . . W ,
L,
,
mc [18]. , -
. , . ,
,
.
, . 5.2.
. (
,
, ,
,
. .), (
, . 5.3)
. ,
, .
. dV 84
,
-
, -
.
-
, . , . 5.3. . (
.
. 5.4)
-
,
. ,
Δ
.
W2 =
v 2 = F2 ⋅
,
, (
2 ⋅ ΔP ρ2
)
,
2 ⋅ ΔP ρ2
(5.8)
.
(5.9)
-
,
-
. 5.4. ΔP .
. , : 85
⎛ m1 m 2 ⎞ W2 W2 ⎟⎟ ⋅ P2 + m1 1 + m 2 2 = ⎜⎜ + 2 2 ⎝ ρ1 ρ 2 ⎠
⎛m m ⎞ (W − W3 )2 + m (W2 − W3 )2 , W2 = ⎜⎜ 1 + 2 ⎟⎟ ⋅ P3 + (m1 + m 2 ) 3 + m1 1 2 2 2 2 ⎝ ρ1 ρ 2 ⎠
ΔP = P3 − P2 =
(5.10)
m1 ⋅ W1 ⋅ W3 + m 2 ⋅ W2 ⋅ W3 − (m1 + m 2 ) ⋅ W32 . m1 m 2 + ρ1 ρ 2
(5.11)
= m2 / m1 W1, , ΔP
,
, ΔP
. .
W2 .
,
W2 W3 W2, W2
W1
(5.8), ΔP
(5.11),
-
ΔP .
W3
W1.
W2, W1.
,
, W1. ΔP , , W3 .
W3
W2, -
-
. ,
,
–
.
. ,
,
, W2
,
. .
F2 / F1, 3. . F2 / F1, , .
,
(
) (
,
).
86
-
5.3.
, . .
, ,
. .
, -
.
-
, – . ,
-
, ,
. .
,
.
-
. (
,
).
-
. , ,
,
"
", . .
-
, . ,
,
-
. (
. 5.5), . -
( , ,
. 1), 2.14. .
. 5.5. ,
,
,
,
. ( . 1
. 3). 3,
-
2,
. . 87
-
"
" .
,
, .
, , ,
-
, ,
. L v1.
. .
[19, 20]
,
-
. , . . . . 5.6 .
,
,
,
. , , . . 5.6.
-
,
, .
-
,
. (
,
,
)
. , . 88
-
,
,
-
. , .
-
. .
-
, . 5.4.
, , (
. 5.7). .
. , ,
.
,
,
-
. – . . .
. 5.7.
( ) ( ) :
.
,
, -
1-
(
); 2 -
. .
,
, ,
,
. ,
–
.
, . 89
-
, (
) .
.
, ,
-
,
.
90
2. 6. (
)
6.1.
, . 3 ,
:
-
. -
. . Q=
dE [ dτ
/c =
τ [ ].
[ 2] q=
[
]
(6.1)
],
d2E dQ ⎡ , = dτ ⋅ dF dF ⎢⎣ ⋅
2
F
=
2
⎤ ⎥ ⎦
(6.2) -
. . ,
"q",
1 ,
1 ,
q
2
dF
. (
) q = −λ ⋅
∂t , ∂n
91
, (6.3)
λ[
/( ⋅ )] –
, ∂t [ / ]– ; ∂n
-
. , ,
,
-
. . λ
, , . (
q = α ⋅ (m t ± t
)
α [
t –
;t – /( 2⋅ )] –
),
(6.4) . –
,
(
) -
. α
. . "
–
–
, ) ^
-
9. . – " ",
-
4 4 ⎡⎛ ⎞ ⎤ ⎞ ⎛ ⋅ ⎢⎜ ⎟ ⎥, ⎟ −⎜ ⎢⎣⎝ 100 ⎠ ⎝ 100 ⎠ ⎥⎦
q =
– = t + 273;
", (
,
(6.5) 0
= t + 273.
5,67
/( 2⋅ 4);
:
q
-
–" "
–" "(
92
).
6.2.
.
, . , –
-
. -
t >t
4 4 ⎡⎛ ⎞ ⎤ ⎞ ⎛ − ⋅ ⎢⎜ ⎟ ⎥ + α ⋅ (t − t ⎟ ⎜ ⎢⎣⎝ 100 ⎠ ⎝ 100 ⎠ ⎥⎦
q=
.
),
t [0C] –
T [ ]
-
(6.6) . -
4 4 ⎡⎛ ⎞ ⎤ ⎞ ⎛ − ⋅ ⎢⎜ ⎟ ⎥ + α ⋅ (t − t ) . ⎟ ⎜ ⎢⎣⎝ 100 ⎠ ⎝ 100 ⎠ ⎥⎦
q=
(6.6)
(6.7) . , t ,
t
(6.7) q t
.
-
t . q = (t − t
⎧
) ⋅ ⎪⎨α ⎪⎩
t -t
4 4 ⎡⎛ ⎞ ⎤ ⎞ ⎛ ⋅ ⎢⎜ ⎟ ⎥ ⎟ −⎜ ⎣⎢⎝ 100 ⎠ ⎝ 100 ⎠ ⎦⎥
+
q (t − t
(t
−t
⎫
)⎪⎬ ⎪⎭
(6.8) -
α α =
t -t,
)
=
4 4 ⎡⎛ ⎞ ⎤ ⎞ ⎛ − ⋅ ⎢⎜ ⎟ ⎥ ⎟ ⎜ ⎢⎣⎝ 100 ⎠ ⎝ 100 ⎠ ⎥⎦ (t − t )
t -t =
93
,
(6.9)
(
)⋅ (
).
(6.10)
q = (α + α )⋅(t - t ) = α⋅(t - t )
(6.11)
α =
100
4
⋅
2
+
2
+
q = (α + α )⋅(t - t ) = α⋅(t - t ),
(6.12)
α=α +α
(6.13) -
(
). :
.
,
(6.10), t →t , ,
4
α
=
4⋅ ⋅ 1004
.
α
-
3
.
(6.14) ,
α
, 4
,
-
.
6.3. 6.3.1.
. .
-
,
-
. . "
" [15]. . 94
. . , . –
,
. (
)
-
. 6.3.2.
.
,
-
, (
) .
-
(
. 6.1). -
. . 6.1. (t5>t4>t3>t2>t1):
. ,
q-
grad t = n0⋅ n0 –
∂t ⎡ ⎤ , ∂n ⎢⎣ ⎥⎦
(6.15)
, . .
,
-
. -
q.
95
q = −n 0 ⋅ λ ⋅
∂t ⎡ ∂n ⎢⎣
2
⎤ ⎥. ⎦
(6.16)
(6.16)
. ( ,
q
. 6.2). grad t
,
-
. " (6.16).
"
λ . λ
. 6.2.
(
,
) – λ = 0,7-1. λ.
λ[
Q Q = ∫ q ⋅ dF = ∫ λ ⋅ F
F
∂t ⋅ dF, [ ∂n
F,
-
. λ = 30-50 /( ⋅ ), λ < 0,2. /( ⋅ )] (6.16). . q ,
].
(6.17) -
. Q = q⋅F, [
96
].
(6.18)
6.4.
( 6.4.1.
)
. .
(
-
. 6.3).
. t tc . . tc
-
. 6.3.
t . (
-
,
)
. (
)
,
-
Q . . ∂t
∂τ
, . . t x = f (x ) ,
0. , Q
= Q yx = Q x = Q
,
-
(6.19) Q x = q x ⋅ Fx
. . .
, . (6.19)
τ = ∞.
,
97
-
Q , Q x = −λ x ⋅
dt x ⋅ Fx . dx
(6.20)
Fx = const = F . (6.20) : λx = const
λ
,
,
t
, (
-
. 6.3).
t
dt x t −t =− dx S
, ,
(6.21) ,
t −t S
= λ⋅
Q
.
(6.22)
-
: ⋅F .
(6.22)
, =
Q
t − tc . S λ⋅F
(6.23)
(6.23)
-
R
Q
(
. . 6.4).
λ1
=
=
S . λ⋅F
(6.24)
t − tc . R
(6.25)
S1 , ( S2
, 98
,
,
).
2 -
λ2 < λ1.
=∑ n
Si , i =1 λ i ⋅ F
R
(6.25)
(6.26). λi = const λ
.
(6.26)
. 6.4.
qx
F ≠F,
(6.26) F F , F =
,
F −F , ln (F F )
F . -
(6.27)
F = F ⋅F . qr = Q
= const, -
(6.28)
Fr = const Fr
. 6.4. r
(
,
2-
-
. 6.5). q ∂tr/∂r
: - λ 1 > λ 2;
- λ 1 = λ 2; - λ 1 < λ 2
– ,
.
(
: Q = α ⋅ t −t Q =
t
−t R
99
)⋅ F , ,
(6.29)
(6.30)
(
Q =α ⋅ t
−t
α =α +α – ;α =α +α –
)⋅ F ,
(6.31) . t
t (6.29) - (6.31) :
t
Q = t −t α ⋅F Q ⋅R
. 6.5.
, =
Q
=t
Q =t α ⋅F
( ) ( )
t
, (6.32)
−t
, (6.33)
− t . (6.34)
Q =Q =Q =Q ,
t −t . 1 1 +R + α ⋅F α ⋅F
(6.35)
1 α ⋅F
R [ /
],
-
1 – α ⋅F
(
R .
)
Q
(6.33)
=
t −t R +R +R
(6.34),
.
-
(6.36) t ,
100
tc − t R +R
=
Q
.
(6.37)
(6.37)
-
. (6.32)
t t Q :
(6.34) t
= t − Qc ⋅ R ,
(6.38)
t
= t + Qc ⋅ R .
(6.39)
Q : t1 - t2
F1 =
Q
-
F2, R 12
t1 − t 2 . R 12
(6.40)
Q t
t ,
t (6.38)
t
12, tc
23
. .
Q = K ⋅ F ⋅ (t − t
),
:
K
[ K =
t
(6.39)
/( 2⋅ )].
1 . 1 S 1 +∑ i + α α i =1 λ i n
. K
K F.
,
-
λt = λ0 + b⋅t. 101
(6.41)
q ∂t x = x = f (x ) , ∂x λ( x ) ( . 6.6).
λ,
-
. :
=∑ n
R
Si , λ i =1 i ⋅ Fi
Fi – . 6.6.
1 - t↑ λ↑; 2 - t↑ λ=const; 3 - t↑ λ↓
i-
; λi –
λ = f(t): λi –
(6.42)
(6.27)
,
-
(6.28),
-
i, λi = (λi + λi )/2; λi
i-
. -
, . 6.4.2.
.
, R
α.
-
(
), R Q
-
= α ⋅ (t − t ) ⋅ F .
(6.43)
6.4.3.
, . .
, .
( 102
-
)F
(
= ΔI = v ⋅ c 0t ⋅ t − c 0t ⋅ t
Q
Q
= F ⋅q
– ; Δt –
(
(6.45)
Δt
(
t ,
v ⋅ c0 ⋅ t t
(t
=
,t – ); c 0t c 0t – 0– t 0– t .
t ln t
t
.
) − (t
:
−t
−t −t
) = v ⋅ (c
),
(6.47)
,
t 0
-
(6.46)
⋅ t − c 0t ⋅ t
(6.48) t –
).
(6.48) ;t –
t c0
;
t c0
––
0– t .
K =
–
ΔI K ⋅ Δt
−t
− c0 ⋅ t
0– t
α
(6.45) ;t –
F =
(6.47)
(6.44)
= F ⋅ K ⋅ Δt ,
( (6.44)
)
, . .F ≈F: 1 , 1 S 1 + + α λ α
; α
–
-
(6.49)
103
; λ
; S– α
.
α
– -
. , =(
+
) /2,
(6.50)
–
. [23]. , F =
χ =
ΔI χ ⋅ Δt
(6.46): ,
(6.51)
1
α
1 −
⋅ Δτ
+R +
; α
α
−
(
⋅ Δτ
(t − t )− (t ln[(t − t ) (t
–
)– )]
; ΔI = v c 0t ⋅ t − c 0t ⋅ t
; Δt ;v –
1
= −
−t
−t
–
[ 2⋅ / Δτ
]; Δτ
Δτ
-
−
– -
20 % – [ ]; t
; t
–
; α
;R – ,
) ⋅Δτ
–
Δτ
–
104
.
7.
7.1.
(
)
.
-
:
, ,
,
. ∂t/∂n )
. )
, (
(
,
.
[
λ
/( ⋅ )]
∂t = ⋅ ∇2 t , ∂τ
= λ/(ρ⋅ ) [ 2/ ] – ; ∇2 t =
(7.1) ; ρ [ / 3] –
∂2t ∂2t ∂2t – + + ∂x 2 ∂y 2 ∂z 2
. -
. , , "
".
∂t ∂t x , τ = ∂n ∂x :
,
105
t = f( ,τ),
-
q x , τ = −λ ⋅ n ⋅
∂t x ,τ ∂x
(7.2) ,
( q x , τ = −λ ⋅
-
)
∂t x ,τ ∂x
(7.3) , . .
-
,
.
( ↑, t↓,
q
∂t x ,τ
( ↑, t↑,
∂x , . .
Q
.τ.
dV,
-
q
. ,
.τ,
Q
∂τ
-
, Q
∂t x ,τ
< 0, qx,τ > 0),
> 0, qx,τ < 0),
.
(
∂x
.
.τ,
Q
∂t x ,τ
, 0- .
, < 0)
Q
.τ
-Q ∂t x ,τ
(
.τ
∂τ ∂t x ,τ
∂τ
dV,
.τ
-
> 0,
-
= 0). -
, , , . .
Qx+dx,τ
Qx,τ
. ,
dV x
,
dV
Fx+dx, dE
.dV
=Q
.τ
= - Qx+dx,τ ⋅ dτ = - qx+dx,τ ⋅ Fx+dx ⋅ dτ [ 106
d
dτ ],
(7.4)
dE dQτ = Q ⋅ dτ /5/. (7.4) dV : dEyx.dV = Q Q
.τ
(7.4) Qx+dx,τ
Q .
Qx,τ = f( ) Qx+dx
= dE
.dV
(7.5)
(7.5) ,
dV .dV
, -
= - Qx,τ ⋅ dτ = - qx ⋅ Fx ⋅ dτ.
.τ
Q x + dx ,τ = Q x ,τ +
d2E
. Fx,
∂Q x ,τ ∂x
.τ
-
: ,
⋅ dx .
(7.6)
dτ
(7.4) - (7.6):
- dEyx.dV = -Qx+dx,τ ⋅ dτ - (-Qx,τ)⋅ dτ = −
∂Q x ,τ ∂x
dxdτ .
(7.7)
dV, dV,
dtτ:
dτ
d2IdV = dV ⋅ ρ ⋅ c ⋅ dtτ = dV ⋅ ρ ⋅ c ⋅ d2E
.dV
∂t
,τ
∂τ
= d2IdV, =−
∂Q x ,τ ∂x
(7.7)
Qx+dx,τ < Qx,τ.
∂t
,τ
∂τ
dτ .
(7.8)
(7.8)
⋅ dx / (dV ⋅ ρ ⋅
∂Q x 0,
(7.9) ,
. ,
dV = Fx ⋅ dx.
:
Qx,τ = qx,τ ⋅ dτ
dV = Fx ⋅ dx
107
(7.10) (7.9),
-
∂t x ,τ ∂τ
=−
∂Fx
=0;
∂x
Fx = 4⋅π⋅x2 ,
∂Fx
q x ,τ ∂F 1 ∂q x ,τ − ⋅ x . ⋅ ∂x ρ ⋅ ⋅ Fx ∂x ρ⋅ Fx = 2⋅π⋅x ,
= 8 ⋅ π ⋅x.
∂x
q x , τ = −λ
,
∂τ
∂ 2 t x ,τ
=a⋅
∂x 2
∂t
∂x
= 2⋅π ,
(7.11) ,τ
-
, -
(7.12)
⎛ ∂ 2 t x ,τ 1 ∂t x ,τ = a ⋅⎜ + ⋅ ⎜ ∂x 2 ∂τ x ∂x ⎝
⎞ ⎟; ⎟ ⎠
(7.13)
⎛ ∂ 2 t x ,τ 2 ∂t x ,τ + ⋅ = a ⋅⎜ ⎜ ∂x 2 x ∂x ∂τ ⎝
⎞ ⎟, ⎟ ⎠
(7.14)
∂t x ,τ
∂Q x ,τ
∂x
;
∂t x ,τ
= λ/(ρ⋅c) –
∂
∂Fx
λ = const, = const
, ∂t x ,τ
(7.11)
[ 2/ ].
>0
(7.9)
. ∂t x ,τ ∂τ
Qx+dx,τ > Qx,τ, < 0. ,
(
, =0
: Q
Q
.τ
.τ
)
= Qx,τ = qx,τ ⋅Fx > 0;
= Qx+dx,τ = qx+dx,τ ⋅Fx+dx > 0;
Q x + dx ,τ = Q x ,τ +
∂Q x ,τ ∂x
108
⋅ dx ;
-
d2E
.dV
= (Qx,τ - Qx+dx,τ) ⋅ dτ = −
∂Q x ,τ
d2IdV = dV ⋅ ρ ⋅ c ⋅ dtτ = dV ⋅ ρ ⋅ c ⋅ ∂t
∂t x ,τ ∂τ
∂t x ,τ ∂τ
Q "
,τ
∂τ
:
=−
∂Q x ,τ ∂x
⋅ dx / (dV ⋅ ρ ⋅
dxdτ ;
∂x
).
∂t
dτ ,
,τ
∂τ
∂Q x 0,
.
,
Qx+dx,τ > Qx,τ,
,
< 0. ,
,τ
,τ
Q . "
(
Q = α ⋅ (t
.
Q
∂Q x >0 ∂x
= 0,
,τ,
∂t x ,τ
- t ),
∂τ
)
dt x ,τ t x ,τ + dτ − t x ,τ dτ
dτ
,
, =
tx,τ+dτ < tx,τ. Q
,τ
Q ,τ Q x ,τ , Q x + dx ,τ , .
-
,
q x ,τ = ±λ ⋅ " "
-
(7.3):
∂t x ,τ ∂x
(7.15)
109
(7.15) (7.3).
(7.15) ∂t x ,τ < 0, ↑, t↓, ∂x ( ∂t x ,τ > 0, , ↑, t↑, ∂x
. (7.15)
, . . ).
(7.15)
.
q x , τ = f ( x , τ) ,
:
.
,
-
. 7.2.
,
-
, . .
.
"
"
. 7.2.1. , ,
, .
. , -
(
.
τ
r),
,
-
. . . ,
, 110
Δτ.
,
,
-
( ) : t;
tc; t
t (
=
. 7.1). -
. ( t ) .
. 7.1.
Δt = t - t ) ,
( ,
t . Δtτ : Δtτ < Δt ,
, Δt
. .
,
-
-
. (
)
I = M ⋅c⋅t .
(7.16)
, (
τ . 7.2), . .
-
tx = const = t
tx0 = f( ). τ (
).
.
-
, , , . . 111
, -
. , . : (
)
Δt
t
Δt
(
, ,
. 7.2.
, ) -
. I = ∫ t dV ⋅ c ⋅ ρ ⋅ dV .
(7.17)
V
,
(7.5)
(7.17)
t
1 ⋅ t dV ⋅ dV . V V∫
(7.18)
t
.
t =
: t , tc 7.2.2.
= ∂t/∂τ [ / ].
. (7.1)
: C , .
=
∂2t ∂x 2 dt , C dτ
τ. =
dt , C dτ
, ,
112
-
q τ,
=
dt . dτ
-
( τ
q dτ.
τ
,
τ
)
.
(6.5)
,
(6.4)
.
,
, (
,
)
,
= q τ⋅F ⋅dτ.
dQ
(7.19)
–
. dt ,
dτ
-
dI = M ⋅ c ⋅ dt .
dQ
= dI,
(7.19)
τ
=
-
(7.20)
(7.20)
dt q ⋅F = τ . ⋅c dτ
(7.21) F F.
-
F =F . – R. R;
–
R; –
R.
-
/F R. F 1
R ⋅ρ , K1
(7.22)
–
, 1
1
=
= 1,
1
= 2,
= 3. (7.21)
C
τ
=
dt q ⋅ = τ 1. dτ R ⋅ρ ⋅c
113
(7.22)
-
(7.23)
. 7.3
-
.
. 7.3
. 7.3.
q τ = const). ( t ( . 7.3 ). ,
( const) t
τ
)– -
(
= const ,
).
( . 7.3
τ
=
, -
,
.
7.2.3.
, .
-
q
Δt c = q q
=Q
⋅
S , λ
(7.24)
/F .
[21] Δt τ = q Rτ ⋅
R , λ
114
(7.25)
q Rτ –
τ,
-
τ.
, , .
. -
,
. ( q = −λ ⋅
(
∂t/∂x . 7.4).
∂t ), ∂x =0
-
=0 ,
q Rτ ≈
-
q τ + q cτ q τ ≈ , 2 2
Δt τ ≈
,
,
τ=0
[22]. τ′. τ < τ′
τ′ S = R,
R. (
,
) ( q τ = const
(7.27)
.
S
. 7.4. (
q τ ⋅R . 2λ
,
(7.26)
)
tx0 = const
–
. .
τ′ S < R.
τ = τ′ ( ), .
115
. 7.5).
τ′ . .
-
: , , . ,
,
τ=0
τ,
R → ∞. ,
,
τ′
,
.
.
,
,
. 7.5.
.
-
"
"
-
. (7.27)
(
) -
. Δtτ = f(q τ) tx0 = const . 7.6.
. 7.6.
tx0 = const,
(Δt) Δt
-
,
Δt q τ = f(τ).
116
-
7.2.4.
q τ = const
.
(
. -
. 7.7), .
(7.21) (7.27)
, Δtτ
. q τ = const
(
. 7.7.
. 7.7 )
t
τ
=t
0
+
⋅τ = t
λ = const (λ
0
+
q ⋅ 1 ⋅τ , R ⋅ρ ⋅ c
). , .
,
(7.28)
,
-
txτ = f(τ)
. ,
t
τ
Δtτ = f(τ), . .
, ,
. ,
(
τ'
. 7.7 ).
.
117
(
. 7.7 ) .
Δtτ
q
τ
a⋅
∂ 2 t xτ ∂x 2
= q ⋅ 1/(R⋅ρ⋅ ).
= const,
, =
q . R ⋅ρ ⋅c
(7.29)
(7.29),
:
q ⋅x ∂t xτ = + C1 , ∂x λ⋅R t xτ =
∂t xτ ∂x
=0 1,
(7.30)
q ⋅ x2 + C1 ⋅ x + C 2 . 2⋅λ⋅R
=0
(7.31)
t = tc.
(7.30),
,
q ⋅R . 2⋅λ (7.27),
tc.
Δt τ
=
(7.31)
2
=R
t = tc +
,
-
q ⋅R . 2⋅λ
(7.32) q τ = const
t xτ = t
τ
+ Δt τ
-
-
⎛x⎞ ⋅⎜ ⎟ . ⎝R⎠ 2
(7.33) -
. .
118
7.2.5.
q τ,
, . 7.8. (7.30) : q τ = const
-
(
1
. 7.8) q xτ = q τ ⋅ q1R =
x , R
(7.34) . 7.8.
q . 2
(7.35)
τ
. .
[21] τ
q axτ = q a τ − τ ' ⋅
"2" (τ↑, q τ↓) q1 τ − τ ' > q
(qxτ)
τ
x . R
τ
"1". 1
q
,
τ − τ'
q
τ-τ'
-
q τ-τ'. = const, " " ( . 7.8)
-
(7.36) q 2 τ − τ ' > q1 τ ,
"3" (τ↑, q τ↑)
q 2τ − τ '
q 3τ − τ '
-
q 2xτ
-
.
q1x = q ⋅
q τ. "2" (τ↑, q τ↓) x , R
2
qR
119
q . 2
q
3
τ − τ'
>q τ, 1
q
τ
q 3xτ
. .
x 2. ατ = const λ = const q τ/q
2
2
,
τ–τ'.
, Δt τ =
[21]
q τ ⋅R , K 2τ ⋅ λ
(7.38) 2τ.
2τ = 2
.
7.2.6.
(7.33) (7.18) dV = F ⋅d , V = F ⋅R;
– – V = π⋅R2⋅ ;
= 2⋅π⋅ ⋅d ⋅
dV
dV
–
( –
= 4⋅π⋅ 2⋅d , V
t
= tc +
Δt ; 3
t
= tc +
Δt ; 2
120
,
: ), = 4/3⋅π⋅R3, q τ = const
(7.39)
(7.40)
= tc +
t
(7.39)-(7.41)
. . t = tc +
3
(7.41) [21]
3
Δt
-
,
(7.42)
3
= 3,
= 5 / 3 = 1,67 . 3
Δt . 1,67
3
=2,
-
" "
.
(7.42)
, , ,
-
tx = f( ). . 7.9 τ
.
-
. 7.9.
. "2" (τ↑, q τ↓) "3" (τ↑, q τ↑) –
Δt.
"1" (
q τ = = const) .
.
, < K3 ,
K3
"3" –
K3
; "2" -
> K3 . K3
= K3
. 2,
.
3
121
-
-
2
= K2
3
= K3 .
7.2.7.
λ,
, ,
α c
α
. λ,
α
λ,
.
(
) . ,
, :Q
= q ⋅ F ⋅ τ , ΔI = τ=
Δi = i - i – ;
. -
⋅Δi .
M ⋅ Δi R ⋅ ρ ⋅ Δi , = F ⋅q 1⋅q
(7.43)
i = c 0t ⋅ t
;
(7.44)
i = c 0t ⋅ t
.
(7.45) , -
. q
. "i"
-
q
. .
: qi=
q i −q ln (q i / q
122
i i
)
.
(7.46)
τ
q
= q 0 ⋅ e Bτ ,
(7.47)
,q 0–
–
.
τ
= const, λ, α ).
t , ( . . q =
λ,
α
1 1 ⋅ q τ dτ = ⋅ q 0⋅ τ ∫0 B ⋅ τ ∫0 τ
τ
τ
d (Bτ ) =
(7.47),
0
(
τ
B⋅ τ
)= q
−1
τ = ln (q τ / q
:
,
q
0
)
−q B⋅ τ
0
-
.
(7.48) (7.48)
(7.46). 0-τ ,
q = (q
0
-
)/ 2 .
+q
(7.49) -
[23]
"i"
(7.49) .
q = q
0
⋅q
.
(7.50)
(7.50)
-
7.2.8.
τ' τ' =
R ⋅ ρ ⋅ Δi' . 1 ⋅ q'
= const, tx0 = const = t Δi' = c ⋅ t ' −c ⋅ t
0
:
⎛ = c ⋅ ⎜⎜ t ⎝
0
+
(7.51) t 'c = t 0,
0
Δt ' −t K'3
τ'
123
⎞
0⎟ ⎟
⎠
= c⋅
Δt ' K '3
(7.52) (7.38)
Δt' =
q ' ⋅R . K ' 2 ⋅λ
(7.53) (7.52) τ' =
(7.53)
⎛ q' ⎜⎜ ⎝ q'
R2 K 1 ⋅ K ' 2 ⋅K ' 3 ⋅
q' – 0-τ' (
⎞ ⎟⎟ , ⎠
(7.51) (7.54)
τ'; q ' –
. 7.10).
q τ = const
τ' =
R2 . K 1 ⋅ K ' 2 ⋅K ' 3 ⋅
(7.55) τ'
'2
. 7.10.
τ' . .
– τ' τ' = R 2 / (6 ⋅
τ'
t
τ
= R 2 / (10 ⋅
(7.56)-(7.58) = const,
: q ' = 2 ⋅ q' . ( i > 100) τ'
τ', (7.56)
),
(7.57)
).
( i = α⋅R / λ) , τ'
124
'3. ,
),
τ' = R 2 / (8 ⋅
-
τ'
τ' . t
τ
(7.58)
, = const
q τ = const. (7.55).
7.2.9.
S. 2
τ < τ', 3
(7.54)
R
K1S ⋅ K 2S ⋅ K 3S ⋅ a ⋅ τ ,
S= 1S
S 5 , , .
Re . ,
-
. . , , .
, . . -
. . Re ϕ = 82°
. . Re
-
, , 148
-
.
, .
ϕ = 140°. .
-
. ,
. -
. 8.4 .
. 8.4 . 8.4 –
,
. .
-
. 8.4 .
, .
Re -
Re ,
. . 8.4.
. 8.4 .
(α )
-
.
,
:
- Re = 219000;
. Re
2-3
α –
- Re = 70800.
.
-
. .
, .
.
Nu
d
=
⎛ Pr ⋅ Re d ⋅ Pr ⋅ ⎜⎜ ⎝ Prc n
m
149
⎞ ⎟⎟ ⎠
α
0, 25
,
(8.53)
, n, m
Red. -
, α
. , ,
(8.53).
8.12.
[5]
S1
. -
S2
. . , . ,
-
, ,
,
, -
. . .
Re < 1⋅105 ,
–
. – .
. . .
, ,
( "
").
, , . . 8.5
α
,
. α
. ,
α = 50°. ,
-
. , 150
.
. -
. ,
,
,
-
, .
-
. 8.5. (α ) ( 1
60 % .
-
; Re = 14000,
70 %.
; α –
7
): . -
-
. 8.6. -
.
.
. ,
. 8.6. ( αi )
(8.53). -
(i -
. . 151
)
8.13.
[5]
,
, ,
, (
. 8.7). ,
. , .
. , .
, -
,
-
. . 8.7. :
,
δ (
); ;
δ; -
-
. δ
;
,
;
-
, .
, δ
.
δ -
. , (
. 8.7).
.
. 8.7. " , " " "–
t 1 > t 2. ,
. 152
-
. 8.8 .
, ,
.
-
, .
α = A ⋅ 4 t − t , (8.54) = 3,3, = 2,6, (8.54) .
= 1,6.
. 8.8. (
)
Nu = C ⋅ (Gr Pr
)0,25 ⎜⎜ Pr ⎛
⎞ ⎟⎟ ⎝ Pr ⎠
0, 25
.
Pr = Pr = 1
(8.55)
(8.54). -
(
. 8.9). . ,
2
) . , .
(8.55)
. (d = 0,02 153
. 8.9.
.
.
-
. q =
λ ⋅ (t
λ –
δ
1
−t
2
),
(8.56) , .
8.14.
[5]
, . Т
х
.
х.
. ,
-
. .
.
( 8.36). .
Nu = A + C ⋅ (Re⋅ Pr )n ,
α (8.57)
, ,n–
. α
(8.57) . Т
.
ых
х.
,
-
-
-
.
, "
.
. "
"
"
,
,
. . ,
-
. ,
, 154
.
-
. Т
.
ы
ых
ых
. ,
. .
-
: i0 = i +
T0 = T +
W2 , 2
(8.58)
W2 . (8.59) 2⋅c
-
. 8.10.
, -
t0 (
. . 8.10 . 8.10 : . – (
x :
3). -
1-
–
.
-
, . , ⎛ r ⋅ W2 −T q = α ⋅ ⎜T + ⎜ 2 ⋅ cp ⎝
r
, .
155
⎞ ⎟, ⎟ ⎠
-
(8.60)
9. λ2 = 400
λ1 = 0,4
.
-
,
-
. , . . 9.1.
,
, (
. 9.1).
, -
. 9.1.
,
,
, dF, ω = 2π. .
-
Q Q /Q
=Q
+Q
+Q
=Q
+ R + D = 1,
–
(9.1)
;R=Q ; D= Q
/Q
/Q
–
–
-
. D = 0,
R =1-
.
( . A0 = 1, . . D0 = 0 D =1 - .
R0 = 0,
"0" = 0. 156
λ=0
) ( .
100 %) λ = ∞.
: R = 0,
9.2. 9.2.1.
dF , .
:
dF. -
q=
dQ [ dF
/ 2].
(9.2) -
E. Jλ , , Jλ =
dq λ ⎡ dλ ⎢⎣
2
⎤ . ⋅ ⎥⎦
-
(9.3) -
: J 0λ =
1
2
–
dq 0λ C1 ⋅ λ−5 , = C 2 dλ T λ ⋅ e −1
(9.4)
. J0λ = f(T)
,
. 9.2. -
. 9.2.
.
157
9.2.2.
-
q0 =
∫ J 0 λ dλ .
λ=∞
(9.5)
,
σ0 = 5,67⋅10
-8
,
σ0 ,
/( ⋅ ) – 2
(9.5)
λ =0
q0 = σ0⋅T4,
(9.6)
4
. , ,
-
. ⎛ T ⎞ q 0 = C0 ⋅ ⎜ ⎟ , ⎝ 100 ⎠ 4
0
(9.7)
= 5,67
.
(9.7)
1879
-
,
, 1893
.
9.2.3.
ελ =
Jλ(T) –
ελT
J λ (T )
J 0 λ (T )
,
(9.8)
λ
ελT .
,
-
. . , .
(
.
. 9.3).
158
. 9.3.
. 9.4. : )
:
; )
ελ
1-ε = 1 ( ); 2 - ε = 0,67; 3 - ε = 0,33.
2
; )
2
. 9.4
2
.
2
,
Jλ = f(λ) -
–q .
= ∫ J λ dλ = ∫ ε λ ⋅ J 0λ dλ .
q
∞
∞
0
0
(
(9.9)
( q
ε
) =ε
⋅ q 0 = C0 ⋅ ε
) ⎛ T ⎞ ⋅⎜ ⎟ . ⎝ 100 ⎠ 4
(9.10) ε
: 2
. ε
q = = q0
, ελ = f(λ),
∫ ελ ⋅ J 0λ dλ
∞ 0
∫ J 0λ dλ
∞ 0
159
-
.
2
(9.9)
(9.10)
(9.11)
⎛ T ⎞ q c = εc ⋅ q 0 = C0 ⋅ εc ⋅ ⎜ ⎟ . ⎝ 100 ⎠ 4
ελc εc
(9.12) (9.11)
.
" " 9.3.
, . . εc = ε.
.
, . , Jλ , q , Q -
, -
= q ⋅F ε ( . . .
ελ
9.8
Q
9.10),
= R⋅Q .
(
(9.13)
. 9.5)
Q =Q
+Q .
(9.14)
, . 9.5.
. Q
,
-
Q Q =Q
Q
-Q .
(9.15) Q
Q
= ⋅Q , Q
Q
=Q
-Q
,
.
= ⋅Q
-Q ,
160
(9.16)
=
Q
Q
+Q
-Q
-Q
Q
.
(9.17) (9.15),
Q -Q .
=Q
Q =Q (9.17)
+Q
: Q
-Q .
(9.18)
=
(9.18) R = 1- A,
, =
Q
R Q A
+
1
Q
.
(9.19)
(9.19) . Q
0
=Q
0, J0λ
, = 1, R0 = 0,
-
= J0λ.
9.4.
.
F1 (
0
. 9.6).
,
F1,
F2
. F1
,
F2 dλ, J0λ1⋅dλ.
F1
-
F2,
1
λ, 2
. -
. 9.6.
Aλ2, ( F1 ελ2⋅J0λ2⋅dλ, F1. Jλ 2⋅dλ - Jλ
). dλ
2⋅dλ = Aλ2⋅Jλ
: Jλ ⋅dλ ε ⋅J ⋅dλ = A ⋅J ⋅dλ ε ⋅J 2 λ2 0λ2 λ2 0λ1 λ2 0λ2⋅dλ 161
2⋅dλ
=
Jλ
2
λ2⋅J0λ1
=
- ελ2⋅J0λ2. Jλ
T1 = T2, J0λ1 = J0λ2 A λ 2 = ελ 2 ,
2
= 0.
(9.20)
. . . (9.20)
-
[25]. F1 (
. )
-
F2
∫
∞
2
q = q
=
2
λ2
⋅ Jλ
∫ Jλ
∞
0
2
2 dλ
2 dλ
.
(9.21)
0
F1 . Jλ.
Jλ
= ελ⋅ J0λ
= 0, Jλ
λ
= ελ
, (9.19) Q = J 0λ . -
: Jλ
(9.19)
,
(9.21)
(9.11)
λ2
A
= ελ2
Jλ ,
2
2
=ε
, . . 2
≠ ε2
(9.22)
= J0λ1.
: A = ε (Aλ2
(9.21), A 2
,
.
(9.21) ), . .
-
. (
)
,
, Aλ2 = f (λ)),
F2 ( . . F1. F1 162
,
F1,
A2
F2.
ε
≠ ε2
. 9.5.
.
(
).
Iϕ
, dF dω ϕ
L, Iϕ =
⎡ ,⎢ dFM ⋅ dω ⎣ d 2Qϕ
2
-
⎤ ⎥. ⎦
⋅
(9.23) dω -
, , M
dFM dFN (
. 9.7.
. 9.7). : dω =
dFN –
dFN , 2 rMN
(9.24)
, rMN. dFN ,
dω =
ϕN –
-
dFN ⋅ cos ϕ N , 2 rMN
(9.25)
dFN
MN, . . (
rMN ( (9.25) . 9.8)
dFN
N . 9.8). dω.
163
. 9.8.
Iϕ = In ⋅cosϕM,
(9.26)
In – ,
-
. (
. 9.9): dF ,
-
, . . 9.9.
In =
,
qM . π
(9.27)
9.6.
. ( = 5)
,
,
. F = ∑ Fi ,
,
,
K
.
i =1
T,
,
,
-
.
ϕ12
F1,
F2 [26] ϕ12 =
Q F1 − F2 Q F1
.
, dF2,
(9.28) dF1
-
(9.23) ,
"N" –
dF1. F2.
" " (9.23), (9.25) 164
F1, (9.27)
d 2Q dFM dFN = I ϕM ⋅ dFM ⋅ dω = I n ⋅ cos ϕ M ⋅ dFM ⋅ dω = =
dF ⋅ cos ϕ N q q . ⋅ cos ϕ M ⋅ dFM ⋅ dω = ⋅ cos ϕ M ⋅ dFM ⋅ N 2 π π rMN Q F1 − F2 =
∫ ∫ d QdF 2
M dFN
[26]
∫ ∫q
ϕ12 =
⋅
F2 F1
Q F1 = ∫ q M ⋅ dFM
cos ϕ M ⋅ cos ϕ N dFM dFN 2 π ⋅ rMN
∫ q M dFM
.
(9.29)
F1
ϕ 21 =
∫ ∫qN
⋅
F1 F2
-
F1
F1 F2
cos ϕ N ⋅ cos ϕ M 2 π ⋅ rNM
∫ q N dFN
ϕ 21 dFN dFM
.
(9.30)
F2
q M = const
qN :
ϕ12 =
qM ( qN ) ( . 9.10), ( . 9.10 9.10 ) F1. . . (9.29) (9.30)
" " = const.
-
1 cos ϕ M ⋅ cos ϕ N dFM dFN , ⋅∫ ∫ 2 F1 F F π ⋅ rMN
(9.31)
1 cos ϕ M ⋅ cos ϕ N dFM dFN . ⋅∫∫ 2 F2 F F π ⋅ rMN
(9.32)
1 2
ϕ21 =
1 2
ϕ
,
(9.32). 165
ϕ12 , ϕ21
, (9.32).
ϕ
,
(9.31)-
.
ϕ = ϕ
≠ ϕ
, ϕ
,
,
. .
[27] .
: -
[28]
-
. (9.31) (9.32) . . 9.10. ,
-
ϕdF-F = const
(
.
. 9.10 ),
-
[26]: ϕ12 = ϕ22 =
F2 F2 , = F F1 + F2
(9.33)
ϕ21 = ϕ11 =
F1 F1 . = F F1 + F2
(9.34)
. 9.10 ,
ϕ22
9.10
. ,
ϕ12 + ϕ11 = 1 , ϕ21 + ϕ22 = 1 .
166
: (9.35) (9.36)
ϕ22 = 0
, (9.31)
ϕ21 = 1.
(9.32)
-
F1 ⋅ ϕ12 = F2 ⋅ ϕ21 .
(9.37)
. 9.10
(9.37)
9.10
ϕ12 =
F1 . F2
(9.38) -
, . ( (9.33)
, .
. 9.10 , 9.10 , 9.10 ).
(9.34) ,
(9.38)
ϕ12
: ϕ22 = 0
,
-
ϕ21 = 1.
9.7.
, . ϕi = ϕ
, Q
2
Q
1 ⋅ ϕ12
=Q
2
-Q
2
Q
2
=
=
.
i
2⋅Q
2
[
⋅Q
(9.15) 2
-Q
1 ⋅ ϕ12
2.
(9.39)
+Q 1
:Q
2,
Q
1,
Q
2.
167
2
]
⋅ ϕ22 − Q 2
Q
2
(9.40) Q 1, Q
2
⋅ ϕ22 .
-
.
2
(9.40) Q
1,
3 Q
2
-
(9.19), Q Q
1
2
=-Q =
(9.40)
2
⎡⎛ R 1
2 ⎢⎜ ⎜
⎣⎢⎝ A1
Q
1
+
1
Q
1
⎞
1⎟ ⎟ ϕ12
⎠
,
⎛R + ⎜⎜ 2 Q ⎝ A2
2
+
1
Q
2
⎞
2⎟ ⎟ ϕ22
⎠
⎤ ⎥−Q ⎦⎥
2
,(9.41)
R 1 1 − A1 1 R 1 − A2 1 = = −1 ; 2 = = −1 ; A1 A1 A1 A2 A2 A2
Q
1
=
⎛ 1 ⎞ ⎟ ⋅F1; Q 0 ⋅ ε1 ⋅ ⎜ ⎝ 100 ⎠ 4
2
=
⎛ 2 ⎞ ⎟ ⋅F2. 0 ⋅ ε2 ⋅ ⎜ ⎝ 100 ⎠ 4
: ϕ22 = 1 - ϕ21 , ε1 = A1, ε2 = A2 (
Q
12
2
=
12
)
4 4 ⎡⎛ ⎞ ⎛ ⎞ ⎤ ⋅ ⎢⎜ 1 ⎟ − ⎜ 2 ⎟ ⎥ ⋅ F2 ⋅ ϕ21 , ⎣⎢⎝ 100 ⎠ ⎝ 100 ⎠ ⎦⎥
–
-
(9.42) -
C12 =
⎞ ⎛1 ⎞ ⎛1 ⎜⎜ − 1⎟⎟ ⋅ ϕ12 + 1 + ⎜⎜ − 1⎟⎟ ⋅ ϕ21 ε ε ⎠ ⎝ 2 ⎝ 1 ⎠ 0
(9.42) q2 =
C=
Q F2
⎡⎛ ⎞ ⎛ ⎞ = C ⋅ ⎢⎜ 1 ⎟ − ⎜ 2 ⎟ ⎢⎣⎝ 100 ⎠ ⎝ 100 ⎠ 4
2
4
⎤ ⎥, ⎥⎦
0 ⋅ ϕ21 , ⎛1 ⎞ ⎛1 ⎞ ⎜⎜ − 1⎟⎟ ⋅ ϕ12 + 1 + ⎜⎜ − 1⎟⎟ ⋅ ϕ21 ⎝ ε1 ⎠ ⎝ ε2 ⎠
168
.
(9.43)
(9.44)
(9.45)
-
. -
ϕ12 = ϕ21 = 1 ( ) (9.44-9.45) q2 =
(9.44) . -
4 4 ⎡⎛ ⎞ ⎛ ⎞ ⎤ ⋅ ⎢⎜ 1 ⎟ − ⎜ 2 ⎟ ⎥ . 1 1 ⎢⎝ 100 ⎠ ⎝ 100 ⎠ ⎥ ⎦ ⎣ +1+ ε1 ε2
C0
(9.46)
, ,
,
-
. 9.8.
– ,
,
-
, . . 9.11)
(
. . 9.11.
.
–
. -
Q
1
1
"
2
"
4 4 ⎡⎛ ⎞ ⎛ ⎞ ⎤ ⋅ ⎢⎜ 1 ⎟ − ⎜ ⎟ ⎥= ⎣⎢⎝ 100 ⎠ ⎝ 100 ⎠ ⎦⎥
1
=Q
ε1 = ε2 = ε . 2
4 4 ⎡⎛ ⎞ ⎛ 2 ⎞ ⎤ ⋅ − ⎢ ⎥, ⎜ ⎜ ⎟ ⎟ 2 ⎣⎢⎝ 100 ⎠ ⎝ 100 ⎠ ⎦⎥
–
" -
". 1
=
2,
(9.47)
169
-
(9.47) -
4 4 4 1 ⎡⎛ 1 ⎞ ⎛ 2 ⎞ ⎤ ⎛ ⎞ = + ⎢⎜ ⎜ ⎟ ⎟ ⎜ ⎟ ⎥. 2 ⎢⎣⎝ 100 ⎠ ⎝ 100 ⎠ ⎥⎦ ⎝ 100 ⎠
(9.48)
(9.47),
F1 F2 Q Q
2
2
=
1 2
(9.48)
1
-
4 4 ⎡⎛ ⎛ 2 ⎞ ⎤ Q 1 ⎞ ⋅ − ⎟ ⎜ ⎟ ⎥= 2 ⎢⎜ 2 ⎢⎣⎝ 100 ⎠ ⎝ 100 ⎠ ⎥⎦
–
2
,
(9.49)
2-
-
. , 2
ε < ε1 = ε2,
.
2
2
, n Q
2
=
1 n +1
1
-
Δt > 0.
.
4 4 ⎡⎛ ⎛ 2 ⎞ ⎤ Q 2 1 ⎞ . ⋅ − ⎢ ⎥= ⎜ ⎜ ⎟ ⎟ 2 ⎣⎢⎝ 100 ⎠ ⎝ 100 ⎠ ⎦⎥ n + 1
(9.50)
9.9.
.
[29]. (1, . .
. 9.12),
3,
. L
(
,
. .) (
-
. 9.12). .
F1
F3 F2
F1,
ϕ13
, F3.
170
Q
3
-
Q
3
=
4 4 ⎡⎛ ⎛ 3 ⎞ ⎤ 1 ⎞ ⋅ − ⎟ ⎜ ⎟ ⎥ ⋅ F3 ⋅ 0 ⎢⎜ ⎢⎣⎝ 100 ⎠ ⎝ 100 ⎠ ⎥⎦
,(9.51) -
( : L = ∞,
).
L = 0, = 0, . . ,
= 1.
. 9.12.
, .
9.10.
9.10.1.
2
2
( (
,
)
,
)
,
. ,
.
-
, -
. ("
")
. .
.
, . .
.
, (
.
).
.
,
, ( 2
171
2
), .
.
N2
-
2
. ε
, . 2
2
( -
2
.
. 9.4)
Δλ3 = 16,5-12,5 = 4 0,3 , Δλ2 = 3-2,2 = 0,8
2
,
Δλ1 = 3-2,4 = 0,6
, Δλ3 = 8,5-4,8 = 3,7
2
, -
Δλ).
2
1500 (
2
2
, Δλ2 = 4,8-4 = 0,8 , Δλ1 = 2-1,7 = 2 , Δλ4 = 30-12 = 18 . 2 . -
2,
,
2
2.
,
-
, 2
9.10.2.
.
2
.
(
. 9.13)
Iλ dFN
dF d
-
dI λx = − I λx ⋅ λ
λ
⋅ dx ,
(9.52)
– [
-1
]. (9.52)
I λN = I λM ⋅ e −
. 9.13.
172
λ ⋅ rMN
,
rMN –
dFM
dFN.
, A λMN =
I λM − I λN = 1 − e − K λ ⋅ rMN . Iλ ελMN
2
(9.53)
AλMN.
λ
-
rMN (
2
). AλMN
-
,
= ρ⋅R⋅T.
:
, -
, 2 2
, .
2
, PCO 2
2
, 2
dFN,
dFM
PH 2 O
.
2
,
-
ελMN = f(T, , %
2,
%
2
, rMN). ,
ελMN = f(λ), ,
.
-
ε MN = ∫ ελMN dλ . ∞ 0
9.10.3. Э
(
)
dF, – . εVM
dF 173
-
εVF
F . VM), εVF (
εVM (
F
-
VF)
. dF rMN.
dF
F
(9.53),
rVM
ε VM =
VM
= 1− e
ε VF =
VF
= 1− e
− K ⋅ rVM
− K ⋅ rVF
– (9.54)
;
rVF :
(9.54)
,
(9.55) . rVF .
(9.55) rVM S VM = rVM
S VF = rVF .
SVM
λ. . .
S VF ,
-
S VF
εVM
εVF
V
R=S
dF
. , :
εVF = f(T, , %
2,
%
2
, S VF ),
εVM = f(T, , %
2,
%
2
, SVM ). 2
,
2
-
. S .
-
174
S = 1,75⋅ , –
(9.56)
.
S = 0,9⋅D, D–
(9.57)
. :S
= 0,5⋅D.
,
, ,
S
S = 0,6⋅D.
> 0,5⋅D. (9.58)
,
S VF
-
. : =F +F ,
F
= V
V V V –
–
=V
, V
-V ,
–
= 4⋅π ( R
V F
( (
4 ⋅π⋅ R = 3 4⋅π⋅ R
R
(9.61)
)2
=
4 = ⋅π⋅ R 3
V
) )
3
2
(9.60)
(
. F
(9.59)
=
3⋅ V 3 F +F
(9.58),
,
175
V F +F
.
),
,
3
,
(9.61)
S VF = 3,6 ⋅ ε0 ε
2
ε
ε0 = ε
2
+μ⋅ε
2
.
(9.62) εVF
− Δε0 ,
(9.63)
–
2
2
1,55; Δε –
1 2
:
V F +F
. ,
2
;μ–
,
2 2
. (μ ≈ 1, Δε ≈ 0).
(9.63)
9.10.4.
:
,
.
, . (
,
), .
-
. , [30].
-
-
. ,
,
. ( (
"0"
(i = 1) Q
i
=
.
" ")
9.7).
(i = 2)
⎛ ⎞ ⋅ εi ⋅ ⎜ ⎟ ⋅ Fi ⎝ 100 ⎠ 4
0
-
176
Q εi –
ik
=Q
k
(
⋅ ϕki ⋅ 1 − A ki
)
i = 1, 2
k = 1, 2, i-
A ki – i-
; k-
. -
Q
=Q
2
+Q
−Q
(
2
2
=
)
⋅Q
2
1 ⋅ ϕ12 ⋅ 1 − A12 + Q
−Q
(
2
Q Q
2 2
=
1 1
Q
1
Q
2
2.
) ⋅ ϕ22 ⋅ (1 −
Q ⎛ ⎞ ⋅⎜ ⎟ F2 + ⎝ 100 ⎠
1
4
Q
[
1-
⋅ 1 − (1 −
0 ε1
Q Q
1
2
⋅ 1 − (1 −
0ε2
Q =
[
2,
1
1 1 1
4
2 2
⋅
[
2.
(
22
≠Q .
12
1
⎛ 2 ⎞ ⎟ ⋅ F2 . 0 ⋅ ε2 ⋅ ⎜ ⎝ 100 ⎠ 4
2 2
)]− Q
(
ϕ21 ⋅ 1 −
2
21
⋅ (1 −
)+ Q
2
(
⋅ ϕ22 ⋅ 1 −
22
(
⋅ ϕ11 ⋅ 1 −
(9.65) :Q 12
=
21 =
11 = 0
Q
1 =
1,
Q 22
2.
)=
-
(9.65 )
)=
)− 1] . 21
11
3
)− 1] .
12
) ⋅ ϕ21 ⋅ (1 −
[
2
1 1
) ⋅ ϕ12 ⋅ (1 −
[
1
2.
11
(9.64)
(9.64) (9.19), (9.64)
⋅ (1 −
)+ Q 1
⎛ ⎞ ⋅ ε2 ⋅ ⎜ ⎟ ⋅ F2 + ⎝ 100 ⎠ 4
0
2
)]− Q
Q
ϕ12 ⋅ 1 −
) ⋅ ϕ11 ⋅ (1 −
Q ⎛ ⎞ ⋅⎜ ⎟ F1 + ⎝ 100 ⎠
)]
2
2 ⋅ ϕ22 ⋅ 1 − A 22 −
1
:Q
=
2
(9.65 )
: ε1 = ε 2 =
= ε0, ϕ12 = ϕ12 , ϕ21 = ϕ21 , ϕ11 = ϕ11 , ϕ22 = ϕ22 :
-
4 4 4 4 ⎡⎛ ⎡⎛ ⎛ 1 ⎞ ⎤ ⎛ 1 ⎞ ⎤ 0 ⎞ 2 ⎞ ε − + ε − F C ⎟ ⎜ ⎟ ⎥ 1 ⎟ ⎜ ⎟ ⎥ F1ϕ12 , (9.66 ) 0 021 ⎢⎜ 0 201 ⎢⎜ ⎢⎣⎝ 100 ⎠ ⎝ 100 ⎠ ⎥⎦ ⎢⎣⎝ 100 ⎠ ⎝ 100 ⎠ ⎥⎦
177
Q
4 4 4 4 ⎡⎛ ⎡⎛ ⎛ 2 ⎞ ⎤ ⎛ 2 ⎞ ⎤ 0 ⎞ 1 ⎞ ε − + ε − F C ⎟ ⎜ ⎟ ⎥ 2 ⎟ ⎜ ⎟ ⎥ F2ϕ21 , (9.66 ) 0 012 ⎢⎜ 0 102 ⎢⎜ ⎢⎣⎝ 100 ⎠ ⎝ 100 ⎠ ⎥⎦ ⎢⎣⎝ 100 ⎠ ⎝ 100 ⎠ ⎥⎦
=
2
ε021 = ε1 ⋅ ε0 ⋅ [1 − (ϕ 22 − ϕ12 ) ⋅ (1 − ε0 ) ⋅ (1 − ε 2 )] / C ,
(9.67 )
ε012 = ε 2 ⋅ ε0 ⋅ [1 − (ϕ11 − ϕ21 ) ⋅ (1 − ε0 ) ⋅ (1 − ε1 )] / C , ε201 = ε102 = ε1 ⋅ ε2 ⋅ (1 − ε0 ) / C
[
][
(9.67 ) (9.67 )
]
C = 1 − ϕ11 ⋅ (1 − ε0 ) ⋅ (1 − ε1 ) ⋅ 1 − ϕ 21 ⋅ (1 − ε0 ) ⋅ (1 − ε1 ) −
–
"
-
"
− ϕ12 ⋅ ϕ 21 ⋅ (1 − ε 0 ) ⋅ (1 − ε1 ) ⋅ (1 − ε 2 ) .
;
2
.
(9.67 )
: .
,
,
,
, . . .
-
. A 1
(9.66 )
Q
1
=0
4 4⎤ 4 A ⎡ ⎤ ⎡⎛ A ⎞ 4 ⎛ 0 ⎞ ⎛⎜ 1 ⎞⎟ ⎥ ⎢ ⎢⎜ 1 ⎟ − ⎛⎜ 2 ⎞⎟ ⎥ ⋅ F1 ⋅ ϕ12 . ⋅ = ⋅ ε ⋅ F C ⎟ −⎜ 1 0 201 0 ⋅ ε 021 ⋅ ⎜ ⎢⎝ 100 ⎠ ⎝ 100 ⎟⎠ ⎥ ⎢⎜⎝ 100 ⎟⎠ ⎝ 100 ⎠ ⎥ ⎣ ⎦ ⎣ ⎦
. . Q ε 012 –
2
ϕ22 = 0,
(9.66 )
1
=
-
4 4 ⎡⎛ ⎞ ⎛ ⎞ ⎤ ⋅ ε ⋅ − ⎟ ⎜ ⎟ ⎥ ⋅ F2 , 0 012 ⎢⎜ ⎢⎣⎝ 100 ⎠ ⎝ 100 ⎠ ⎥⎦
"
178
-
(9.68) -
"
ε012 =
ε0 ⋅ ε2 ⋅ [1 + ϕ12 ⋅ (1 − ε0 )] . ε0 + ϕ12 ⋅ (1 − ε0 ) ⋅ [1 + (1 − ε 2 ) ⋅ (1 − ε0 )]
F1 / (F2 + F1))
(ϕ12 = ϕ22 = F2 / (F2 + F1), ϕ21 = ϕ11 = :
. .
Q
2
⎡⎛ ⎛ ⎞ 0 ⎞ ⎟ −⎜ 2 ⎟ 0 ⋅ ε 012 ⋅ ⎢⎜ ⎢⎣⎝ 100 ⎠ ⎝ 100 ⎠
=
4
ε012 =
, , . . f0(λ)
2
(9.69)
4
⎤ ⎥ ⋅ ϕ 21 ⋅ F2 , ⎥⎦
(9.70)
ε 2ϕ12 . ε0 + ϕ12 ⋅ ε 2 ⋅ (1 − ε0 )
(9.71)
ελ1 = f1(λ), ελ2 = f2(λ) , . 2 .
ϕ ≠ϕ , ),
ελ0 = -
,
, (
.
179
3.
10.
10.1.
. . .
-
, . , ,
-
.
,
:
1) 2)
; ;
3)
. , ,
,
H,
,
. Fe,
-
l,
S,
Si, ,
. . .
,
,
,
-
,
-
.
. 10.1, . 10.1
,
,
,
,
,
, ,
, ,
,
, ,
180
,
,
, ,
-
10.1.1.
, . : m
, : ) SO2,
n.
(
2,
4
( H2O
)
, : CO , CO c2 , CH c4 ( CO , CO 2 , CH 4
2,
-
N2. . " "( " " " "
. .),
CO , CO 2 , CH 4
. .). ,
-
.
(t = 0
0
f [ / 3], 1 3 . .).
, = 760
ii
=
=
⋅
i
(10.1)
1 , 1 + 0,001242 ⋅ f
–
(10.2)
i
=
f
i
. :
100 − H 2 O , 100
H 2O p =
– (10.4)
,
(10.3)
100 ⋅ f [%] 803,6 + f
, [ / 3]; 803,6 / ( . .).
181
(10.4) . 3
–
-
10.2. 10.2.1.
Qv [
. Q [
/ ]–
. (
,
/ 3] – . – ,
)
-
( ,
). Q
Q .
-
. (
. 10.1.
.
. 10.1).
: 1 13 212 ; 5; 7; 9; 11 -
;4; 6; 8; 10, 14
. v
; ;3 -
. m
. t
-
15 –
t
.
.
,
t t, . .t =t =t.
t Q= Q
-
.
m
⋅c
⋅ (t
−t
)+Q
,
v
–
. 182
-
(10.5)
t < 100 ° , .
,
-
2
.
2
,
2
-
. ,
-
,
,
, -
. ( t = t = t ), Q
,
t =t =t =0° .
Q.
0 °C.
(10.5)
t,t
t
, ,
.
-
2
,
.
20 ° .
Q
-
v 100 ° . Q
, :
Q
VH 2 O [ 3/
2018
/
3
3
(600
Q − Q = 2018⋅ VH 2 O [
]–
/
3
],
(10.6)
,
1
3
,
/ )– 20 ° .
, -
, ,
-
,
Q
,
t < 100 ° .
Q , . .
Q –
,
,
, . ,
, .
183
100 °
-
Q
10.2.2.
. 10.2. 10.2 / 3)
Q ( 12770 H2
10800
CH4
35800
C2H6
63600
C3H8
91300
C4H10
118500
C5H12
146500
10.2.3.
Q = Q
(
)
⋅ Vp + Q
V p = CO p /100 [
CH 4p /100 [
3 4
Q
/
( 2)
3
⋅ V p2 + Q
/
3
]
(
4)
⋅ Vp 4 + Q
( m n)
], V p2 = H 2p /100 [
3
⋅ V pm
3 2
/
n
3
,
(10.7) ], V p 4 =
. .
100,
(i)
Q = 127,7⋅ CO p + 108⋅ H 2p + 358⋅ CH 4p + 636⋅ C2 H 6p + 913⋅ C 3 H 8p +
+ 1185⋅
4
10
p + 1465⋅ C5 H12 [
/ 3],
(10.8)
p p CO p , H 2p , CH 4p , C2 H 6p , C3 H 8p , C 4 H10 , C5 H12 – , 2 6, 5 12 .
. -
, ,
. :
Q = 340⋅
+ 1030⋅
- 109⋅( 184
- SP) - 25⋅WP [
/ ],
(10.9)
,
SP – ,
,
( ( )
,
34100
/ . -
Q ≈ 36000
3
/ . ,
. . : CO ~ 30 %,
.
Q
(
)
= Q
(
)
2
Q
(
)
=Q
(
4)
⋅V
, ,
~ 10 %,
⋅ Vcop = 12770⋅0,30 ≈ 4000
/ 3. H 2p ~ 60 %,
. +Q
4
( 2)
⋅V
2
= 35580⋅0,25 + 10800⋅0,60 ≈ 15000
2 4
/ 3. -
.
. 40000
.
–
. CH 4p ~ 25 %.
; WP – ) .
,
86-87 %
12-13 %
.
-
/ . 10.2.4.
, , Q
(
)
. = 29308
/
(7000
/ ),
-
. ,
-
,
,
= b[
b ( 29308
.
./
/ ]– . ,
1
. 185
),
(10.10)
10.3.
,
( ,
), ,
,
. , 3
1
-
. 3
1
. (
) . ,
-
, .
, . : + 0,5⋅ 2
4
+ 0,5⋅
+ 2⋅
2
=
2
=
2
=
2
2,
(10.11)
,
(10.12)
2
+ 2⋅
.
2
(10.13) :
1
2
1 = 760
. :
.) 22,4
22,4 3. 11,2
3
22,4, : 1
3
1 (t = 0 ° , 22,4 3 2.
2.
1
3 2
3
3
0,5
-
2
2.
. 4
2 m
: m
n
6,
3
8,
4
n⎞ n ⎛ + ⎜ m + ⎟ ⋅O2 = m⋅CO2 + ⋅ H 2O. 4⎠ 2 ⎝
(10.14)
5
12.
(10.14)
. ,
4
,
(
10,
n
). :
186
⎤ ⎡⎛ n⎞ LO 2 = 0,5VCO + 0,5VH 2 + 2VCH 4 + ∑ ⎢⎜ m + ⎟C m H n ⎥ − VO 2 , 4⎠ ⎦ ⎣⎝
LO 2 [ 3
3 2
3
/
3
[ / ]–
1
2
V ,
2,
4
]; VC [ 3/ 3] –
=
1
3
(10.15)
3
; VO 2
. . " ", /100, VH 2 =
, 2/100,
VCH 4 =
.
4/100
. .,
–
,
,
-
(10.15)
⎡ ⎤ ⎡⎛ ⎤ n⎞ L O 2 = ⎢0,5CO + 0,5H 2 + 2CH 4 + ∑ ⎢⎜ m + ⎟C m H n ⎥ − O 2 ⎥ ⋅ 0,01 . 4⎠ ⎣⎝ ⎦ ⎣ ⎦
1
(10.16)
: K O 2 = O 2 /100 [ 3]
3
L [ 3]
;
L O 2 [ 3] L = LO 2 /
O2
[
3
./
3
.
]
(10.17)
⎧ ⎫ n ⎡ ⎤ ⎨0,5CO + 0,5H 2 + 2CH 4 + ∑ ⎢( m + )C m H n ⎥ − O 2 ⎬ ⋅ 0,01 4 ⎣ ⎦ ⎭ , L =⎩ K 2 KO2 –
.
(10.18)
(10.17)
-
, . . . 2
= 21 %
N 2 = 79 % ( K O 2 = 0,21, K N 2
=
0,79). . f
K
(
,
187
). O2
-
KO2 , .
(10.18)
-
" "
. , L .
-
n = L /L .
(10.19)
L
"n"
n nt ,
–t
t .
1.
-
, (
)
(
). η
4. ( K O 2 > 0,21).
t
.
V (
) N2. -
η
-
. .
, . , .
202
-
10.7.
[31]
10.7.1.
, . .
, . : . .
, -
. > Q , , "
Q
" .
, ,
,
-
.
, ,
. 1000-2300
(1-1,5 %).
,
,
-
, .
,
, -
. . .
,
-
. . 5-10 .
-
.
(
)
(
)
-
. , . 203
. . . , 2
2
+
2
=2
2
. .
. . ,
,
-
, 2
+
=2
+
,
–
-
. (
2,
2
) (
-
2
) +
,
2
=
(
)
+ ,
, +
2
=
+
2
;
+
2
=
+
.
2 + 2 +
2
+ 2
2
,
. ,
. 2
2:
204
1) 2) 3)
+
2
+
2
+
=
+ + + ; + 2 .
= 2
=
;
,
-
– .
:
2
700 0
.
,
.
2
. 4
, →
3
(
2)
→
)→
(
→
,
2
,
2,
1
3
.
, . 10.7.2.
.
,
.
-
, ,
. , -
-
. ,
,
. ,
,
(t ). . -
, : .
, ,
,
,
,
.
,
,
, ,
,
.
,
. 205
,
. . -
,
. (
,
-
) ( ,
);
-
. 550
750 °
2,
4
-
. , . 10.7.3.
-
.
-
N. t = 20 ° ,
N , .
-
N ,
. ,
-
, , . ,
-
. . ( K O 2 > 0,21) . .
(t ) (t ) 206
-
, . .
-
. 10.7.4.
V = const (
) ,
,
, ,
,
.
. . ,
, .
–
-
. ,
, .
,
,
(
). , .
(1-3
)
. :
, . .
-
:
,
. ,
. ,
.
t =t .
-
W t
. 10.4. W = 0,2 / .
207
-
10.8. Э 10.8.1. [31]
. . -
,
. 10.4. ,
(W ) (t ): 1-
, .
,
;2;3-
2
;4-
. -
-
–
. . -
4
, . . ,
,
. 10.8.2.
[31]
,
, .
, -
L
,
, . . 3 :
1
.
. .
,
L
-
. "
". 2
.
,
. -
, , , 208
,
. .
-
. .
3
,
-
. . .
, ,
. .
10.8.3.
. -
. , . 10.5 (
).
: .
. ,
-
. . . , .
.
– – -
, . 10.5.
.
.
. 209
-
.
-
. .
,
.
. (
. 10.6). W , . W .
: , . 10.6.
, . 10.6. -
-
.
–
(
, , . 10.7). ,
. 10.7. , 210
-
.
L ,
= f(W )
-
(
. 10.7). Re > 8000-10000.
Re = 3000.
10.8.4.
[17]
,
. -
, [17], W [31].
[17]
.
, -
L ,
L
(
. .
. 10.8). .
, . . 10.8. –
L . L
=L
+L .
(10.55) (5.5)
L m m +m = m0 m
L
=
⎛ L ⋅ρ 1 ⋅ d 0 ⋅ ⎜⎜1 + ρ0 0,316 ⎝
= 1+
0
L ⋅ρ ρ0
0
:
⎞ ⎛ L ⋅ρ ⎟ = 3,16 ⋅ d 0 ⋅ ⎜1 + ⎟ ⎜ ρ0 ⎠ ⎝
211
-
(10.56)
0
⎞ ⎟, ⎟ ⎠
(10.57)
L – (t = t = 0 ° ,
= = 760 ;ρ0– (5.3) ( ) d
1 3 .); ρ 0 –
.
. L
⎛ L ⋅ρ = b ⋅ 3,16 ⋅ d 0 ⋅ ⎜⎜1 + ρ0 ⎝
= b⋅L
L
= ⋅d .
L
= L ⋅(1 + ⋅b) = 3,16 ⋅d0⋅(1 +
0
⎞ ⎟ ⎟ ⎠
-
(10.58)
5.1 L ⋅ρ ρ0
0
)⋅(1 + ⋅b). α = 24°
≈6
b = 2⋅tg(α /2) = 0,425 L
=11⋅(1 +
L ⋅ρ ρ0
0
(10.59)
)⋅d0.
(10.60) -
. , . .
. [31]
10.8.5.
. ,
[17]
: 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11)
d0; Q ;
; ; ; , ;
; ; ; ; . .
1.
. 212
,
, , ,
.
. 10.9
-
, .
,
-
(10.60): d0. .
,
2.
-
. ,
, (10.60),
, .
–
-
, Q
[
3
/ ], Q [
3050 / 3, , 2575 / 3. ρCO = 1,25 3 / Q ( CO ) = 2440 / , / ].
,
ρ H 2 = 0,0893
Q
(H2 )
= 28800 L = 2,3
2
3
/
. 10.9.
/ . 3
– L = 2,38
. / 3
3
; 3
./ :L
(
)
. = 40⋅d0, L
(10.60) ( H 2 ) = 407⋅d0.
,
. –
2 2
L . 3.
.
2
,
2
,
2.
213
,
L ,
d , L
L
. ,
-
,
, . .
.
4-11
-
(10.60) . 4.
. ,
(
)
( ).
. 5.
-
. -
. . , . ,
. ,
-
, . 6.
,
. .
" .
-
" ,
-
, . 7.
. -
d0 . . . ,
, ,
. 214
,
-
8.
. , .
9.
. , . ,
,
-
. , .
,
, . 10.
. , , .
,
,
-
. . ,
. -
.
, , . .
-
450
.
. ,
,
(
), . , .
11.
. .
. , ,
, .
-
. ,
.
215
10.8.6.
. . , .
, . 10.8.5, .
,
216
-
-
........................ 156
.....................................35
............ 24 ...................................... 20 ...................... 74
............................................72 ...................................................173 ................................................172 ..........................................27 ..................................162, 173 ...................12 .......................... 157, 163, 164 ....................... 26, 92, 134, 135
........................................ 92, 95 ........................................... 129 ...................... 112 ........................................... 56 ....................................... 181 ....................................... 205 .................................................... 24 .............................................................. 11 .......................................... 35 .................................... 64 ........................................ 66 ........................ 53 ............................ 95 .................................. 35 1 .................................................. 35 2 .................................................. 35 3 .................................................. 35 ........................................ 35
......................................27 .................102 ..............................................98, 100 ...............................................157 ...................92, 158
................46 ..................................................91 .......173 ................................................156 ..................157, 159 .............................157
........................................... 139 ................................................... 12 ........................................ 12 ................................. 13 .............................. 13 .................................... 15 .................................. 12, 19 ........................................... 12 ....................................... 68 ............................................... 12 ........................................ 13 ............................. 87
..........................157 ...................................................84 ...............................................84 ..............................................85 .............159 ..................................66 ..............................67 ...................26, 42 .........................................42 ..............................32 ...........................................32 ...............................113 ....................134 ................................................134 ....................................139 ..........................................139 ........................................140 .......................................18, 69, 86
................................... 134 .................................. 21, 26 ......................................... 134 ............................... 21, 26 ........................ 188 .......................... 18, 56, 69, 75, 86 ................................ 211 ........... 45, 211 .......................................... 208 .................................................. 11 ........................................... 35
..........................................50 ...........................171
217
.................... 26
...............54 ....................130 ..............................................................6 ...................................................8 ............................8 ......................................8, 64, 84 ..........................................9, 79 ....................................71 ...............................................9 ....................................................8 ........10 ..........................8 ....................................8, 18 ....................................8, 18 ......................................................8 ......................................9 .......................................................8 ....................9 .........................................8, 64 .............................................8 ..............................9, 74 ...........192 ...................91 ........................................72 ..........................67, 69 ..............................................141 ..................................145 ....................................56, 85
.......................................... 27 ........................................... 92 ................................ 158 .......................... 197 ................ 26 .......................................... 50 ..................................... 129 ............................. 172 ......................... 200 ............. 121 ............................................... 66 ............................... 188 ................................................ 65 ............................................. 65 ............... 105 ............ 93, 94 .... 92, 94, 134 ................................. 101 ............................. 92 ................................................. 53 ........................................ 143 ....................... 143 ........................ 49
................143 ...................................138, 144 .............................26
.......................... 120 ...................................... 113 ............................... 86 .................................................. 19
.............................................206 ..............................................206 ......................................48 ....................................................203
.............................................. 37 ........ 105, 110, 133 ............................................ 30 ...................... 105 ................................................ 30
.............................................15 ............................................14 ...................115
............... 110, 116 ................................. 87 ................................... 35
............................................145 ...........................................138 ( ) ...............................26 .....................................................21 ...........................................41
................................................. 115 ................................ 46 ............................... 15
..............................................37 ..............................165, 176 ....................................................14 .....................................45 ....................................................69
................................... 140, 142 .................................. 105 ................. 113
218
....................................... 68 ......................................... 39 .............................................. 112 ........................................ 16 ................................... 39 .............. 207 .................................... 69 ............................. 49 ................................ 17 ....................... 49 ..................................... 76 ................................ 58, 138 ............................................ 69
....................................160 ...........................................8 ..................................97 ......................................97 ....................................94 ......................................................91 .....................182 ..............................................182 ............................................182 ...............................................182 ...........................................182 ..............................................6 .............127 ....................................................180 .....................................180 ..................................180 ..........................................18 ............................26 ........................................22 ..................................24 ..........................22 .............................23 ................................81 ..........................163, 164
............................................ 158 ............ 158 ................................. 156 ....................... 156, 162 ............................. 156 ............................................. 17 .................................... 86 .................. 205 ................................ 191 ......................... 190
..........166 .........164 ...................................171 ..............................82 ..........................212 .....................200
..................... 191 .................... 117 ........................ 92 ............................. 40 ........................... 186 ........................ 203
.............................................18 ............................. 33, 34, 137 .......................32, 85 ..............................................37
.................................. 198 .................................... 198 ................................................ 196 ........................................... 197 ............................................... 196 ............................................. 198 ......................................... 196 ................................ 197 ....................... 100
.......................141 .......................141 ....................... 33, 34, 137 .............. 17, 30, 35, 137 .....................................37, 145 .........................................41
-
.......................................... 135 ........................................ 91
................................................136 ........................147
..................................... 160 ........................................ 160 ................................... 160 ............................. 160 .................................... 160
-
219
.............................136 ................105 ..............................136
............................................. 136
.......................122 ........................................178 .........................................82 ................58, 138 ........................................................169 .........................................169 ...............163 .................................203 .......................174 ....................................................164
............................................. 47 .................................................. 56 – ................................ 53 ...................................... 184 ......................................... 169 .............................................. 161 ......................................... 179 ........................................ 67
220
. . . 1. . .,
1. /
. ., , 1986. – 424 .
2.
. / . ., , 1986. – 320 . . .
3.
: .–
. .
. .:
14 -
: . .,
. . .–
.– .:
-
.:
, 1936. –
21
22
275 c. 4.
.
.–
.:
, 1951. –
22, 24
575 . . ., .:
5. .–
. ., . . , 1981. – 416 .
. .,
6. .–
. . , 1975. – 328 .
.:
8.
.
24, 38, 39, 39, 40, 43, 43, 148, 150, 152, 154 24, 30
.
: :
.–
, 1975. – 228 . : , 1976. – 504 . : . . . – .: : .
. . .:
9. . ., 10.
:
. .
7.
:
. . 1973. – 360 .
.– / .–
. .
11. 12.
. ., , 1987. – 304 .
.– /
. .
.–
24, 43, 43 27, 40
. .,
31, 37, 40, 51
.:
,
31
.:
, 1957. – 784 . , 1965. –
37 40
.:
722 . . . .
13. 14. . IV. 15. . 3. – 16.
., .: . .
.–
.:
, 1974. – 712 .
// . ., . , 1976. – 440 .
.
43 49, 81
.
53, 94
, 1948. – . 3-18.
.–
.:
57
, 1960. –
464 . 17.
. . .
.
III. – .:
. .
18.
// , 1955. – . 83-103. . – .: , 1976. –
81, 83, 211, 211, 211, 212 84
888 . . .1/
19. 20. 21.
, 1964. – 440 . . ., , 1977. – 464 . . .,
//
. .
. .
,– .–
.: .:
. . .
. .
22.
.
.
IV. –
:
// , 1958. – . 3-17.
-
88
-
88
-
114, 119, 120, 121
-
115
, 1937, № 12, . 29–42.
221
23.
.
.
.
. – .:
i ,
104, 123, 131
1969. – 540 . 24.
25. 26.
. . . . ( : .,
130 // . ). , 1999. . 226–235. .
. ., , 1998. – 240 . 27. . ., . , 1961. – 680 . . ., . 28. 294 . 29. . ., .– . ., 30. , . , . 31. . .,
2.–
. .,
. .
.
. . . .2. – .:
, 1975. – 934 . / :
.–
-
.–
.
. .:
.
.:
, 1971. –
166 166
. . .:
162 164, 165, 166
-
170
-
176
-
203, 208, 208, 211, 212
, 1970. – 400 . . .
III, № 4, 1967, . 463–467. . ., . . . – .: , 1965. – 390 .
222
-
Ч
............................................................................................................................................... 3 ...................................................................................................................................................... 6 1. ........................................................................................................................ 12 1. я я я . ........................ 12
1.1. 1.2. 1.3. 1.4.
........................................................................12 ................................................................14 ...........................................................15 ) .........17 ...............................18 , ........................................................................................19
, . ( 1.4.1. 1.4.2.
2. Х
я
2.1. 2.2. 2.3. 2.4.
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.
2.5. 2.5.1. 2.5.2. 2.5.3. 2.6. . 2.7. 2.8. 2.9. 2.10. 2.11.
.
(Wz = 0) 2.12. 2.12.1.
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3.1. 3.2. 3.3. 4.
4.1.
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.
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....................................................................................................................... 64
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(
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я
................................................................. 71
..........................................................................................................71
223
4.1.1. 4.1.2.
..............................................................................72 ......................................73 ............................................................................................75 ...............................................................................75 ........................77 ....................................................77
4.2. 4.2.1. 4.2.2. 4.2.3.
Ч
5.
............................................................. 81
5.1. 5.2. 5.3. 5.4.
................................................................................................................81 ............................................................................................................................84 .........................................................................................................87 .........................................................89
2. 6.
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6.1. 6.2.
..............................................................................................91 . ........................................................................................93 ..........................................................................94 ..............................................94 . ..............................................................95 ( )........................................97 . . ....................................................................97 ...............................................................................102 ........................................................................................102
6.3. 6.3.1. 6.3.2. 6.4. 6.4.1. 6.4.2. 6.4.3.
я
7.
7.1. 7.2.
.................................... 105
(
) ..........................................105 ...................................110 ..........................................................................110
7.2.1. 7.2.2.
..................................................................................................................112 7.2.3. ...........................................................................................114 q τ = const .....117
7.2.4. 7.2.5.
............................................................................................119 7.2.6. 7.2.7. 7.2.8. 7.2.9.
............................................................................................................120 ....................................................................122 .......123 S. 2 3 .....................................................................125
7.2.10.
τ → 0......125 ......................................................................................126 " ...........................127 α, λ , ................................................129 .......................................................130 .........................................................131
. 7.2.11. 7.2.12. 7.2.13. 7.2.14. 7.3.
"
8.
................................................................................................. 134
8.1. 8.2.
.................................................................................................................134 ..............................................................................................................135
224
. α .........................................................................................137 .......140 ................................141 ....142 . .............144 ......................................................145
8.3. 8.4. 8.5. 8.6. 8.7. 8.8. 8.9.
.......................................................................................................147 ..................................................148 [5]......148 [5] ........................................150 [5] ..................................................152 [5] ..................................................154
8.10. 8.11. 8.12. 8.13. 8.14. 9.
....................................................................................................... 156
9.1.
, ..................................................................................................156 .................................................................................157 ..........................................................................................................157 ....................................................................................158 .......................................................................................158 . .................................................160
9.2. 9.2.1. 9.2.2. 9.2.3. 9.3. 9.4.
.
9.5. 9.6. 9.7.
.
........................................................................................167 .................................................................................169 . ..............................................................................................................170 ...........................171 2 20 ..........................................................................................171 . ....................................................................................................172 ( ) ...................................................................173
9.8. 9.9. 9.10. 9.10.1. 9.10.2. 9.10.3. 9.10.4. Ч
.............................................161 ...........................................................................................163 ...............................................................................164
.......................................................176 3.
10.1. 10.1.1. 10.2. 10.2.1. 10.2.2. 10.2.3. 10.2.4. 10.3. 10.4. 10.5. 10.5.1. 10.5.2. 10.5.3.
10.
..................................................................................... 180
................................................................................180 ....................................................................................................181 ............................................................................................182 ...................................................182 ............184 .....................................................................184 ................................................................................................185 ............................................................................................186 ...............................................190 ...................................................................................................192 ...............................................192 . .........196 .....198
225
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,
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