-
26.325.31 50 622.276.1(075.8)
fl-
: fl- fl (- .-. .. ); - . ..
.. 50 fl : . fl -
. 2- ., . . .: , 1998. 365 .: .
ISBN 5-247-03806-1 fl fl-
, fl fl fl . - fl - , , - , fl - flfl -. , fl, fl, -fl .
fl fl .
ISBN 5-247-03806-1 , 1986 .. , 1998 .
, 1998
-
3
fl fl flfl fl -. fl , 2030 . - fl fl . - fl . -fl fl fl , : - ,
-- fl fl , -fl , -, fl. fl flfl : , fl fl , .
1020 -fl fl. . - . fl -. . , fl .
fl -fl fl fl -. fl fl -fl fl , , , fl fl
-
4-fl fl (), - fl - , -fl fl fl fl .
fl fl -- fl fl-fl, - .
fl fl flflfl ,fl -, , - , , fl . - fl, - , -fl , , flfl flfl -
.
fl fl - ., fl - . - , fl - fl - fl -fl . - fl - .
fl fl fl - fl , , 1030 , , , fl fl - flflfl , . . fl fl . -
fl.
flflflfl
-
5fl , fl.
flfl - fl:
1. fl ( ) ( ).
fl -, , fl , fl - , .
fl fl -fl .
fl -fl , - , flflfl . , fl flflfl , fl .
2. fl fl , fl - , -fl fl , fl fl , 9-- , -.
fl fl , , ; fl , fl -fl ; -fl .
3. - -, flfl fl - .
-
6 fl - ; - fl , .
4. fl 50100 .
fl -flfl . fl - - , - fl fl fl , - .
fl fl, fl fl, fl , fl fl, fl - fl fl , - .
fl -, .. , , fl, 100 , fl- 2060 , fl ( ) 5 . - 23 , , , , ,
.
5. 6- fl 5-.
fl, .fl fl fl .
6. fl ( 510%) fl .
fl flfl , - - flfl fl -fl .
-
7 fl - fl . , 5% fl - fl 10; 10% fl 5.
fl , fl fl -.
fl - - . fl, fl , , . -, fl - . fl,fl , , .
, fl , flflfl - .
, -fl fl - fl , -flfl , .
flfl fl fl. -fl fl, flfl -fl .
7. ( ) - , fl - .
, - fl fl .
( -fl ) fl, , - . fl, fl . , .
-
88. 4- fl fl - fl .
fl fl - , fl .
9. fl , fl .
100 4 - . 4 fl 64 , fl- - fl , -. , - fl.
10. fl - ( , , , ).
fl fl - fl - , - , , - .
fl fl - fl fl -fl . fl , -fl, , , - fl flfl - .
fl -, fl flfl -fl fl , fl -fl flflfl fl, -, () - fl ( - fl: -, ,
, - fl), fl,
-
9fl fl - , - fl fl ( , , - , fl ). , ,flfl fl fl, flfl fl fl ,
fl fl-fl ( , , fl , - fl fl .).
fl fl : . fl fl, fl fl -. flfl -, , fl , fl , - fl fl fl, fl , -
. fl .
, - - fl , , , , - fl , - -fl.
fl flflfl fl - fl. -fl , , fl -, ,
-
10
- 1986 . - . - .
.. 12 fl - () . .. , fl, , - fl -fl .
- .
, - , ..
- - fl ,- , ..
-
11
fl - fl fl . .
fl fl . fl -. fl . fl fl fl , .. .
fl ( XIX .) fl .
fl - 1864 . . .. . 7080 .XIX XX. fl - - .
, fl - , . fl - . , fl , fl fl, , -fl, , .. , .. , .. , .. .
20- . . - fl fl - fl . - 1856 . fl . , -
-
12
fl fl fl fl -, XIX . fl- fl 30- . .
fl- , fl , .. fl fl . - fl .. , .., .. , .. , .. -, .. , .. , ..
, .., , , , . - 30- . fl fl - . - fl - . , 20- . .. - .
20- 30- . - fl - fl - , , fl- .
, - , .. , .., fl fl . - fl - .
fl - fl , 30- 40- ., fl flfl fl - .
fl fl -, fl , 40- . , , fl , flfl ( ), , , -
-
13
, fl - .
fl - fl - fl .. , .. -, .. , .. .. fl , -fl 1948 . . fl , - fl
fl -, fl , fl fl , fl flfl , , - .
- fl - fl. 40- 50- . - fl , . fl - . fl fl - - . - fl fl- . -
fl.
50- . fl -fl ( -), - fl fl -. . fl fl - fl fl, -fl .
50- 60- . - fl fl, -fl , fl -.
fl, fl -
-
14
fl fl - . 30- 50- . - fl , 50- 60- . fl -fl .
50- 60- . - fl fl . fl, fl - fl , - fl . fl - fl, fl - fl , fl
-. - - fl , , -fl, , fl-- .
fl - -, , , - fl , .. -fl -.
fl -flfl . fl fl , - , - fl , , , - fl fl, - fl , .
fl fl - - fl .
. -. - flflfl fl.
-
15
flfl - . - fl fl- , fl , fl - , , , - fl , fl , - , fl fl fl - ,
.
, -fl .
- fl , fl. fl - fl , - , fl , - .
fl fl - . - , , , - fl , , fl , - . -fl . , - fl - . fl-flfl fl
, -- fl- (fl ) , - - . , fl - fl , - flfl - fl .
fl fl , , , ,
-
16
, -, fl.
fl , , , flfl fl fl , fl - , fl - , fl , .
-
19
1.
fl - fl fl , , .. , flfl . -, fl fl, flfl , - , - -. fl - -flfl
fl.
fl , .
fl fl. - fl (, , , ), , flfl -. , fl fl, , -fl . , fl, . ,
-fl.
fl, fl - , -
I
-
20
fl. fl , - fl fl -- .
fl , - . , - . 1. , -fl , fl fl (. 1). 1 fl fl 15 2, 2 3 1000 .
(. . 1) 1, 2 3, -fl. , - , 1 2 ( I), 3 ( II).
1
- (. . 1)1 2 3
, . 200,0 50,0 70,0, 10,0 5,0 15,0, 10-3 2 100,0 150,0 500,0fl ,
10-3 50 60 3
. 1. - fl -fl
-
21
1 2 , fl fl flfl fl -. 2 - . 3 fl 1 , fl- . , , , . , 3, fl , -
fl, 1 2, fl fl , -fl fl , - fl , - (fl ) -fl.
, , fl - 1, 2 3, - - fl -.
fl -: fl, .. fl, , .. , fl -, .
fl fl - fl -, fl ; fl ; fl fl ; , - -; , -fl, . - fl .
fl fl fl . -. , fl flfl , -fl fl fl -. - fl - - .
-
22
fl - .
1. - - . fl , - , fl , - fl , , -, , - .
fl , -fl fl. -, , -fl , - , fl - , -fl (,). fl flfl .
2. - . - -. fl fl , -fl , fl . -, , , - - - -fl fl .
3. fl . - , -, fl fl flfl - . , - fl fl fl , -fl , - fl ,
-
23
fl fl -fl , fl fl fl .
4. fl fl fl -. , -fl fl- (fl fl ) , fl - , fl -. fl -fl .
5. fl . , -fl -fl fl . , , - -, , fl - , fl , fl .
, fl - - .
2.
1 fl fl , - , fl fl .fl - . fl :
-
24
fl -fl ;
.
fl . , -
.1. S,
, flfl , , flflfl . fl S, - n,
S = S/n. (I.1)
[S] = 2/. fl -
S, , flfl - .
2. .. N, - N -:
N = N/n. (I.2)
[N] = /.3. ,
n n:
= n/n. (I.3)
.4. , -
, flfl , . fl fl , - flfl - fl - fl , ( -, , ..). - fl n, n,
= n/n. (I.4)
.fl fl ,
fl fl fl , , flfl fl
-
25
, fl .. .
fl fl .
1. fl -. fl, fl fl , fl -fl , .. , fl , - - (. 2, ) (. 2, ) .
fl, fl - fl fl -, fl (. 3).
Sc flfl fl -fl . , fl (fl fl 10-3 ) -fl 12 104 2/. fl fl - (
2)
. 2. -- () () :1 ; 2
. 3. - fl :1 ; 2 ;3 ; 4 - ; 5 -
-
26
S = 10 20 104 2/. , -
fl , - fl S , .. fl .. fl - , .. . fl S = 25 64 10
4 2/.
S 70100 104 2/. .
N flfl -. fl - fl fl , . fl - flfl l (. . 2) fl :
l S= c1 2/ , (I.5)
l , S 2/.
(I.5) fl fl fl fl.
fl fl -fl , , , - fl 0,10,2, fl fl -fl .
fl -fl fl , , - fl -fl ( 50- .); , -, fl , , . fl fl fl-fl , , ,
fl - .
2. .2.1. ().
. 4
-
27
- fl -fl - fl. fl - - - -. , -fl fl -.
S fl - , , fl fl l0 1, - fl l1 2 .., flfl 2. - -. fl (. . 4) fl
-. , flfl fl, - fl -, 500600 , fl b -fl 22,5 . fl - fl fl . fl , fl
fl -, . fl fl fl fl -fl , - , fl - , fl -
. 4. - -:1 -; 2 -; 3 fl ; 4 -; 5
-
28
() . -, fl - .
C fl fl - fl, , fl fl , , fl S N, .. . fl, -, -, fl , -fl -fl .
-, flfl-fl fl - , , fl , flfl .
fl -fl 1 1/5 .
fl fl - fl - 0,10,3.
2.2. , fl, fl, fl -, fl fl .
flfl fl - .
2.2.1. fl . - . fl, , , fl . fl- -, - flfl fl ,fl fl fl , fl- fl
, flfl fl . fl fl fl , , -, fl , fl , -fl fl.
-
29
fl fl - fl , fl fl fl - . fl fl fl.
fl fl . - . 5. fl ( ). , - flfl 2 -flfl 2 L (. . 5).
S N fl-, - flfl - fl, fl . . fl fl , fl . -fl . , , fl - fl 1. ,
- ( !) -, fl flfl 2
. 5. fl fl :1 ; 2 fl ; 3 fl -; 4 fl
-
30
2 . - fl fl 11,5 , - fl fl.
fl , fl. - - . , fl , fl -fl , - fl . - , fl , fl -, fl - fl, -
fl fl fl .
fl - (-), fl . fl, fl.
- - , . fl fl . fl-. , fl , fl -.
fl . 6. (. . 5) fl 2 fl - 3.
fl, fl - flfl , - .
- fl fl fl . fl - flfl
L, flfl - fl l01, - fl l12 (. 7), fl fl flfl
-
31
l23 (. 8). L fl- flfl . , -, fl flfl l01 = l12 = l23 = 700 ,
L=4,2 .
fl fl 1/3, fl flfl 1/5. - - flfl - - fl . , fl-
. 6. fl :1 ; 2 ; 3
. 7. fl :1 ; 2 - ; 3; 4 fl
. 8. flfl :1 3 . . 7
-
32
fl fl, flflfl, - fl . fl flfl fl , - fl, fl fl fl .
. 9 fl . - flfl flfl -.
2.2.2. . - fl - : fl-, - fl.
fl fl (. 10). fl , flfl - , fl. fl - -fl 1 : 1, = 1.
. 9. fl - :1 -; 2 fl; 3 -
. 10. fl :1 -; 2, 3 - -
-
33
fl (. 11). fl . , fl . = 1/2, .. - flfl .
fl fl (. 12). - fl 1 : 3, = 1/3.
fl fl flfl, flflfl. fl, -, fl fl - fl fl fl - fl fl , , -, fl .
, , , ( - flfl) flfl- fl , -flfl fl. fl - fl - , - (), fl fl . fl
fl.
. 11. :13 . . 10
. 12. fl :13 . . 10
-
34
fl fl - , fl - fl . - . fl fl - fl. - - , - . fl, , fl - c - - .
, fl - .
. 13. fl -, fl- :1 fl ; 2 ; 3 ;4 ; 5 fl
. 14. fl fl fl fl :1 ; 2
-
35
fl - fl fl (-, ). , fl , fl , - , .. . . 13 fl - . fl fl - , fl
.
fl fl fl - fl - .
fl fl , , - fl fl, - fl fl . . 14, -fl fl 90, fl fl, -, fl .
, - , - , , - . fl . fl -fl , - (. 15). fl , - (. 16, ), fl. .
16, .
3. - . - - , , - -, , fl fl , - fl.
flflfl , , - , . - , -fl fl .
fl
-
36
. 15. fl , :1 fl ; 2 fl; 3 ; 4 -; 5 , ; 6
. 16. fl , - : ; ; 1 -; 2, 4 ; ; 3 ; 5 fl
-
37
() , . -fl , -- .
fl fl fl -, , ( ), , , fl - . fl fl -. fl , (- ), fl (fl- 100 )
. - - fl , flfl .
fl fl flfl . fl flfl (fl ) - fl .
. 17. fl () - () -fl :1 ; 2 flfl ; 3 fl - ; 4 ; 5
-
38
fl fl -fl . fl, , , flflfl .
. 17, fl fl fl -fl , . 17, , - , fl - fl fl ,.. - . , , fl (..
17, ) , , .17, .
3.
fl fl : , -; , - fl ; , fl fl ; , fl , . fl fl . fl fl . fl flfl
, fl n. N, n, fl ..
N = N /n . (I.6)
w().
w() = n/. (I.7)
(I.6) (I.7)
-
39
N = N n = N w( ) . (I.8)
fl z(t), ,
z( ) = q ( )/N . (I.9)
flfl . t n , fl :
q = N z (t ) = N w( )z (t ) . (I.10)
(I.10) z fl t . fl fl t, (I.10) fl d, = 0 = t. , fl t fl :
q t N w z t d N w z t dt
tt
( ) ( ) ( ) ( ) ( ) .= = 00
(I.11)
fl flfl fl .
. I.1. , flfl ,
z z( ) .= 0e- (I.12)
, fl , . , fl , .. fl .
z dt( ) . =
10
(I.13)
flfl (I.12) (I.13), , = z0. . 18 z() (I.12). = 0 , z0, z0. ,
(I.12) , , fl fl
-
40
z(). fl , flfl fl . , , fl. fl w fl t, . fl ,
wt = c = const, (I.14)
. flfl w1 > w2, fl t1 <
< t2. (I.12) (I.14) (I.11),
q t N wz d N wz t z tt
0 ( ) ( ).( )= = e e- -0 0 1
0
(I.15)
(I.15) 0 t t. fl fl t t, , t t* fl w (fl w). (I.11) t t
q t N w
z t t z t
0( ) .( * )=
e e- -0 (I.16)
(I.16) , q0. fl (I.15) (I.16), , flqmax t = t. (I.14) (I.15)
q N
ct
z tmax =
( ).1 e- 0 (I.17)
(I.17) , t, .. w ,fl fl q max fl. fl fl
. 18. z() z0 = 0,1
-
41
q N cz Nzmax = =0 0. (I.18)
N , , , N = N, . . fl . . 19 q t fl w1 w2.
, fl fl fl - , -. , fl fl , flfl -- , . fl fl, fl.
. I.2. flfl ,
z t
z t
>
const 0 = =
0
. (I.19)
flfl :
w t
w t( ).
=
0 10 1 > 0 (I.20)
, flfl -fl. flfl (I.19) (I.20) (I.11), fl:
q t N z w dt N z w t t tt
0 0 0( ) ;= = 0 00
q t N z w t N z w dt N z w t t t tt
t
0 0 ( ) ;= =
0 0 0 0 1
. 19. q t N = 10
5 /; == 200 ; z0 = 0,1:1 w1 = 40 /; t1 = 5 ; 2 w2 = 20 -/; t2 =
10
-
42
q t N z w t N z w dt N z w t t tt
t
0 0 + ( ) ( )= = 0 0 0 0 11
t1 t t1 + t*.
q(t) fl . 20. fl flfl .
4. ,
fl fl fl fl - fl fl . fl fl fl- , , .
fl- : , - , .
flfl fl ( ), fl fl .
fl fl , fl flfl, fl fl -, , .
. 20. q t N = 10
5 /; t = = 5 ; z = 0,056; w0 = = 50 /; t1 = 10
-
43
fl flfl, - . fl , fl fl .
flfl , fl (). fl - , .
fl fl fl, fl flfl , , -. .
fl fl - . fl fl - fl . , - fl flfl , , () . , , , - . fl fl fl .
- , - fl , fl - .
fl , , -.
fl -fl , fl fl fl . fl fl fl . fl . fl -. - . , fl -, fl - .
-
44
fl fl -fl fl. -, fl . - .
1. fl -. , fl -fl . - (. . 21, I), fl , fl, - ( ) -, , - fl flfl
-.
fl fl (. 21, II) fl . -fl -, , , .
fl fl (. . 21, III) fl - ( fl ). (. . 21, IV ) fl , , fl - . - .
, fl -fl fl , fl fl , , fl . fl - fl - - fl, , -, fl fl fl ,
-fl.
2. fl z(t), flfl t, q(t) fl:
z(t) = q(t)/N. (I.21)
fl fl , fl -
-
45
, .
fl, t == 0, fl t, N.
zt
t dt0
=( ) .1 (I.22)
z(t) fl fl. fl fl ,
z t dt0
=( ) ,1 (I.23)
z(t) = 0 t t . fl -
fl , N, z() - w(t). fl (I.11) (I.21),
z t z t dN
Nw
t
( ) ( ) ( ) .=
0
(I.24)
fl fl fl q(t) G fl. flfl fl :
N = G, (I.25)
. 21. q, q t:1, 2 q q
-
46
fl .fl (I.25), -
fl, fl
z t q t
G( ) ( ) .= (I.26)
fl (I.21), (I.25) (I.26),
z t z t( ) ( ).=
(I.27)
, fl , fl q(t) () N(t) fl, ..
( ) ( )
( ).t q t
N t=
(I.28)
fl N(t) :
N t N q t dtt
( ) ( ) .= 0
(I.29)
(I.28) (I.29),
ddt
dN
dt
dq
dtN
+ = . (I.30)
fl, N = q/, dN/dt = q, q = zN, fl fl:
d
dt
z dz
dtz
= . (I.31)
z = z(t) , , - (I.31), = (t).
. I.3. , fl flflfl , . 22. fl z(t) flfl :
z(t) = t; 0 t t1.
, fl , fl fl, zmax:
z(t) = zmax = const; t1 t t2.
fl fl z(t)fl ,
z t zc t t
( )( )
;=
maxe-
2 t >t2.
-
47
fl , flfl fl (t),fl fl.
-, , t1, t2 zmax , , - fl fl, flfl (I.23).
fl fl (t) fl -fl z(t) - (I.31). fl (t) (I.28) (I.29).
q aNt q t dt aNtat
at
t
== =
; ( ) / ;/
.22
0
21 2
(I.32)
z(t) (t). , , t1 == 5 z = zmax = 0,05 1/ , , = 0,01 1/
2, = 0,057. fl (I.32), (t) q(t) fl . . 22 (t) fl .
fl fl (t) z = zmax ==const, fl , (I.31).
d/dt = 2. (I.33)
= 1/( t), (I.34)
flfl, fl fl
=
=
at
at c t1
12
11 2
1
/ t = t1. (I.35)
(I.35)
C t
at
at= +
1
12
1
1 2/. (I.36)
zmax = t1, (I.34) (I.36)
=
z
z tt
max
max11
2
; t1 t t2. (I.37)
. 22. z(t) (t) :1, 2 - - (t) - z(t)
-
48
t2 = 10 , .. -fl 5 fl . t = t2 = 0,08. (I.37) , (t) .
fl
= const; t > t2. (I.38)
, flfl (I.37) (I.31), - :
dz/dt = Cz. (I.39)
z zc t t= max( ).e- 2 (I.40)
(I.40) fl - fl. , fl - z(t), fl - , , (t), fl ,fl fl . : - fl fl
fl .
3. fl. -fl -fl . , . - fl . .21 fl fl q q = q ++q (q ). . fl -fl
fl , .
4. . - . - . fl - . fl .
fl , fl . fl .
fl fl
-
49
, fl ,fl - , . . 23 t. t fl , fl . - , , fl, , - , , fl - -, , ,
- - .
. fl , fl fl , , -fl . fl fl:
= 12, (I.41)
1 fl ; 2 - . fl , - , fl -fl , fl . 12 fl fl -. .. - fl. 1 - ,
fl , . 2 , -
. 23. t
-
50
, .
fl fl fl , - fl. fl fl -fl , fl, .
5. fl fl . - fl , - , fl -fl fl, flfl. fl fl fl fl fl fl fl . fl
fl fl , .. fl, fl fl , fl - .
fl -fl fl , .. - , fl, . fl - fl fl . - fl.
6. - . - fl fl fl , -, flfl , , , - . flfl fl. - fl , fl fl
.
7. fl . fl fl flfl .
-
51
, , . , - , ( ). , fl , . fl
p p x y dxdyS S
= 1 ( , ) . (I.42)
(I.42) fl S -fl.
fl fl fl . fl fl , fl fl p, fl - p (. 24). - fl fl - .
8. . fl fl fl , fl , .
9. fl . fl - - . fl-fl fl flfl , fl fl. - -
. 24. fl :1 fl ; 2 ; 3
; 4 -fl; 5 ; 6 -fl ; 7
; 8 ; 9
-
52
, , fl -. = = -fl. fl fl . , - ( ) , - fl fl. fl , -, fl - , fl
fl .
10. fl . fl- fl flfl fl , fl ; , fl ; - - fl. , fl , fl-flfl , ,
, -. fl, fl , . , , -.
fl fl , - . , - , - - fl fl . -fl fl , -fl fl ..
-
53
, , - fl fl fl, fl. fl,, fl, , . . fl fl -fl, , , .
1. fl- fl.
2. , fl fl.
3. -.
4. , fl - .
5. fl.fl fl , - fl-fl, fl fl- fl.
6. fl fl .
7. - fl.
-
54
5.
,fl . - modulus, - , . - fl . -fl flflfl - - .
fl - fl -fl.
- fl-, fl, -fl - fl -fl . fl - fl -, fl - fl.
- - , fl - fl. - fl - fl . fl, fl fl - - , fl - .
II
-
55
- -.
, , , fl ., -. - , fl- ..
fl - , .. -fl fl.
fl , fl - fl fl, fl , - - fl -fl, .
- fl -fl - fl .
flfl -- fl . . fl fl fl, fl fl .
6.
fl fl . , , fl , , -fl fl, .
- (, -) . - - .
fl fl - , .. .
-
56
- fl fl .
-fl fl-.
fl - .
, , -, flfl . fl - fl . fl - . , . 25 - mi - ki. , , . - . fl -
- . fl fl fl , - . fl , -, .
fl flfl - fl, -fl .
fl- fl . - fl -
. 25. :1 -; 2 - mi ki;3 - -
-
57
, fl-, -. - -fl fl-- flfl .
1. . - (, fl -fl ), flfl , -fl. , fl , , .. , fl -. . , ( fl) fl
- . fl- fl - .
2. . fl (), fl mi ki (. 26). , h mi ki fl hi. - , , -, .., fl -
, fl, - h h1 k1.fl h2 k2 .. fl -
hi/h = f(ki)ki (II.1)
, fl fl , fl fl - (II.1), .
(II.1) (. 27), , -.
. 26.
-
58
3. - . -, fl -c , - -
, l, fl b. , . - S . 28, i-fl li bi. . 29 S , fl l b. , fl-
.
, vi fl fl - , fl (. . 28), flfl :
vi i
x
ib p
x
b p
x= =
2
0
2
12 12
. (II.2)
q, S x, fl :
q v b lb l
p
xi i i
i iS
S
= =
3
12
. (II.3)
fl , fl
l
S
iS
S =
2 0, (II.4)
b. (II.3), (II.4) - fl
. 27. -:1 fl, fl
-
59
v q
S
bl
S
p
x
b p
xS
iS
S
6= = =
0
3
0
3
12
. (II.5)
(II.5) fl - .
k b = 3 6/ . (II.6)
fl m,fl fl .
m b
b l
S
b l
S
i iS
S
iS
S = = =
0 02 . (II.7)
. II.1. - , k = 1
2, m = 0,2 10-2. -
fl b* . (II.6) (II.7)
b
k
m=
121 2
/
.
b
=
=
12 10
0 2 107 74 10
12
2
1 2
5
,, ;
/
= 77, 4
. 28. :1 ; 2
. 29. S:1 ; 2
-
60
m
b
2 /.= =
=
0 2 10
2 7 74 1013
12
5
,
,
, fl 13 - 1 .
4. - . -, , fl - , , . l*, b*. fl , - - , -, . fl fl flfl -, ,
fl -- .
(, , - , - ) -fl- . - , - . fl .
7. -
fl fl fl - fl fl fl , , , fl fl . fl- flfl fl- .
1. fl fl. fl fl-fl fl ( ), - (, ), - flfl x x + x ( x fl ).
fl
-
61
hi 0 , - fl (II.1). (II.1)
SS
ii if k k= ( ) , (II.8)
Si S - ki. fl f().
2. fl fl ,flfl
F x f x dx c( ) ( ) .= + (II.9)
f(x) = F(x).
3. () x,
M x xf x dx( ) ( ) .=
(II.10)
fl flfl fl.
fl fl- fl fl k fl - fl .
1. fl ( -). fl fl fl :
f kk k
( ))
,=
1
2
2
2 2
e
(
(II.11)
. fl fl k
: k . fl k, , , , . -fl -. fl fl fl , fl -
-
62
k 0. fl - fl F(k) - :
F k dkk k
k
( ) .)
=
1
2
2
2 2
e-( -
(II.12)
fl (II.12). fl - (II.12) :
F k dk dkk k
kk k
( ) .) )
= +
1
2
1
2
02
2 2
0
2
2 2
e e( - ( -
(II.13)
fl k k = , (II.13)
F k d d1
02
2 2
0
2
2 21
2
1
2( ) .= =
e e (II.14)
2 2= =; , d d
1
2
1 1
20
2
2 2
0
2
= =e ed d ; (II.15)
F k dkk
k kk k
20
2
2 21
2
1
2 2( ) ;
( )
= =
e erf -
erf -
--
k k
k kk k
dk
2
2
22
2 2
2
0
( )
= e . (II.16)
F k k k( ) .= +
1
2 21 erf -
(II.17)
-
63
. 30 fl f(k), (II.11), . 31 -fl, fl fl - (II.17). - -fl fl - fl
k, k fl - fl flfl flfl , -fl.
erf() = 1, , (II.17), F() = 1. - (II.10) flfl k . , fl - (II.11)
(II.10).
M k dkkk k
( ) .=
2e
( - )2
2 2 (II.18)
. 30. - fl - = 0,7, k = = 0,8 2:1 fl fl; 2
. 31. fl, fl -fl = 0,7, k = 0,8 2
-
64
fl fl (II.18) - :
M k dk I Ik k kk k
( ) .
)
= = + +
2 22
2
2
1 2e- ( -
(II.19)
fl I1 :
I dkk kk k
1
2
2
22=
e- ( - )
. (II.20)
= (k k )/ 2 ). (II.20)
I d1
2 22 2
20= = =
e e- -| . (II.21)
I2 :
I k dk k dk dkk k k k k k
2
2
2 20
2
2 2
0
2
2 21
2
1
2
1
2= = +
e e e( (
() ) )
.
(II.22)
(II.14) (II.15) , -fl (II.22), 1/2. , , - (II.21), I1 = 0, I2 =
k , (II.19) fl . , , fl fl.
D k k k f k dk k dkk kk k
( ) ( ( ) ( .)
= =
)
2 2(
)
2
2
2 2e
(II.23)
fl fl (II.23) , , = (k k )/( 2 ). (II.23)
D k d d d d( ) .= = + =
2 2 42 22
2 2
0
22
0
e e e e-
2 - 2 - 2 - 2
(II.24)
fl (II.24) . , , fl :
-
65
2
0
2
4
=e- d . (II.25)
(II.24) (II.25)
D(k) = 2. (II.26)
2. . fl - :
f k kk
k k
( ) .)
=
1
2
2
2 2
e(ln ln
, 0 (II.27)
fl - . 32. F(k). flfl (II.27) (II.9), -
F k dkk
k kk
( ) .
)
=
1
2
2
2
2
0
e
(ln ln
(II.28)
d(lnk) = dk/k, (II.28)
F k d k
k kk
( ) (ln ).
)ln
=
1
2
2
2
2
e
(ln ln
(II.29)
(II.17)
F k k k( ) =
1
2 21+ erf
ln ln .
(II.30)
- - fl (II.10).
M k k( ) = e2/2. (II.31)
. 32. - - fl = 0,7, k = = 0,8 2
-
66
3. - . --fl fl - :
f k kk
k
k k( ) , .
/
( )=
10e
(II.32)
= () =
e
>x > 0, 0
1 0x dx x , .
-fl . 33. fl
F kk dk
k
k kk
( )( )
/=
1
0
e. (II.33)
fl,
F() =
k dk
k
x dx
k k x
= = 1
0
1
0
e e/
( )x k k
( )1, = / . (II.34)
-- flfl :
M k k k
x
( ) .
( )
( )
( )= = =
+
e x kdx
0
1(II.35)
4. fl . fl fl , fl fl fl . .. .. fl -fl . fl .. fl fl -:
f kk a
k k
k ak( ) ,=
+ +
2 1
0 0
0
e _
a k , (II.36)
. 33. -fl = 2, k == 0,8 2
-
67
a, k0 fl, fl - . fl , .. -,
f kk a
k k
k a
k1
2
1
2 1
2
124 1
( ) ,( )
( )
=+
+
e (II.37)
a, k2 fl. . 34 f(k),
(II.36). , . , , , fl-fl 0 k , , fl fl fl fl -.
8. -
- - - , fl-fl , . . - fl fl, , fl , . fl .
. 34. -fl , - .. k0 = 0,8
2, = 0,1 2
-
68
fl fl fl - ; , ; -- fl ; - fl fl ; .
, fl fl - , , , - fl fl, , fl.
fl - .
1. fl fl -fl, fl fl - (, , ..), fl fl , (, fl ..).
2. fl - , , fl -
fl flU -. . 35 U, -- - .
. 35. U, - - -
-
69
3. , - . fl , fl, -fl , , .
4. fl (, , ) - (flfl, fl .). fl, - fl - . . 36 - fl flU lnk ( k
fl ). fl U - fl , .
5. fl - fl fl - , , fl , - . -fl - fl , - flfl , ..fl.
6. fl - . fl fl -, fl - . fl - , fl , flfl - .
7. fl - -- fl, fl -fl , - ( , -
. 36. -fl -fl U lnk
-
70
..) - .
8. , - , flfl , flfl - .
-
, fl - .
fl -fl fl.
1. fl , hi - ki.
2. , , fl h = hi .
3. fl
hii
h
=
1
ki , flfl - ki.
4. fl
h
h
i
ii
n i if k k
=
=
1
( ) .
5. fl- fl fl - .
fl , -fl, , fl, -, , - fl- fl. fl, -, fl - , - fl . fl fl , fl,
.
-
71
-, -fl - fl - fl .
, -fl fl - fl fl fl -, .
6. fl- - fl fl fl fl - . fl - fl- - fl fl fl , .. .
-
fl , fl , fl - fl . -fl , - flfl, , . fl , , - fl . , , fl, .
fl, , , , .. -. fl flfl - - -, , . fl. fl
-
72
, , fl - - . fl - . fl - - . fl fl - (, fl ), fl fl.
fl , , -, , , - , . -fl - , .
, -- -fl .
- , fl fl. fl fl fl -- fl ( fl fl - , fl, - fl , - fl, fl , ,
.). - , , fl , , .. , - - . - fl - - - . fl fl -fl, -
-
73
fl - , - . , - , .
, - , ,fl fl fl . fl . , fl .
9.
- fl fl fl. fl - fl. fl fl , . fl fl . fl fl fl, .. .
fl - fl fl - , fl, fl. .
fl, fl , - - fl fl , fl , -, - .
fl - fl . fl -
-
74
, , fl- fl fl - fl .
fl fl fl , , , - . fl - fl -, - .
fl . M (. 37) x, h b, fl , -fl , mM = mhbx. (II.38)
, vx, flfl
vx +
v
x
x x ,
M fl t, , , :
v bh x t v bh x t M m bh xx x
xv
x + = =( ) ( ) . (II.39)
(II.39)
( ) ( ).
v
x
m
t
x + =
0 (II.40)
. 37. fl
. 38.
-
75
t 0
( ) ( ).
v
x
m
t
x + = 0 (II.41)
(II.41) fl . fl fl, V = xyz (. 38). -fl fl -fl , ,
( ) ( ) ( )( ) .
v
x
v
y
v
z
m
t
x y z+ + =+ 0 (II.42)
(II.42) :
div v
m
t( )
( ) .
+ = 0 (II.43)
fl (II.42), (II.43) fl fl fl . fl , -flfl , , flfl (-) .
fl fl fl -fl fl fl . -fl fl E U, z - , fl - w.
E = U + z + w2/(2g). (II.44)
fl , , - , E W - Q, - A, ..
E + W = AQ, (II.45)
(II.44)
-
76
U z W A Q
w
g + +
+ =
2
2 . (II.46)
fl (II.46) .fl flfl fl U fl fl ,
U Ac T = , (II.47)
c fl ; T . -, . c = c(1 m) ++ cm (c fl ; c - fl , m ). c = =
1,046 /( K), c = 4,184 /( K), T = 1 K, m == 0,2. c = 1,046 (1 0,2)
+ 4,184 0,2 = 1,67 /( K), U = 102 1,67 1 = 170 . fl flfl z flfl -
fl fl fl . fl .
fl -. w fl - flfl 0 10 / = 3650 / = 1,16 10-4 /. fl , , -fl fl
flfl fl , .. . fl fl -fl fl fl flfl . fl -
=
m
m m+ ( ),
1 -
; -; , -, . = 10
3 /3, = 2,25 103 /3 m = 0,2, =
= 0,1. fl fl -
w
g
2 4 210
2
0 1 1 16 10
2 9 810 68 10
= =
, ( , )
,, M.
, fl ,
-
77
fl ,.
-fl fl 100 , - 10 . - 200 . fl , - flfl , fl flfl fl - . , - .
W, - , :
W p V g V= /( ), (II.48)
p ; V , ; ; g fl.
fl, fl, , flfl fl . fl -. (II.48) V, -fl . -, , , flfl, - . , -
M = V fl -.
M = V + V = 0 , ,
V/V = /. (II.49)
flfl (II.49) (II.48),
W
p
g
p
g= =
2
1. (II.50)
, ., . fl , fl p/ = p0/0, p0, 0 fl. fl
-
78
W
p
g
p
p= 0
0
. (II.51)
fl p = 10 105 , p = 100 105 , p0 = 10
5 , 0 = 1 /3, = 0,1.
W = =
0 1 10 10 10
1 9 81 100 10
5 5
5102
,
,M.
fl , , - , fl , fl- , fl, , .
, flfl flfl (II.45) (II.46) Q. , fl . U. - fl- . fl fl fl -fl .
fl fl, - fl , :
N
g V m g
v
m gkv p
grad= =
1 2 . (II.52)
, fl fl = 0,02 10-3 w = 106 / 86,4 10-3 /. k 0,1 2, m = 0,2, -
fl 1 /3.
v
m gk
2 3 12
13
60 02 10 10
0 2 10 9811 02 10= =
,
,, /.
1 fl flfl1,02 10-6 0,864 105 = 0,088 / . , , . , ,
-
79
104 / . fl, , v2/(mgk) 102 /. 1 fl fl 9 . , , - fl - . - , fl fl
, fl fl-fl .
fl , fl , fl-fl .
(II.48) (II.49) fl - :
= = = W m W mp mp
V
g V
2. (II.53)
W fl fl Ep,
= = W m E mp
P 21
2
, (II.54)
1 2 .fl, fl
fl , u = cT fl Ep, fl, - - fl, .. AQ = v gradp,
A u m E v v p
u
t
E
t
+
+ +
=div div grad
ppvE . (II.55)
vE ; v . (II.55) fl , - fl.
. - flflfl . fl .
-
80
. , , fl fl fl -fl :
v v
kk s p
x
kk s p
x
= = ( ) ( )
, ,
(II.56)
v ; v - ; k(s), k(S), k(S) fl , fl - s; p p . fl , . 39, : s s.
s = s -fl fl , k(s) == 0. s = s fl fl k(s) = 0, fl s = s - , s = s
fl . s = s, flfl , , , flfl , - , .., flfl s = s, , flfl . fl . fl
, , fl fl . - fl , fl fl , (fl fl), fl . ( ) , fl
. 39. k k s s
-
81
fl k(s) k(s) s s.
s s s s s + = = +1; , (II.57)
s, s -, fl:
s
s
ss
s+ = 1; / . s = s (II.58)
fl k(s) k(s), flfl s (II.58). , , ( ) :
v = =
kk s p kk s k s p
( ) ;( ) ( )
;
x xv
v =
kk s k s p
( ) ( ) .
x(II.59)
p, p, p , . fl fl fl.fl , - fl (, -); ; - fl , ; - fl .. fl , fl
- , . - - fl fl - :
vz =
kk s pg
( );
z
vz = +
kk s pg
( ),
z(II.60)
p , fl- .
-
82
fl - fl, .. fl. fl. -. fl fl : fl - fl , , , fl, fl . fl fl - fl
, fl . , fl , fl - fl. , fl fl . -, fl NRe = vd/ (v - ; , fl ; d -
, , ) fl . fl , - , fl 7,5 9,0 .. , 0,22 0,29 .. 1 12 .. . , - d. ,
, , , -fl . - , - , fl . , fl . , :
+ =
k p
xv v
2 ,
, fl .
-
83
fl - fl fl - .
10. ,
, fl -fl -, fl fl , , fl- . , -, , fl , , - fl. fl fl , , - fl ,
- fl fl fl . , fl fl - , .
, , , , flfl -fl fl. (. 40) fl dx, dy, dz, fl fl - fl fl - x, y,
z, yz, xy, xz (x,y z , xy, yz,xz flfl). z - , x y , - fl z =
. 40. fl-
-
84
. - x y , . fl x = y = . fl,
= H. (II.61)
, /3; H fl . fl fl
= , (II.62)
fl. - flfl ( 0 1), - fl, -. fl fl . fl fl . , -, fl , . - fl p,
.
fl fl fl - fl , fl
= + +( )/ .x y z 3 (II.63)
, - fl p - fl
= + p. (II.64)
, - , m fl k, fl flfl, fl . . 41 - m , . 42 k . - fl , -. , = 0,
m = m0, k = k0 (m0, k0 fl ). fl , fl-fl (. . 41, 42). -
-
85
m k = 0 , -fl fl . , , - , flfl fl . fl, fl , flfl - flfl , -
flfl.
fl ( 4000 ) - (p ) flflfl , fl . fl flfl .
. fl flflfl , flfl ( flfl) flfl , , fl fl fl flfl . - flfl
m m c= 0 01[ ( )], (II.65)
m0 = 0; ;0 fl.
. 41. flfl
. 42. flfl
-
86
flfl fl :
m m=
00e
c( ). (II.66)
, flfl , t. -, flflfl , .. fl , t
dm
dt
d
dt= +
, (II.67)
fl . , , , - , - flfl .
. - , . fl , flfl . fl , : , , . fl fl fl - fl, fl fl. - flfl ,
- . fl , - , fl -fl .
flfl , , fl , fl - . fl fl : .
, fl (T = const) flfl , ..
V/V0 = p, (II.68)
V -
-
87
, V0 ; ; p .
, V0 fl V0 , p . fl.
,
p = V0/(V0). (II.69)
flfl - flfl fl - . , -fl fl. fl -, flfl , . fl, -fl , flfl, fl ,
.
-flfl , fl fl. flfl - fl fl (fl). -fl flfl fl . - ( ) fl , . , -
. fl (, , ) fl - (pT ) fl . . 43 fl fl , , , flfl 2, - fl, fl , . 3
2 fl - . p -fl T. , -fl , fl- fl fl. - fl, fl , .
-
88
V fl , fl-fl -, pT- , . 44, - pT-fl . fl
1 fl fl fl , 2 -fl . fl 6 fl fl , 5 fl . flfl fl fl 3fl fl fl .,
, 1 , , 2 , 3. 4 flfl fl . -, . fl fl - fl fl , fl -.
fl fl, -, fl
. 43. - fl :1 flfl; 2 flfl; 3 fl ; 4 -
. 44. - fl -
-
89
- -. - fl - fl . -fl, fl fl flfl-fl . Kip fl i- n fl
Kip = yi/xi, (II.70)
yi i fl i- . . Kip( , ) = 1, , . - fl (. . 44) , fl fl . fl, ..
- fl , fl fl fl fl -,
K Ki ip
p
T
Tp p =
, , (II.71)
- fl . , fl -, fl -fl Kip. - fl . N V, N - ( ) N .
N = N + N. (II.72)
fl (II.72) fl , fl V,
n = n + n , (II.73)
n ; n n .
fl fl yi xi fl
-
90
y xi i i
i ii
i i
i i
N M
N M
N M
N M= =
; /
/
/
/.
(II.74)
fl i- - :
i i i
i i
i iN M
N M
N M
n= =/
/
/ .
(II.75)
in = yin + xin . (II.76)
fl, yi = Kipxi, fl n /n = Y,n/n = , (II.76)
x yi i
ii
i i
iY K
K
Y K= =
+ +
( ) ( ).
p
p
p;
1 1 1 1(II.77)
fl (II.77) fl fl .
flfl - . , , i, p, T Y, xi yi -fl (II.77). i, p Y , , xi = 1,
(II.77)
i
iY K( ).
p +=
1 11 (II.78)
Y fl fl (II.78). , i , -
xi, yi, Y , fl (II.77) - flfl. fl fl , -, fl flfl - fl , , flfl
. flfl
F(p, V, T) = 0. (II.79)
(II.77) (II.79) fl . - .
-
91
fl, , -fl . - fl fl - - , , flfl . - fl xi, yi, Y , N . fl s -
V, fl -fl . fl i fl , .
sV = Li/i. (II.80)
flfl .fl fl .
fl fl flflfl fl - , flfl, , -fl . -flfl , fl- i, fl fl
( ); ,= = iCi
i i iC n n/ (II.81)
fl i- Ci., , fl 1 fl 1, () fl2 fl 2 fl, - fl 3 fl 3.
C1 + C2 + C3 = 1. (II.82)
(II.81) (II.82)
= = =
11
22
33
21 1 3
11
33
2 1 21
3 23C C C C C C C C C( / ) ( / ) . (II.83)
fl , fl , fl , fl , - , fl fl. fl
-
92
flfl , fl , fl .
, , , , . , - fl fl . , fl , fl- , fl , ...
v p g
k=
(grad ),0 (II.84)
g0 fl. -fl (II.84), - grad < g0.
fl fl flfl - .
II.2. , V flN1 1, .. , N2 - 2, .. , fl = 0 = const. - . flfl - .
, V -, fl fl, - . fl - V s .
fl (II.80) :sV = L1/1 + L2/2, (II.85) L1 ; 1 flfl -; L2 = N2 ,
fl. L1 = V01, 01 fl. ,
V = L2/2,
2 flfl . - , (II.68)
L1 = 01L2p/2 = 01N2p/2. (II.86)
fl , fl flflfl .
= 01/0,
0 ( 0 = 105 ). -
fl
G s V
s V p
p101
01
1= =
( )
( ). (II.87)
-
93
G1 + L1 = N1.
flfl (II.85), (II.86) (II.87),
ap2 bp + c = 0;
a
N
pb
N p V N
p= =
+
012
2
1 2 0
01 2 0 01 2 2 01
2 0
; . (II.88)
flfl. V = = 1 3, N1 = 25 , N2 = 500 , = 0,810
5 3/(3), 1 = 0,2103 /3,
2 = 0,8103 /3, 01 = 0,8 /
3. (II.88), = 1,61013, b = 0,7105, = 25 ( ). - fl , fl - fl,
p =
=
0 7 10 0 33 10
3 2 1039 10
5 10 1 2
135, ( , )
,
/ .
s = 0,7, L = 15 , G1 = 10 . , . fl ,
fl . fl fl ( -fl).
, , fl , - , .. G2 = 0. (II.71)
K Kp
p
T
T x1 11
p p 1
=
=, ; K2p = 0.
fl fl fl,
K
N M
M L12 1
2 11p = + , sV = L1/1 + N2/2;
G NN M
M Kp
G p
s Vp1 1
2 1
2 1
1 0
011 1=
=
( );
( ).
(II.89)
(II.89) , - K1 / , / - , - fl - fl .
-fl flfl, . flfl fl , fl.
-
94
11.
fl fl flfl , fl- , , . fl , fl, - -. , fl .
11 fl fl - , fl fl .
fl flfl . fl -fl , fl fl, fl. fl fl . , - fl fl , -fl fl ( ), -,
, fl - .
flflfl - fl fl - . fl ().
1. , -fl , , fl (II.42), :
v
x
v
yx y+ = 0. (II.90)
flfl
-
95
v vx y
k p
x
k p
y= =
; , (II.91)
2
2
2
20p
x
p
y+ = . (II.92)
= kp/.
fl (II.92)
2
2
2
20
x y+ = . (II.93)
F(z) = + i; z = x + iy. (II.94)
flfl (II.94) fl = (x, y) -fl . fl, F(z) fl -fl fl
x y y x= =; . (II.95)
, fl fl fl z = x + iy . , ,
F z i z
q
h( ) ln .= + =
2(II.96)
fl z = rei, ( = arctgy/x), (II.96)
F z i r i r i
q
h
q
h
y
x( ) ln ) ln ,(= + = + = +
2 2 arctg (II.97)
= =
q
h
q
h
y
xr
2 2 ln ; ; arctg
r = (x2 + y2)1/2; p x y
q
kh= +
2
2 2 1 2ln( ) ./ (II.98)
-
96
- , - (II.96) - -fl - . (II.98), r =
=0 fl , r -. fl fl fl - (-), fl fl, (II.90) (II.98) fl
(II.90).
, (. 45) fl fl (-). fl fl fl 2 -. fl - , 2, y.
fl - (II.98) fl , c fl- fl 2n (n = 1, 2, 3...) , fl-fl . , , - z
= x + iy (. . 45), - = + i. fl
= sin .
z(II.99)
z1 = z/,
. 45. - :1 ; 2 - 2
-
97
sinz1 = sin(x1 + iy1) = sinx1cosiy1 + cosx1siniy1 =
= sinx1chy1 + icosx1shy1;
sh chy y
y y y y
1
1 1
1
1 1
2 2=
=
+ e e e e; ; (II.100)
x1 = x/; y1 = y/.
, = + i
=sinx1chy1; = cosx1shy1;
= (2 + 2)1/2. (II.101)
, fl (II.99), -fl .
F() , .
F
q
h
q
h( ) ln , ln .
= =
2 2 (II.102)
, - , . , fl . fl
qh
=2
( )
ln( / ).
c
c(II.103)
z. fl y - y. fl (II.101)
shy/.
(. . 45)
sh
1
2
LL
e .
fl
ln = L/ ln2.
flfl y z >> . -
-
98
ln L/.
y/
e e
y y
y r 2
c .
,
lnc =ln(rc/).
flfl fl ln ln (II.104),
q kh p p kh p pL r
kh p p
Lr
= = =
+
2 2 2
( )
(ln ln )
( )
ln
( )
ln
. c
c
c
(II.104)
(II.104) - , - , , , fl z , - r fl .
2. -, - fl . - fl S, - . fl t = 0 0, t > 0 - fl = 0 (. 46) 1,
fl t 0. fl t. fl fl , -fl .fl v :
v
x
T
tc + = 0. (II.105)
. 46. fl - - :1 -fl S; 2 t
-
99
fl ; .
v
v
T
x =
, (II.106)
.flfl (II.106) (II.105),
2
2
T
x
T
t c= =; . (II.107)
(II.107) fl , fl - fl - . fl
T = T0 > 0, t = 0; t > 0, x ,
T = T1 x = 0, t > 0. (II.108)
f(x, t), fl -:
f(x, t) = (T T0)/(T1 T0). (II.109)
fl (II.108) fl - :
f = 0 x > 0, t = 0; t > 0, x ,
f = 1 x = 0, t > 0. (II.110)
fl f(x, t), , fl (II.107), (x, t), ..
2
2
f
x
ft
= . (II.111)
fl fl fl , fl - (II.111) st (s ) fl .
2
20 0
f
x
f
tst stdt dt
=e e . (II.112)
-
100
f(x, t) F(x, s),
F x s f x t dtst( , ) ( , ) . =
e0
(II.113)
fl x t, f(x, t) . (II.113), fl, s ,
2
2
2
20
F
x
f
x
stdt=
e . (II.114)
fl fl (II.112) -
f
tdt f x t s f x t dt sF x sst st st
0
= + =e e e | ( , ) ( , ) ( , ).
0 0
(II.115)
(II.115) , fl - , , f(x, 0) = 0 .
(II.115) (II.112)
2
20F
xsF = . (II.116)
fl (II.116)
F Cs
x
=
e . (II.117)
fl fl fl fl (II.110). , F(0, s). fl (II.110)
F s f t dt dtst st
s( , ) ( , ) .0 0
0 0
1 = = =
e e (II.118)
F x s
sx
s( , ) .
=
e
(II.119)
f(x, t) F(x, s) - .
-
101
f x t dzz
x
t x
t( , ) . erf= =
1 12
2
2
0
2
e (II.120)
, , fl = 0. fl (II.106)
v Txx x
T
x
f
x 1=
= =
= = =00 1
= =
=
1
1
T
xt
xt
T
t
e
2
4
0
; 1 = 1 0. (II.121)
q fl S == 0
q T St
=
1 . (II.122)
3. () fl - q , - fl h - . fl , . t = 0 fl fl . t > 0 - fl q =
const, fl r .fl fl - .
fl :
( ) ( ).
v
r
v
r
m
t+ + = 0 (II.123)
fl ( ), (II.123) - :
k p
r r
p
r
p
t
2
2
1+ =
;
= c + m, (II.124)
-
102
- . fl , fl . f(r, t) :
f kh p p
q= 2
( ) (II.125)
(II.124).
2
2
1f
r r
f
r
p
t+ =
. (II.126)
. (r 0), fl :
q r qkh pr
rf
rr r
= =
2
0 0
.
, fl
r fr
r
= 0
1; f(r, 0) = 0. (II.127)
,
= r t/ . fl , - , .. . f = = f().
f
t
r
t t
f
r t
f
r tf f f= = =
2
1 12
2; ; . (II.128)
flfl fl (II.126),
+ = = u u f
u
20; . (II.129)
(II.127) fl:
f = 0 ;
df
d
=
0
1. (II.130)
fl (II.129) . - (II.130), fl , -
-
103
f d z
z
z
dz
z( ) ; / .
= = =
e e
2
421
24 (II.131)
(II.131) (II.125)
p p dz Ei
q
kh z
q
kh
r
t
z
z = =
4 4 4
2e. (II.132)
fl
Ei
r
t
2
4 0 z ,
z 0 . - fl fl fl , (r = r), .. . -
fl
Ei
r
t
2
4 -
.4. fl
h b, fl fl (. 47), fl = 0, fl = l. (t = 0) fl, 0. fl fl x = l t
> 0. t = 0 ( = 0) - fl q. -fl .fl - fl - t > 0. -, , fl
fl
. 47. fl -fl fl l :1 ; 2 fl - fl; 3 -fl fl
-
104
, , :
2
2
p
x
p
t= . (II.133)
fl fl - :
= x/l; = t/l2. (II.134)
flfl (II.134) (II.133),
2p/2 = p/. (II.135)
fl fl fl fl (II.135)
p(, 0) = p(1, ) = p0;
p q l
kbh==
0
. (II.136)
, t fl fl fl
p p q l
kbh01 = ( ). (II.137)
= 0 (II.137) ql(bh) = p0 p1. fl - :
p0 p(, ) = (p0 p1)(1 ) (p0 p1)f(, ). (II.138)
f(, 0) = 1 ; f(1, ) = 0; (II.139)
f
=
=0
0.
,
f(, ) = ()(). (II.140)
flfl (II.140) (II.138) (II.135),
= . (II.141)
-
105
(II.141)
/ = / = c = const. (II.142)
fl fl (II.142) flfl - fl, :
p0 p(, ) = (p0 p1)(1 )
8 1
2 10 1
2 20
( )
( )
p p
n
+
+
+e
( )
cos ,
2 1 2 2
4 2 1
2
n
n
n = 0, 1, 2... . (II.143)
fl:
1 8 1
2 1
2 1
22 20 =
+
+
( )cos .
n
n
(II.143) fl flfl fl fl flfl (fl ), fl, fl fl.
fl - .. .. -. fl -, fl fl , fl fl - , . fl fl .
. - fl . , (II.104) :
-
106
p p qq L
r
kh
L
kh
r
kh cc c
2 2 = =
+
+
ln ln
.2
(II.144)
fl, fl (II.144), - - 2 fl 0 L, - r = / - r. ..
=
L
kh2 ,
c
c
= ln /( )r
kh2
, fl fl - fl - .
-fl fl - fl - .
fl- -fl , - . 48. - - - h. fl - -fl fl , fl-
. 48. flfl fl- :1 -; 2 -; 3 fl ; 4 fl
-
107
. fl k, - fl , flflfl -fl fl , k k, r, r. -fl t = t1 flfl / (. .
48). flfl . , , fl fl q. fl fl - .
(. . 48, ) b = 2. fl , r = /, .
q kk h p p
r
= 2
c
( )
ln
.
- fl : ( ) r /, fl (- ) = 0, , x = l, , ( ) /, , r. fl, fl- q/2
( q/2),
q kk h p p
l2
2=
( ) .
, fl
q kk h p p
r
= 2
c
( )
ln
.
fl -
-
108
p p p p
qr
kk h
q l
kk h
c
c
2 4 = =
ln
; ; =p p
qr
kk h
c
2
ln
.
fl. fl
p p qkh
r
k
l
k
r
k
c
c
2 2 = + +
ln ln
. (II.145)
, (II.107) (II.108), .. , - flfl . , - fl - , fl, fl fl n fl. -
, fl- - fl -flfl , - . fl -
x dx x dxnl t
l tn
l t
l tT
x
T
t1
2 2
21
2
( )
( )
( )
( )
, = (II.146)
n , , fl fl. fl n = 0
T T
T T
x
l t
x
l tA A A
= + +0
1 00 1 2
2
2( ) ( ). (II.147)
fl, - , , :
T = T0 = l(t); T = T1 = 0. (II.148)
flfl l(0) = 0. - - fl
-
109
T
x x l t==
( )
.0 (II.149)
fl fl,
0 = 1 0 = 1; 1 = 21; 2 = 1.
,
T T T
x
l t
x
l t = +
0 1
2
21 2
( ) ( ). (II.150)
fl fl l(t) fl (II.150) (II.146) n = 0, fl l1(t) = 0.
6dt = ldl.
l t= 2 3 , (II.151)
.. ., II.4,
= 0.
v xx
T
x
T
t
1
==
= =00 3
. (II.152)
fl (II.122), , , fl -
, /3 , .. 2 %.
fl fl -- . - fl, fl- , fl - -. - fl - - -. fl fl fl fl fl (fl
-fl).
-
110
- , fl fl. fl ,flfl ., - -fl - (. 49) - . -
2
2
2
2
p
x
p
y
p
t+ =
. (II.153)
fl fl fl , y h fl x, y z. fl , fl ( 0, y 0) fl . , fl pij.
(II.153) fl fl fl -
p
p p
xi j ij +
1, ;
2
2
1 11p
x x
p p
x
p p
xi j ij ij i j +
, , ; (II.154)
2
2
1 11p
y y
p p
y
p p
yi j ij ij i j +
, , ;
p
t
p p
tijk
ijk
+ 1
.
flfl (II.154) (II.153),
. 49. fl -- fl:1 ; 2 fl
-
111
1 11 1 1 1 x
p p
x
p p
x y
p p
y
p p
yi j ij ij i j i j ij ij i j+ +
+ =, , , ,
=
+ p p
tijk
ijk1
. (II.155)
pi jk, fl t; pi j
k,+1
fl t + t. fl -
fl -- . (II.155) fl - . , -- - fl.
fl- (. . 49). () fl - , . 50. , fl ix iy fl y fl
i ix y
S U
x
S U
y= =
; , (II.156)
S -fl -; ; U - flfl.
fl (II.156) , - -- .
v vx y
k p
x
k p
y= =
; . (II.157)
. 50. :1 fl
-
112
fl (II.156) (II.157) , fl, , k/ S/. fl . , , - fl S/ fl, fl - k/
.
flflfl fl . , -
p aU b cC
k S= =; , = ;
(II.158)
a, b .flfl (II.158) ,
b cS
C
U
x
U
y
U
t
2
2
2
2+ =
. (II.159)
, (II.159), - , -, fl fl - fl . - (II.158) , - fl , - .
12.
, fl , , , , - .
fl -fl fl - . fl -flfl , , -, . , -
-
113
fl -. -fl - fl 2020 , 5050 , 100100 , - , - . - fl , , , fl,- e
, - - fl. fl - - . , , - fl 50 2 (510 5107 2), 10 , 5108 3 51014 3.
fl, 5 3, fl1014 fl, flflfl fl -fl .
flflfl - , - fl -, -- fl. - . -fl . - .
fl fl . flfl - . fl , -. , , fl - . fl - - .
12 -fl .
fl -
-
114
. flfl -, fl fl fl - . , - , fl-fl , fl fl . , -fl, -. , -
flflfl - , fl -.
- - ( 1 ). -- .
fl -, fl . -fl flflfl - fl , flfl , - - .
- fl, fl - fl, .
1. flfl, , .. -. , . 51 fl flflfl 1, 3, 5, 2 4 fl , , , , fl fl
, .
fl - fl , . 4 19.
2. (. . 51) - fl , fl fl -, fl .
3. fl fl fl .
-
115
4. fl k s( ) -
k s( ), fl s , fl
k s k k q q ( ) / / ;= =0 k s k k q q ( ) / / ,= =0
q fl (-fl) ; q = q + q; k, k - , - ; k0 fl .
5. fl s flfl :
s s Q mV= + / ,
Q Q Q = ;
Q q t dt
t
= ( ) ;0
Q q t dt
t
= ( ) .0
fl fl , --, fl .
. 51. - fl fl :15
-
116
- fl - , - , fl 2 4 (. . 51).
1. .2. , fl -
. fl , .
3. fl fl - .
4. fl - fl -.
5. fl --fl .
6. fl - fl - ? fl?
7. fl fl (- fl) ?
8. , flfl. - ?
9. fl -flfl ( ), - fl . fl?
10. fl fl -fl . , fl. - ?
11. fl -fl - .
-
117
13.
fl fl - fl fl, - fl, fl fl - , , fl, flfl .
flflfl fl, fl-fl , - . -fl , - fl - fl, -fl fl -. fl , fl fl .
,, fl . - fl, .. - fl , . -fl - , , .
fl fl, , fl, flfl - fl fl .
flfl fl -.
III
-
118
1. fl - , fl , fl fl .
- fl fl fl -fl ( ). - , fl q fl , fl. (. 52) , - fl t. , - (t =
0), . , fl - (), - fl . fl . fl fl - fl = (t), fl -fl - . . 53 fl
flfl fl fl = (lgt).
. 52. fl fl:1 ; 2 (); 3 ; 4 ; 5 ; 6
. 53. fl fl -fl, fl (1) - fl
-
119
2. -fl fl fl fl fl -- fl , .
, , fl fl , flfl - . t = 0 fl, -, . qA (. 54). - . , - , fl fl =
(t).
(. . 54) fl fl (1 < 2 < ), fl fl -fl fl fl . - fl fl = (t)
- . . . -fl fl, .. fl . , , - ( , fl - ..). fl fl fl - fl .
3. fl fl fl - fl - fl.
fl fl -fl - , fl fl -.
. 54. fl fl -fl
-
120
. 55 fl fl - , - . , fl - 0, fl fl fl . fl . , 1 2 - fl - fl - ,
flfl . 3, , - , -fl . 5 ( fl), - (. . 55), -fl fl . fl
. 55. flfl -fl fl:1 -; 2 - -; 3 -; 4 - ; 5 ; 6 - -; 7 fl fl
-
121
() 4, fl -fl , fl, - flfl - 6. , fl = (t) = (t). fl - q . -, - -
fl q = q(t)., , fl fl = (t) - fl t1.
= (t) . 56, q = q(t) t1 - fl . 57. , - t1 - fl . fl . t > t1
fl flfl , : fl, fl.
. 56. t:1 ( - ) t1; 2 - fl q (t > t1)
. 57. q t:1 q - t1; 2 fl q t > t1
-
122
(t) -fl = (t) - t1 fl, fl t > t1. = (t) -fl .
4. fl fl - fl fl - , .
fl fl -fl, fl, flfl . - fl fl - fl fl, fl .
-fl , (. 58) , -fl , - .
5. , -- - fl fl .
, - - - fl fl -. - - - fl
. 58. fl- fl fl:1 -; 2 -; 3 -; 4 ;5 -
-
123
, t = 0 .
fl fl -, fl fl . , fl fl fl fl fl-fl fl fl ( fl - ), .. fl cfl
fl. fl fl fl- . - fl fl fl - fl fl . II.
fl fl fl , -, fl fl - fl , - , . II, :
m
t tm v+ + =div 0. (III.1)
m, . II, flfl . - fl 10 flfl , :m = m0 c( 0). (III.2) ; 0
fl.
fl , fl (-) , fl (II.64).
(II.62) , = const
t
p
t= . (III.3)
fl (III.2) (III.3),
m
t
m
t t
p
t= = =c c . (III.4)
-
124
fl - fl , ..
= 0 [1 + (p p0)], (III.5)
; 0 0.
(III.5)
t p
p
t
p
t= = 0 . (III.6)
fl fl k fl fl ,
div div grad
v p
k= . (III.7)
(III.4), (III.6) (III.7) (III.1). - :
c 0 div grad
t
p
t
km p+ = . (III.8)
fl , - (III.8) 0. :
p
t
kp= div grad ; ;=
= c + m. (III.9)
( .. ).
fl - fl fl .
fl fl fl (III.9). fl - fl fl, . - - fl , , fl - fl, .
-
125
fl
V/V = ; = + m, (III.10)
V - fl , .. - V.
III.1. fl flfl. , V = 109 3 = 1 3. , - 20 5 . fl 10 . -, 16 ,
-fl 6 . - fl, fl . - fl - . fl. fl : fl
p 10 fl fl?fl fl
fl . = 104 1/. (III.10)
V V p = = = 10 10 10 109 4 6 3.
, , fl 10 fl fl 1 . 9.
14.
fl fl - fl - fl = (t) - fl fl . fl , -fl fl, fl fl -fl, fl ,
.
fl - -
-
126
, - . , , -fl (1520 %) - flfl - (, , - fl fl - ), .
, , - fl fl - fl fl , fl fl (). , - fl - fl , -fl fl -.
fl fl - -fl - -.
, , fl fl (. 59), - fl - . fl - fl, , , . fl fl fl -fl fl - fl ,
fl. , , fl fl , flflfl - fl - fl .
fl, , fl fl - fl- , R (.60). , fl fl
-
127
fl fl - , fl .
, (. . 60) fl , - fl fl q(t) - fl - q(t), .. q(t) q(t) .
fl q(t) flfl , . 57. fl (t) - (R r ). fl fl fl (III.9), - :
2
2
1p
r r
p
r
p
t+
= , (III.11)
(r, t) r (. . 60).
. 59. fl -fl :1 ;2 fl - R
. 60. fl fl fl - fl:1 fl fl; 2 fl ; 3 ; 4 fl
-
128
, fl fl -fl : = t = 0, R r :
q r
kh p
rr R
const=
=
=
2
. (III.12)
-fl fl (r, t)
p r s p r t dtst( , ) ( , ) , =
0
e (III.13)
p r s( , ) ; s -fl.
:
p p f
q
kh =( , ) ( , );
2
f
u J u Y u Y u J u du
u J u Y u( , ) ;( )[ ( ) ( ) ( ) ( )]
[ ( ) ( )]
= +
2 1
21 0 1 02
12
12
0
ee (III.14)
= r/R; = t/R2.
J0(u), J1(u), Y0(u), Y(u) fl fl fl.
fl f(, ) -.
fl fl fl (t) - fl = r/R = 1(. 61).
, f(1, ) lg(1 + ) - :
f(1, ) = 0,5[1 e8,77lg(1+)] + 1,12lg(1 + )
f(1, ) = 0,5[1 (1 + )3,81] + 0,487ln(1 + ). (III.15)
, fl q = const (t) - , (III.14) (III.15):
p t p f
q
kh
( ) ( , ).=
21 (III.16)
-
129
-fl, , fl .
(t) q = q(t) fl.
fl fl q = = q() , q flfl -, , fl qi fl i. : , fl fl, i, qi =
const.
, q , i (. 62).
(III.16), -fl . 62 :
p p q f
kh
q
00
( ) [ ( , )
= +
21
+ + + = q f q f1 2 ( , ) ( , ) ...]1 11 2
= p q f
khi
q
i
21
0
( , ). (III.17)
, fl (III.17) , .
p p f
kh
q ii
0 ( ) ( , ) .
= 2
1
(III.18)
. 61. f(1, ) lg (1 + + ):1 ; 2 -fl (III. 15)
. 62. q3()
-
130
(III.18) , fl 0. fl ( i )
p p f
kh
q
0 ( ) ( , )
= = 2
1
0
= p f dkh
q
20
1 ( , ) . (III.19)
(III.19) fl. fl
flfl , fl fl , fl fl fl.
, - , - fl , fl . fl , .
fl , - :
1) q = 0 1 = 1;
2) q = q1 = const 1 = ;
3) q = q1 = ;
4) q = q2 = const . (III.20)
fl = - . 1 = 1 fl - fl. = - , fl,fl. , fl, fl . fl , fl -
-
131
fl, fl - fl fl . = flfl , - .
fl = = (R, ) , .. 0 1. (III.20)
q const= = .
p p f d q
kh kh ( ) ( , )
= = 2 20 0
1
+ +
=
+ 0 5 1 0 487 1
1
1 3 81, , ln[ ( )]
[ ( )] , d
= +
+
pkh
d
2 10 5 0 5
3 810
, ,[ ( )] ,
+ +
= 0 487 1
0 2, ln[ ( )] ( );
d p J
kh
J( ) , ,
( ) ,
=
+
+0 5 0 178 1
1
1 2 81
+ + + 0 487 1 1, [( )ln( ) ]. (III.21)
= () 1, - (III.21) = () > 1, - q = . > 1
p p J J
kh kh( ) ( ) ( )
=
=
2 21
= p J J
kh
21[ ( ) ( )]. (III.22)
, .. > , fl fl = () (III.22) , q (III.20).
-
132
p p J J J
kh kh( ) ( ) ( )] ( ).[
=
2 21
1 (III.23)
>
p p J J
kh( ) ( ) ( )][
=
21
1
2 khJ J( ) ( )]. (III.24)
fl fl . () fl q = q().
- fl , fl.
- . -fl, fl , fl -, . , fl fl fl fl = = (t) , fl - t = 0 fl q.
fl fl , - , (. 63). (t) - , fl b . fl fl -fl (t) : , fl fl qflfl ,
fl n qi,
. 63. fl fl fl :1
-
133
q qi
n
= 1
. (III.25)
, , (. . 63)q = q0 + q1 + q2. (III.26)
q0 , q1 q2 flfl . , fl . II, - fl fl flfl fl
r x y= +2 2 :
p t p p tq
kh
r
t( ) ( )= =
02
4 4
Ei
+ + + +q
kh
x a y
t
q
kh
x a y
t
12 2
22 2
4 4 4 4
Ei Ei
( ) ( ). (III.27)
(III.27) fl fl fl -fl (. . 63).
p t p p tq
kh
b
t Ei( ) ( )= =
02
4 4
+ +( ).
q q
kh
a b
t
1 22 2
4 4
Ei (III.28)
fl. III.2. fl -
, , (. . 60), , - fl . -fl , , = 20 r = R = 310
3 . - k = 0,1 2, fl = 103 , = 109 1/, h = 10 .
, fl , (III.20). 1 = 2 , = 4 , 1 = = 0,1368
3/. fl fl -
fl. .
= =
=
k 10
10 1010
13
3 91 2/.
-
134
(III.14)
= =
= =
t
R
tt t
2
1
67 310
9 100 111 10 0 96 10, , ,
t . , () = (). t = 2 = 730
= 0,96103730 = 0,708. (III.21)
p
khJ
kh ( ) ( ); , ;
= =
2 22 182 107
J( ) , , ,( , ) ,
= +
+0 5 0 7008 0 178 1
1
1 0 7008 2 81
+ + =0 487 1 0 7008 1 7008 0 7008 0 311, [( , )ln , , ] , ;
p = =2 182 10 0 311 6 787, , , .
t = 3 () fl (III.22).
= = =0 96 10 1095 1 051 0 70083 1, , ; , ;
p
khJ J( ) [ ( ) ( )];
=
2 1
J( ) , , ,, ,
=
+0 5 1 051 0 178 1
1
2 0512 81
+ =0 487 2 051 2 051 1 051 0 5768, ( , ln , , ) , ;
J( , , ) , , ,, ,
1 051 0 7008 0 5 0 3502 0 178 11
1 35022 81 =
+
+ =0 487 1 3502 1 3502 0 3502 0 1006, ( , ln , , ) , .
() = 2,182107(0,5768 5,1006) = 10,4 .
4 = 1460
= 0,961031460 = 1,402; 1 = 0,7008;
1 = 0,7012;
J(1,402) = 0,8805; J(0,7012) = 0,3113;
() = 2,182107(0,8805 0,3113) = 12,4 .
, , 5 = 1825 fl () (III.23).
= 0,961031825 = 1,752; = 1,402;
1 = 1,0512; = 0,35;
-
135
J(1,752) = 1,212; J(1,0512) = 0,577;
J(0,35) = 0,1005;
() = 2,182107(1,212 0,577
0,1005) = 11,7 . , -
() - fl. . 64 t.
III.3. - fl - . (. . 54) fl 1 fl . - qA t = 0. . qA = 100
3/ = 1,16103 3/. k = 0,1 2; fl- = 103 , h = 10 ; = 10101/. . .
fl fl R =103 . .
fl . - (II.132), fl . .
z = R2 = 4t.
= k/ = 1013/(1031010) = 1 2/.
t = 1 = 0,315108
z =
10
4 1 0 315 100 8 10
6
82
,, .
z
-
136
fl fl , fl fl fl, - - .
15.
fl fl -fl fl - . - , fl , , fl . fl fl - , fl , fl fl -.
-, , fl, flfl , fl - .
flfl , flfl -fl, . -, , . - fl, flfl .
fl fl - fl -, . - fl - -, -fl. - , . - .
- , - .
-
137
, (. 65). fl -fl - fl - ( ). fl -. - - , .
fl fl . -fl r - flfl . r = r, = < ( fl). - -fl = (), fl .
, - r = r fl fl fl , , , fl - , - fl - q = q(t).
fl, , -, -, - - , .. q = q.
fl fl- , , , fl fl - .
. fl - , fl fl- () fl -fl = (). fl
. 65. fl fl , :1 ; 2 fl - R; 3 -
-
138
rc r r fl -, .. .
fl fl . fl -fl fl- . ,-, - fl . fl :
V = 0V, (III.29)
V , (-) fl, ; 0 -; V fl ; .
fl z = z(p, T). flfl
p/z = p/ z, (III.30)
, z, , z -fl.
fl v
v z zkk s p
p
p
r
u = =
( ) ; / .
(III.31)
fl
v kk s p p
r
= ( ) .
0 (III.32)
, , v fl - :
v kk s p
r
= ( ) .
(III.33)
-fl ( ), fl, , . fl fl fl-
-
139
rc r r (r ).
(III.31), (III.32) (III.33)
pp
p
k s
k s= + =
const
0
( )
( ). (III.34)
(III.34) , fl p - ( )s. , fl
p = p(s). (III.35)
fl, , -fl fl
k = k(s). (III.36)
(III.35) (III.36) , - fl fl
k = k (p). (III.37)
fl - q.
q khk p r p
r
=
2
( ). (III.38)
fl fl (III.38) H, fl
H k p dp C dH k p dp= + = ( ) ; ( ) . (III.39)
fl (III. 38) (III.39), flfl
q H H Hkh Hrr
c
= = 2
ln
; , (III.40)
H, H fl fl (r = r) (r = r). fl - fl - , fl - , H = H(p),
(III.40) , fl - fl . fl
-
140
fl fl ,fl , fl .
, fl - . fl - . - , , fl - , , - fl , flfl fl, fl -fl. fl fl
.
, - , fl , - - . fl fl .
fl fl c, , - r (. . 65), -fl , flfl -.
fl , - - s, ( r r r) - , s. - , , p .
fl q, -,
q rh k s p
r
= 2
( ). (III.41)
q h rk s k s p p
r
= +
2 0
( ) ( ). (III.42)
fl fl
-
141
sp= +[ ] ( ) ;0 0
( ) ( )/ ( ); / .s k s k s = =0 (III.43)
fl fl - r:
M = V; M = 0 p V + V;
V = V + V, (III.44)
V V . (III. 44)
M = 0 p V +0 p V + (V); M=V. (III.45)
fl - fl :
= M/M= p
V
V
+0 p +
( ).
V
V(III.46)
fl,
s V V s V V s V V 1 ,= = =/ / /; ; (III.47)
=
0 0s pp
sV
s V
+ + ( ) . (III.48)
fl . fl , (III. 30)
= cp. (III.49)
(III. 48) (III. 49), flfl p s ,
ds
dp
s c s
cp s
=
+
0
0
1( )
( ). (III.50)
(III.50) - .. , fl - fl -, fl .
fl (III.50), - s fl p . , - fl -
-
142
fl fl , fl - .
L2 , L1 , . fl - V.
L1/1 + L2/2 = V; L1/L2 = p , (III.51)
1 flfl ;2 .
fl
= =+
+
+
+
L L
L L
p
p1 2
1 1 2 2 2 1
1
1/ / /. (III.52)
, -:
G = m(1 s)V, (III.53)
fl; m -; s fl ; V . , :
G = m( s s)V. (III.54)
(III.53) (III.54) fl -fl 1
1 1 1= =
G G
G
s s
s
( )
( ). (III.55)
1 , , flfl .fl , , p .
- .
, flfl -, (. 66). , fl fl . . fl . - fl r = r p. fl fl p , - fl
p, -
-
143
fl . V, :
V = m(1 s)1V, (III.56)
V . , -
, p fl p.
-fl - . fl
p , fl fl, -fl .
fl fl: N1 fl , fl , ; N2 fl ; L1 , ; G1 fl - .
fl :
N1 = G1 + L1; N2 = L2, (III.57)
L2 N2 fl . , , :
L1/L2 = p . (III.58)
fl fl - fl
G1/2 + L2/2 + L1/1 = V, (III.59)
1 2 - ; 1 flfl
. 66. fl fl :1 ; 2 fl ; 3 fl
-
144
. fl (III.57) (III.58) - flfl (III.30),
p /1 = p/1. (III.60)
fl fl fl
p . . fl fl - - , = .
, N1 N2 - t. fl :
N N q dt N N q dtt t
1 01 1 10
2 020
= = 2 2 , ,
N01, N02 - ; q1 fl fl , -fl fl; q2 fl - .
flfl (III.57), (III.58) (III.60) (III.59), fl fl p :
p bp c N2
2 10 + = =; / ;
b V N p N= +
2
1
2
2
;
cN p
= 1
1
. (III.61)
fl fl, :
p b b ac
a1 22 42,
.= (III.62)
fl , , - fl fl (III.61).
y ap bp c= +2 . (III.63)
a fl, - (III.63) fl y. b c . fl -fl (III.61) . - (III.62) b -. ,
( ) , (III.63).
-
145
dy dp ap b/ .= 2 (III.64)
2ap b < 0, fl dy/dp fl y .
p
1. 2ap b > 0
p
2. , fl, -
fl
2ap b , fl(III.61).
G1 = N1 N2 p. (III.65)
V1 = p/1(N1/p N2). (III.66)
III.4. fl fl - . fl = 5 10
-3 , fl = 0,02 10-3
fl. fl, fl - flfl ,
/ = 0 = 250 = const.
fl fl s, fl
( ) .s
s s
s s
=
s = 0,7; s =0,5. fl (p = 5 ).
2 = 0,9 103 /3, flfl
1 = 0,3 103 /3. fl fl 1 -
, s 0,5.
= 0,7 102 /(3 ), = 0,7 /3.
, -fl (III.50) . (III.50) -fl
ds
dp
s
cp s
=
0
0( ).
flfl ( s) fl,
fl fl s -
p
p A
s s
s
s c
s=
=
( ) ;( )
.
1 0
0
A flfl fl s s = , p = p. fl fl (III.55) III.52 = 0,0544.
s = 0,5, p = 0,577 ,
-
146
3
3 / /=
+
+
= =+
+
=1 0 0544 5
1 110 0544 5
0 3
0 631 0 0544 0 577
1 110 0544 0 577
0 3
0 85,
,,
,
, ;, ,
,, ,
,
, .
2
0 30 7 1
0 850 63
0 5 0 051 0 05
0 361= =
=, ;
,,
( , , ),
, ;,
= 0,253.1
III.5. fl , , , , - R = 3 103 . fl , .
, fl fl p = 8 10
6 . - - . , fl p = p. m = 0,25 , h = 25 , fl s = 0,05. - 2 =
0,8. 2 = 0,85 /
3, - fl 1 = 0,85 10
-3 /3, flfl 1 = 0,3 /
3, = 8,5 10-9 /( ), = = 0,9. 10 fl fl
q = 1,5 106 /. flfl 10 -
:
qt
t t
3
3
0 ;
[120+ 42,43( 2 10 .=
120 10 2
2 10
6
1 2 6
/
) ] //
, fl 2 - 10 fl.
fl fl , . - , . (III.56)
V = m(1 s)2R2h = 0,25(1 0,05)0,8 3,14 9 106 25 = 134,24 106
3.
fl , fl , - . (III.59)
N02/2 + N01/1 = V; N01 = N02p,
N01, N02 .
NV
p02
2
6
9 66134 24 10
10 85
8 5 10 8 100 3
95 7 10=+
=
+
=
1
1 ;
,
,,
,
,
N019 6 6 68 5 10 95 7 10 8 10 6 508 10= = , , , .
2ap b p = p.
2ap b =
2
1
1
1
Np V
N p
pN02 2 2
2
+ =
-
147
=
2 95 7 10 8 5 10 8 10
0 3134 24 10
6 9 66, ,
,,
+
=
95 7 10 8 5 10 10 0 9
0 85 10
95 7 10
0 85
6 9 5
3
6, , ,
,
,
,
= + = 43 38 10 134 24 10 86 13 10 112 6 10 64 39 106 6 6 6 6, ,
, , , .
, p = p 2p b . p < < p . , fl (III.61), ..
p
b b ac
a=
2 4
2.
p 10 .
a
NN N= =
=
2
1
9
29
28 5 10
0 328 33 10
,,
, ;
b N N= +
=
134 24 10
8 5 10 10 0 9
8 5 10
10 85
134 24 10 0 27669 5
3 26
2,, ,
, ,, , ;
c
N pN= =
=
15
38
110 0 9
0 85 101 059 10
1
,
,, .
fl N2 = 95,7 10
6 1,5 106t;
N1 = 6,508 106 0,102 106t 0 t 2;
N1 = 6,508 106 0,102 106t 0,02405(t 2)3/2 2 t 10.
, 10
N2 = 95,7 106 15 106 =- 80,7 106 ;
N1 = 6,508 106 0,102 106 10 0,02405 83/2 = 4,944 106 .
a = 2,286; b = 112 106; c = 5,236 1014; p = 5,23 . , 10 fl
2,77
. . 67 q, - fl p fl .
fl , - .
= =
=
V
V
p
V
N
pN2 1 2
1
=
=
10 0 9
0 85 10 134 24 10
4 944 10
5 23 1080 7 10 8 5 10 0 205
5
3 6
6
66 9,
, ,
,
,, , , .
-
148
, 10 fl 20,5 % , . - 12,6 %.
15 - - .
- fl fl -fl fl, , - . fl fl () flfl - (- ).
fl -fl , fl , , fl -. , fl - fl fl , , fl . fl fl fl - fl . - fl
fl.
fl - . -
. 67. q, fl
-
149
fl 35 % fl - fl 15 10-3 . , fl fl, -, .
fl - , fl - . fl -, .
fl fl fl 30- . . 40- . fl , fl , flfl , -, .
, - fl - . fl fl-fl fl - , fl fl , .
1. .
2. fl - fl -fl fl fl - .
3. fl fl - fl.
4. .
5. fl fl fl - fl fl -.
-
150
16.
fl fl- fl fl fl .
fl fl fl -. 90 % - fl . - .
fl fl: - fl -fl fl . - .
flfl -. fl, , , - ( ) (- ). (). , fl fl fl fl , fl . , - , flfl
fl. fl, 5 / fl 20 /fl .
-fl 510 , fl 1520 . -
IV
-
151
, - . fl fl fl- , q, , , - fl. , , - fl, fl (. 68), fl pc q fl.
, - fl p = p p = pc - fl fl - .
fl -fl - , .. , , , - . q , - , q fl ( ), q - , fl.
1. - t
Q q t dtt
= 0
( ) . (IV.1)
2.
Q q t dtt
= 0
( ) . (IV.2)
3.
Q q t dtt
= 0
( ) . (IV.3)
. 68. , - , q fl
-
152
= Q/G fl- Q/V Q/V ( V ; G ). fl = = (Q/V), fl , fl (fl 15 10-3
), - fl . 69.
N fl, , :
N = G. (IV.4)
fl Q/V , fl fl, , . 70.
fl , fl,
= q/(q + q) = q/q; q = q + q. (IV.5)
. I, - fl , fl, fl 1 2 fl.
fl 1 fl -fl fl , fl , - . -
. 69. - Q/V. : 0 fl; fl
. 70. - - Q/V:1 fl ; 2 -fl
-
153
- 2 fl - , - fl , - , - .
fl flfl fl - fl - - -fl fl- (. 71). - (1, 2, 3 4), -, , , -fl -
fl - (x = 0) (x = l), fl fl - fl .
G = G1 + G2 + G3 + G4. (IV.6)
G :G = G1 + G3 + G4. (IV.7)
= Q/G = (Q/G )( G/G)= 12. (IV.8)
fl -fl , . , . 71, - fl 2 fl l2, 3 fl l3, - 4 fl l4, 2 G02, - 3
4 G03 G04. -
G = G02 + G03 + G04. (IV.9)
fl -
. 71. fl
-
154
= =
