. .

-

-

1963

1352 532. 529. 5 + 532. 546 (022)

, -

-

. -

, -

, -

.

-

.

-

, -

, - -

.

, -

,

-

.

1. .2. . .

- -

, -

.

, -

- -

.

. . . -

, -

30- , , , -

.

. . . . -

(, 1949), . . (, 1956), . . (, , 1956)

. .

(, 1961). , - -

,

, ,

.

:, ,

-

. . . . . .

19561959 ., (, 1948), 1960 . -

, .

, -

, , -

,

.

,

--

, ,

-

,

. ,

,

. . , -

-

.

, -

,

.

,

, , -

.

,

-

, -

-

.

10 , , ,

.

-

-

. 4

. -

-

. , ,

, -

. , ,

, , -

. -

-

. -

, -

.

. -

. 3 8 - .

-

. . -

,

.

,

.

, -

.

,

, -

, . . ,

-

, -

.

,

, -

,

-

. , -

, -

, .

38 -, ,

-

-

. , -

. -

.

, , , --

. -

, -

, , -

, - --

.

, ,

.

,

-

.

.

- -

,

, -

. : -

.

,

, ,

. -

-

.

, -

-

.

-

.

, -

, - ,

, -

, . . -

, -

.

,

.

. .

4, -

. . .

-

, -

. . . -

,

.

-

. ,

,

.

,

. . .

, -

,

.

-

.

,

.

.

- .

-

, , .

9, . . . . .

,

. ., -

.

, -

,

.

- ,

, -

.

,

, -

, -

. ,

. . -

,

- , -

,

,

.

-

-

.

.

- -

, . . -

, 1957 . - (, 1960), - 2000 . -. -

,

Applied Mechanics Reviews, - , ,

-

, ,

,

.

-

,

.

-

,

-

, .

. . .

. . . , . . . . -

,

. -

. . , - . .

.

. . . -

. . . - .

. . , -

.

I

1. . .

.

.

,

.

,

.

.

, ,

, -

.

, -

, .

.

1 3, , 10000 2. - , ,

,

.

, -

.

. . , . .

[1, 2, 3], , -- .

-

[3, 4, 5]. .

.

10 . I.

dx

/

,

, ,

.

, ,

, . -

. , , -

.

.

, ,

.

-

.

-

".... , ; / , . J . - ..-..... ".;' - ' ' " - - - - .

,

'

(. I. 1).. I. 1. -

. -

.

-

. ,

2, , .

-

.

-

. -

FnycT V : = Vnyc-v/V.

,

.

, -

. ,

Fn y C T . ,

, -

. , -

, ,

,

, ,

. -

. -

,

0,150,22, , , .

1. 11

,

. , -

, . , ,

, -

.

, . I. 2, , -.

(. I. 2, ), -

.

,

-

, -

[6,7]. - -

- . I. 2. , ,

. ; - ,

, -

. / (. I. 1). .

, /, /

,

.

,

/ , .

.

w - Q / :w = Ql f.

, w .

>

( - ) , Q /- /, - :

^ = -, > ~ = w-/ I

12 . I.

w wae

%CTB- .

dx . , , - ,

dt. dV, .

, : , ; , , -

/ dx.

dV = Qdt = mf dx,

Q dx= 171f - " ' dt

Ho dxldt , a Qlf .

, w -

:

W = ?

. ( 1 . 1 . 1 )

, ,

, : , (I. 1. 1),

Q w Q

^ 2 = . (.2)

. -

.

-

, -

,

. .

,

(. I. 3). -

, -

0 di, di

1. 13

,

,

.

. , , . . -

[6] [8].

dt - i; di = -=- (d4 + d4)

20

. I. 3. - .

di.

-

.

-

, -

,

-

, ,

, . .

-

,

,

.

,

, ,

. -

,

-

[3, 4, 9]. . . - . . [10],

-

.

,

, ,

v () (. I. 4). v () , ,

14 . I.

v () dr, , -f- dr, , -

. ,

f v () dr = 1.

-

-

-

, -

-

[3, 9, 10].

. I. 4.

.

. I. 5. .

, ,

, .

-

, ,

-

.

-

1856 . , Hi -. Q, - /, (. I. 5).

:

, 2

t

z ; ; ; .

1. 15

,

:

-

, -

.

,

. -

, . .

, . - / 2

-

Re =

. I. 6. -

| -.

= 2- - ReK p, ,

.

Re: Q ; JJ, -; ; - , -

- [3, 11, 12, 13]. .

= (s, t), s (. I. 6); t .

(I. 1. 4),

- -

1" " . = -

1 (1.1.5)

w gradfT. (I.1.6) -

. -

,

.

16 . I.

.

,

w = !

ds

"> = 4 ^ , (1.1.7)(j, ds ' v '

(j- ; Y ; , -! = \ . , z = 0.

[] = 2. , [] = /2, [] = 0,01 / . = 1 , [s] == , . ,

1 , , 1 , 1 /2 1 - , 1 2, 1 3/.

-

1 10~8 2. - .

(1.1.4) (1.1.7) =^-. (1 .1 .8)

== 100 - 1000 . , .

(- ). -, = 0.

-

, . . .

[3, 6, 7, 11], -

( ), ( ) . . - , ,

,

.

(I. 1. 7) , -

, -

2. 17

.

, , -

[14, 15, 16]. - .

2. .

-

(. I. 6) - 1 , Q (s, t), 2 Q -\- - ds, :

ds - U '

, Q , -

IT 1

(1.2.1)

. = const,

, ,

, Q = const, (1.1.5)

Q = ~c4rf&> ( J - 2 - 3 ) s:

(1.2.4) s s = sx s, a

,

rw- (L2

-

5)

18 . I.

s.

2 su s2, (1.2.5)

H l~

f f i i

1~

(I 2 6)ds

cf(s)

i ? i v s2) = J4

dscf(s) (1.2.7)

.

(I. 2. 6) . -

, , -

.

-

.

1. / (s) = const, H = (s) -

. (1.2.2) :

" = 0 = 1$ + 2, (1.2.8). .

.

2. - - ( ). , - . 1.7, h ;

;

;

-

; = RK. / = 2 rh -

(I. 2. 2) s :

- f - - = 0 . (I.2.9). I. 7. -- -

. :

= In +

, (1.2.10) = 0 , -

, .

2. 19

= =

,

=

= RK,

1 = 1 ! - (1.2.11)

( 1 . 1 . 5 ) ( I . 2 . 1 0 )wc = c ( I 2 1 2 )

, \ > ,

< 0 . , -

-

20 . /.

(1.2.16) :

= ^ 1 + , (1.2.18) > 0 ;q < .

3. - .

/ = 4 2 (1.2.2) :

dr, (1.2.17),

^ ( ^ ) 0. (1 .2 .19)

, -

= ^ . + 2. (1.2.20)

w

,

> 0 ,

< 0 .

Q = 4 21 w | = 4 |

|,

= ^ - + . (1.2.21)

Q ]> 0 Q

$ 2. 21

-

(1.2.21) ( (1.2.22).,

Q .

.

:

, (I. 2. 24) - .

(I. 2. 24) (1.2. 14) .

(I. 2. 18) (I. 2. 22). , -

,

.

(I. 2. 18) q > < 0 .

(I. 2. 22) - ( ? < Q > 0 -.

(I. 2. 18) , - , , , -

.

,

=

=

.

(I. 2. 18) ,

, -

.

(I. 2. 18), -

.

(I. 2. 14) .

22 . I.

,

RK. -

(-, 23 ).

,

.

in + lnn. (I.2.25)

'"

RK/rc - . , (I. 2. 25) . 67.

2 : = 2, In 2 ? 0,6. , (I. 2. 25) .

23

-

,

10%. (I. 2. 22) (I. 2. 24). (1.2.22)

.

11

> ., (I. 2. 22) :

, RK^rc.1 I

> -5 (1. 2 24) . (1.2.24) - :

Q = 4 ( ] ; ~ ) = 4

(

-

). (1. 2. 26)

-

, . ,

.

, , ,

.

,

:

=f= . - (I. 2. 26) . -, ,

(. I. 8, ).

2. 23

. -

,

(I. 2. 26):

24 . I.

,

Q= 2 * ^ - > =

2

( 0 - ) .

-

, . ,

__ 2/(

) _ 2/(0) = 2() ,j 9 2

,

. . [25], i?0^ 1,5. , , r

c

$ 3. 25

, G:

= - l W

, l ' ' --f(s)y(p)- (1.3.2) . . ,

Pi (p) =

(1.3.2) :

(1.3.3)

(1.3.4)

(I. 3. 4) (I. 2. 3) -

: / (s) - Q G , Pi, - ki (s), w yw . ,

.

.

w =

dpdsdpds

apds

\ dp \\\\ ds \)

m l\ Vl

,1 /M

v \ ) -

dpds

ww\

(\\\II

dpdsdpds

(I.\

/

3.

3

5)

6)

; ' , . -

dp

W = dsdpds

r dpds

(1.3.7)

.

< < 1.

26 . I.

[3, 19]. -

< (1.3.8)ds ' \w\ * \w\ g

,

, , ,

,

,

, . . -

b [12, 20, 21].

,

(, , ),

, . -

w (I. 3. 8) - , .

s

(1.3. 5)

(I. 3. 10) - , -

. , -

- , / (s) - / = const, / = a s , / = C2S2, [8, 19].

(I. 3. 10) w (I. 3. 9):

dp _ ( ) G G* , , , 4ds )**() y(P)f(s) "*" g fHs)y(p) * V--i4

= (), = ki (s) kz (p) (I. 3. 11) , -

(1.3. ) - , -

.

| () = fi = const, = const (I. 3. 11) - , -

:

4. 27

, (1.3.11) {),

dP

dpds

U.

GfU

G

0k G*g /2 (S)

i b G2

S! Si

s1? s2.

4.

, .

,

.

-

,

.

-

, ,

. . [6, 7 ]. , -

. -

-

. -

, -

, . -

-

-

.

, ,

. -

[3] [22, 23, 24].

-

,

-

( - ), -,

. .

,

28 . I.

. -

* , " .

,

, -

,

.

. I. 10 - - . -

.

, , , -

.

,

, -

-

.

, , -

, -

.

-

, -

_

. _

. I. 10.

. -

,

- ,

-

, -

. , ,

(I. 3. 8). h% ftM -

, . .

:

X , ; d ; I ; . ,

,

. - ^ - . $ * 2 . (1.4.2) * 2 , -

. Z,

4. 29

. , , , -

, -

,

,

.

% 2, - , , -

L -

~ * const,

v = ; = 32 . , , -

w = ,

d. (I. 4. 3)

!

2 . , -

2 - (1.4.5) d

max/d .

.

,

[3, 23]. - -

, , , ,

-

. , -

X (1. 4. 1) X - . , ,

.

1. . . . -, 1945.

2. . ., . . , . . . . , . 28, 5, 1940.

30 . I.

3. . . . . . , 1960.

4. . ., . . ., 1955.

5. . ., . ., . ., . . - -

. , 1962.6. . . , . II. -

, . . , 1953.7. . . -

. , 1947.8. . . . , 1961.9. ., ., .

. . . , 1962.10. . ., . . -

. . . , . .

. . 4, 1961.11. .

. . . , 1949.12. . . . -

, 1956.13. . ., . . -

. . . , . , 1956.14. . . -

. , ., 1960.15. . , . . -

. , 1953.16. . ., . ., . ., -

. ., . ., . ., -

. ., . ., . . -

. , 1962.17. . ., . .

. . , ,

, 5, 1961.18. . . , . .

. . ,

, , 1, 1962.19. . ., a n y . . .

, 1949.20. . .

. -

. , . -

, 1951.21. E n g e l u n d F. On the Laminar and Turbulent Flows of Ground

Water through Homogeneous Sand. Transactions of the Danish. Academy of Tech-nical Sciences, No. 3, 1953.

22. M . . - . . , . 118, 2, 1958.

23. . . - . . , , , 4, 1959.

24. . , . ., . . , - . ., . ., . . -

. , 1962.25. . .

.

, 1956.

II

1.

-

. , -

[1]. [. I. 6, 7, 2].

,

(1.1.6)w= gradp,

= ; ; - . -

-

.

,

, :

-

,

mdV, dV ; , , :

d^ ) = 0, (. 1.1)

w .

32 . II.

dpU =

dp

v '

7 = ~ .[. OZ

, v, w, p,Q, m , -

.

, ,

, ,

[3, 4, 5, 6]. -

= ,

= = const, . . .

, , v, w, p, Q,m (II. 1. 1) (II. 1. 2). - ,

Q = Q(P,T) (. 1.3)

m = m(p). (II. 1.4)

, .

-

, . . Q = const, m = const. :

&ivw=0. (. 1.5) .

( I I . 1.5) (II. 1.2) const, -

^ V2 ~ grad/cgrad p = 0. (II. 1.6) k = const,

V 2 P = 0, ( I I . 1 . 7 ). . = const . (1.2.17)

V 2 O = 0, (II . 1.8). . = const . (II . 1.8) -

2. 33

,

- -

= (), (1.2.9) (1.2.19) .

const (II. 1. 6) . ; = {, , ,, z, t) . ,

= (, , z), [II. 1. 6] .

= (, , z) . . [7 ] - . [8].

, , , z (II. 1. 2)

(, , , z, t), kv (, , , z, t), k2 (, , , z, t) .

, -

, --

, -

. [.1.3]. -- ,

,

, 2 , -

. ,

( 3, . V). , , -

.

2. . .

. . -

, ,

.

:

, , , v

1 dpdt dz Q

dv , dv . dv . dv -,, i dp . . . . ..-dr+u4r + v-W + w^r = Y-TW^ ( - 2 )dw . dw , dw , dw 1 dp

34 . II.

, v, w ; X, Y, Z - , ; Q ; .

, -

, , z - (. II. 1, ),

V 7 / 9 9\ U, I = V, li g, (H. . )

g = 9,81 /2 .

Z'-c

. II . 1. ( -

).

( )(. II. 1, ),

X = 2 cos = 2 ,Y = (2 = (2/, (II. 2.3)

( z; r ; .

, -

,

. , ,

.

2. 35

,

.

, (II. 1. 1) , , -

:

X = X, + 2; Y = + 2; Z .-= Zx + Z2,

Yi, Zx ; 2, Y2, Z2

, .

, v, w -, , ,

1 1 / , . \ 1 . v

. v

-W+^{u + v + w j = + X + X1 dv 1 / dv , dv dv\ 1 dp ,

7. . T7- / T T ,.

Ur +i(u + v + wdi) = ~ T"^7 + ^ 1 + ' ( I L 2 " 4 )+ w j = ~ ~$~ ~dT~ + Zl + z*-

-

(. 2. 4) . , ,

, . (II. 2. 4) :

ur

ny,

n _ n / K\

oy x '

, Q X2, Q 2, Q ^2 -

:

QX2 = - ^ u ,

QY2 = --^V, (II. 2. 6)

e Z/

36 . II.

, -

:

I (

, -

(. II. 1, ). (II. 2. 2) (. 2.7) :

' ,

(

(-2-8)

, ,

(II. 2. 4), [9, 10].

, ,

, Yz, Z2 - .

. . [. I. 6, 7].

, 23 I, - . -

, ,

. . [11], . . [12] . - [. I. 21].

, -

.

, U (, /,z, t), . . \ Xi, Yi, Zt

F = gradZJ (II. 2.9)

, \i Q , =(), = (),Q = e(p). (II. 2. 7), Q (p),

2. 37

(. 2.10) Q , QV,w

* ( ) ( ) i *()'()

_ k(p)Q{p) dp A(p)Q(P)

(. 2.11) :

^ = () = - ^ . (II. 2. 12), = () -

.

. . -

. .() - .

(II. 2.11), , :/ , dU \ ( . dU \

v ' J' \ * ]

,^-(^- + . (.2.13,

, (II. 2.12)

.() " " ^ dp

dz dt_ () Q ()

dx, dy, dz, dt , dx, dy, dz, dt . (II. 2.10) (II. 2.13).

(.2.13) (II. 1.1), -

* . ^ , I~ dU ,dt * ' * ~ dz2 ~ I

38 . II.

(II. 1. 3) (II. 2. ), (. 2. 14), , , ,

, , Q. , - (II. 2. 12) = (). , = () = () =

()() () () ( ) ( ) ( [ ( ) ] ( )

() 1 ( ) ] ( ) () [ ( ) ]= @(). , (II. 2. 14)

Q. , , , , -

.

, ,

.

. -

, , (II. 2. 13)

2 = 0, (II. 2.15)

-

. , ,

, ,

. . [. I. 8], , , ,

,

w -

Q W. Q W

w = g Q W. -

() = = const, k(p) = k= const{

)1 = ^-, (.2.17)

P = fy(p)dp, (. 2.18) -

.

2. 39

, , ,

(. 2.14) ^- = -~^

- (. 2.19), , -

(. . ) . (II. 2. 12) (II. 2. 18) - J, , -

.

.

, , =

= Y (, )

, (. 2.20)

R ; ; z

40 . II. ,

3.

-

, ,

, , -

, , .

.

,

-

, ,

. , , -

.

, , -

. . ,

,

[5, 6]. -

, -

.

?

-

. , w, - g \ \ , , -

, -

, ,

.

-

.

-

, , -

, ,

,

; ,

, .

,

. , -

,

-, - , -

.

.

- , , , ,

, -

,

.

, ,

, .

, . . ,

2 .

, ,

4. 41

[13, 14, 15], -

.

-

/ (s). , , ,

.

, , -

f2 (. II. 2).

. ,

>/, w - J1 ; .

. II . 2.- ,

.

t + t (. . 2)., :

( 1 ) , . (II. 3.1)

,

, -

/

At, ( 1 ) 0 d t

, -

, ,

.

-

.

4. :

C i - G 2 = ^ - JmydV, (II.4.1)dt

( y ) Gi G2 /2; V /2.

, dV = f(s)ds (II. 4.1) - :

G(s, t)-G(s + ds, t)= 2) fWd*

_ [_[.. . .

42 . II.

,

==

~1~ f(s)- (. 4. 3)as at

: (yw

x) ( w

v) ( 2) "1 ()

| dz I dt ' w

x, Wy, wz w , , z.

5.

,

/2. -

-

, , . , -

.

:

I v 1 / 1 17 I I D I 7> I ] rp | rp i (- \

(V) _^ _^

/ 2 = I Qdq; / = I Q dq (II. 5.2)(/2) (/1)

-

/2 / ; dq = wndf df, w

n df -

;

2

/ l f /2; Rn - ; R

n

, ; W , , , -

. . 7\ ; 2 .

, -

dV , - .

.

(II. 5. 1) , . , , , -

,

. w/m 4 I ,

.

5. 43

, , (II. 5. 1) s , - /i /

ds:

-dTls-dT2s, (. 5.3)

| - ,

[16, 17]

jwndf

(-5. 5)

(.5.6)

w . , [16, 17], % = 1 / 3 ,

=: 0,03. I 0,2. - ,

.

% (II. 5. 5) . I. 4.

i. (. 5. 7)

0 , gj, .

(1.4.3) (1.4.4)

(II . 5.8)

h = H1H2 . (. 5.9) -

. . .

1 S = QQ* 1 gh

\A v I 4

44 . II.

,

J r*v(r)dr f( I I . 5 . 1 1 )

[J0

,

, , -

.

, z (. II. 1, ). , (. 5. 3), , , :

dP = d[pmf(s)], ( I I . 5. 12)(dR

n)s = Pd{mf(s)], (. 5. 13)

dzdWs=-ymf(s)ds.~ , ( I I . 5 . 14)

(dR'n)

a = O. (II. 5. 15)

-

/ (s) ds. .

(II. 5. 15) . . (dR

n)

s. (d/?

n)

s

-

s - .

1. , s.

(i-m)f(,s)p. (a)2. , s -f- ds.

()

3. , .

Pd[(l-m)f(s)]. (),4. ,

. , ds , - , -^ (lm)f (s)ds, (1 ) / (s) ds . , - ,

(d)

$ 5. 45

,

'

).=. () dTis dT2s : dTla -

/ (s)ds - .

, (II. 5. 3)

= dp-mf (s) pd [mf (s)]+pd [mf (s)] Y mf (s) ds dT2s =

= ~^-dsmf(s)-ymf(s)ds p dTZs. ( I I . 5. 16)os ds

(II . 5.3) ds :

dT2s -, . . ,

flS *.

(II. 2. 6) -, , ,

u w,

kQdT2s=

r v mf(s)ds = -Zjmf(s)ds. ( I I . 5. 18)

( 3, . I ) , - ( I . 3-8), -

^^ __ w ( I I . 5 . 19)ds * | | '

Z, , . ,

, -

, , , -

, . . . ( II. 5. 19) 1 , [24] . . , -

,

1 1 U W

-. ,

( I I . 2. 7). 124] , , , [2] , -

46 . II.

, -

-. , , [. I. 11] ==

$ 5. 47

(II. 4. 3) ,, ,

[ 1 + | 1 1 1 + | w dG i (y dw i wi ( ig m ds+\g dt + g dt

:

1 -j- w d dw wg m dt g dt g

(II . 5.22) :

, mf (s),. . \

m ds \ g m j g m dt

j- , - .

5 = 0 \ - (. 5.23) . | = 0 < 1 (II . 5.23) .

,

:

gm dt n| w

x \ 9y _ 1 dp 1 l\i\w\

g m dt dx i T B / I " 7

gm dt +-m-\w*-di[g-

m-) + wy-dj[g-

m-)+W*dz\ g m

I wy I dy = 1 dp 1 / p, | w | e - Wg m dt dy \ ^

4 . II.

6. , ,

, -

Y = Y () (II. 4. 3) (II. 5. 22) (II. 5. 23) Y, , w.

-~ (, ) - , -

, .

-

, , -

.

-

, .

/2,

(/)

(V) (/l)

jLE- + i\ydq_. fyZmdv+LBH + -^f- . (.

(/2) (V)

(II. 6. 1) , ~ (, ) , ;

, /2 ; ,

.

-

, , -

.

QBH

1 : = j~= /- .

,

.

LBH = 0, ,

, ,

( ) -

-

.

6. 49

, LBB = 0. ,

~\, (II. 5. 1) (II. 5. 3). , - 2,

. ,

.

, -

, ,

, LBH = 0 - ,

. 1.

.

50 . II.

, , -

(II. 5. 10) (II. 5. ) , :

jyif ' (IL6'4) v () (. 1.4)

J rv(r)dr[ f)

[ f r* v (r) dr]30

, (II . 5.11) (II. 5. 12), 0 .

\2 w mdf, 771 / WI

(/) .

(II . 6.6) w /(). w

n, | ' = , | -

(II. 5.5). , , g ' . / I I . 6.2) ds (II . 6. 3) (II . 6.6) :

(II. . 7) 7"i -

. -

,

.

,

. ,

, -

. ,

, -

, .

.

1 = 1, (. 6. 8) Cj / .

6. 51

:

( l - m ) (), (.6 .9)

Xi . (II. 6. 9)

. , -

(II. . 7). - s, - .

(II. 4. 3), (. 5. 22) (II. 5. 23), (II. 6. 7) (II. 6. 9) = Y (> ) - w, , , , 7\.

(II. 6. 7) . -

i = i(p,T)=u + A ^ . ( II . 6. 10)

-

[%)]p, ( . 6 . 1 1 )

; v = v(p, 7") =1 , ( dv\

= -.=- ; \~^f) v , , .

(II. 6. 10) (II. 6. ) (II . 6. 7) . (II . 6. 11) ,

, ds dt,

di . . / \ ]

(II . 6. 12)

(. 6. 7) :

52 . II.

{ +

. (.6). . [. I. 19]

, i == i (, ) = const, . ., -, , -

. -

[. I. 19]. (II. 6. 13) , i (, ) const .

,

.

i (, ) = const .

(II. 6. 13) - (II. 4.3) (II. 6.12),

( ) 4 ^ +

S 6. 53

, -

(II. 5. 23). (II. 6. 14) mf(s), -

[ 1 J dv\

">)*

2g \ m ) dt ^ dt [ ^ 2g \ m ) J [ )p dt

'

1 1 f 9T\ \mf (s) ds I ds w J \ dn Jcp f (s) J '

mj - , (II. 6.15), (II. 5. 23), -

w > 0:

_

F-Hf i^- < " " 1 6 ) (. 6.15) :

ffs\ g m

g dt g m dt J ~ ds L^ \ 2 i ay , 1 + 6 ' ( ' | [\ dp__m) dt "^ a t L 2g \ m j J \dT jp dtA dt ' 2g

f cr, a r I i / ay

Jw\ (w)y w I 1 + g u > \ ] 1 \ , m j 1

/ ^ \ Y \ m ) ,m ds \ g m ) \ g dt ^ \dT jp g dt """

$4 . II.

HLT() LJL?y + JL\S+Aygmdt \ jp g m dt + ds[Z+ 2g

CP ^ | E ' - i ()' i ay , 1 + 6 ' / f f t A _4 + 2g \ m / Y di "*" dt [ "* 2g [m I \ \ dT )p dt ~~

w dT , 9 T

~m~ ds + d t J [y~1 [ d T ) p \ m \ k^{__1+61 N Y 4 j _ A ( 1 + 1 \ ,

,( 9v\ \wy_dz- jvy_J_ ' * N a |\dT jp{m ds ' m ds \ g m j ' mg 9

1 1 v"/W

,

1 / \ 1 (\ 1\,,(\]

/ ^ \ 2 i _ay , \%> tw\*] ( d y \ [_^dz_g \m) dt ^ dt [2g \m) J y\dT)p\mds^

w_ 9_ I J _ + | _ w\ _w_ d_ lw\ _1_(2__1__)==

m ds \ g m j mg dt \m j g\mj dt dt j

m Y Ym/ (s) 5 s L 3 s J V d n /cp Y / (s) J ,

6. 55

-

.

Q . \ - .

1

[6, 18] *. , \ = . - (II. 6. 9) . mf(s):

1- CiYi 9TX _aQ (T-TJ 1 ,~~^ ~ Tj~H + Aymf(s) W [1~

A {i7m)f^ (II. 6- 10> / m/ (s)

(. 6. 19) (. 6. 15), (II. 6. 19) (II. 6. 18). , -, . \ = , ^

(w \ 1- ClYi w (dv \ 1_1 _

A \m ds "*" dt / "*" Am dt m [ \ ) J ds^

dv\

, _ , 1 1 ( \ n w( vM-^ ^L ^

, Am ,

(.6.20,

[mycp-\-(l m)c1y1] m%-\-(i m) %

.

4-(1 )11 = /-^, ml-\-(l m)%1 = A, (. 6. 21)

* , , -

, , , -

,

1 -

56 . II.

, (II. 6.17),\ I \

w-AmT[-r)-T

) Tff (" 22)JCp f (s) v '

Bj :_ l + J ! / u > V ] S ' - E x / \ 2 1 a Y

-

, (II . 6.19) (. 6.18)

T (\ I dp 1 __\ _ 1 / \ (s)

1 a L 9 1 / \ (1-)(1)+ ^Ym/W "

( )/()J~l^'*r/' ^v/W , Amy (II. 6. 21),

_ ( A * L ) " M - . (. 6.24)V an/cp /(s) '

e t

w { \i+^ ()] w

2 m I a* L 2g \ m) \ m ds g m

( aY a [ l ' . _ N ^ 1

7. 57

-

. , ,

:

&% w -- , , :

,

* + 9 + (II. 6. 27)3s dz

, ,

, I

\ , I. \ , (. \ -- - + -%- -% + -~ ~

\ I \ J dz \ dz = const ^2 - .

-

, , -

. : .

, -

. ,

Y = Y ( ^) -, .

-

.

-

. , -

, , -

, ,

-

.

7. , -

, , -

ei ^ , ,

. (II. 6. 22) (II. 6. 24) ,:

.

-5S . II.

(II. 7. 3) , :

,

f = const, 6 = ,

iI_ = il/'ji^-(-i.Ou)2) = *L (II 7. 5)

(II. 7. 5) - , -

,

. ,

(II. 7.6) , -

.

pv RT, R - ,

( * ) , 5 = - ^ _ = - ^ - = 0. (II. 7. 7)v

, ,

J- 0, . , ot

.

,

, ( \ I -^=-1 ~~

Y \ / ot

Y RT ' \ }

. _ ( \ dp Amp dp dp+ C ^ j = = _ = y l m . (II. 7.8)

.

7. 59

[19, 20]. (II . 6. 11) di , ,

- * * . . (.7.9)

-

[20, 21]. -

, ~ 0. , , 0, > 0 < 0 [19, 20, 21,22]. (II. 7. 1) (II. 7. 2), -

, \ , \af) " (II. 7. 9)

(\_ (

\Y \dTJ- V )

(II. 7. 1) (II. 7. 2) : . . dp AmT

=

6

>-- d s

( \ = _ e Y C p U , [-JL^-L., (. 7. 10)

^ -~ I - ( )

(, ) (5

, (II. 7.1) (II. 7. 2)

:+ = - ev CPW i + A m T P w =^ . . ( II . 7. 12)

(II. 7. 9) (II . 7. 11)

60 . II.

( I I . 7.12)

Y^."L+ cwL=__i_ [ 1_p ( P ir ) n Y e p I P-OS Ot Cp

^ T^(P,T)^- . (. 7. 14)

(II . 7.13) ,

^ (. 7. 15)

, , ,

8. 61

mf(s)ds,

62 . II.

ds _ dTv cpw ~~ dp

- * = ^ . (II. 8.4, Q -

, . .

p = p(s). (II. 8.4)

d

(. 8. 5)

[(const)j (const)2] = 0 . , ,

(consl)3 = i

i); V . s V (),

(II . 8.2):^^. (.8.7,

Y .

- ( = 0 Q - (s) , , (V).

(II. 8.7) () + ^-=^()- (.8. 8)

|5 - p(V). (.8.7) ( II . 8. 8)

" ~ ' P [ V ^J?I ()- ( I I . 8 . 9) 1 6 /

, (V) - V, (V) -

= v1 v =

S 8. 63

, s = s b V=V1 7 (V

x, t). (. 8.9)

, Fj ,

Vx, , ' ?, .

(II. 8. 10), ,

, ,

. ,

64 . II. ,

-

-

, . (

) - , -

.

. (II. 7. 17) - . ,

, :

W , a V = V(s) ( I I . 8. 11). s = 0 F = 0

=

(') ( I I . 8.13)

T(O,t) = Tc(t) = W(t), ( I I . 8. 14)

( I I . 8. 15)

(h) tj At V,

CV

= ^1 (. 8. 16)

, -

,

.

(II. 6. 21)

ycvQ _ ycpQ Q 1 ( 8 1 7 )

_

)eiYi m 1- Ci Yi"" m cp Y

. (II. 8. 17) , -

. ,

.

. . [5, 6],. . [23], . . [3, 4] .

: -.

8. 65

1. H u b b e r t M. . Darcy's Law and the Field Equations of the Flowof underground Fluids. Petroleum Transactions AIME, 1956.

2. - . . - . , 1952.

3. . .

. . , 1959.4. . ., . .

. , 4. 1958.5. . . . .

- . . , , 1961.6. . .

. .

, 1962.7. . .

. . , . 105, 6, 1955.8. O r o v e a n u . Asupra miscarii unui fluid incompressibil printr-un

mediu poros neomogen, comunicarile Academiei Republicii populare R mine,I. VIII, No. 1, 1958.

9. . . . , 1948.10. . .

. , . III ,1958.

11. . . , . . . ., . IV, . 1, 1940.

12. . . . . . ., . XIII, . 5, 1949.

13. . . . -, 1957.

14. . . . - - , 1958.

15. . ., . . , . . , . II. , , 1948.

16. . . . -, 1937.

17. . 3. . , 1956.18. . .

. . . 2, 3, 1953.19. . . . , 1956.20. . X. . -

, 1953.21. a n d b k of Chemistry and Physics, 37 ed. Chemical Rubber

Publication, vol. I, II, 19551956.22. . . . , 1961.23. . . -

. -, . II, 1958.24. . .

. . . . , 2, 1961.25. . .

. , . I I I . -, 1963.

III

1. . .

,

, -

, -

-

.

. :

z w = 0, = = .

-

:

, v (III. 1.1) (III. 1.2), -

V-g + -0. ( I I I . 1 . 8 ) .

1. 67

. ,

, .

, -

. , -

, . -

,

. -

, -

, .

. -

, . .

, (12, , , V.

dx cos = = -^~

its \V\

cos a, = =

dy vCOS do = = -=r-

ds \V\dz_ds

(III. 1.4)

ds dx, dy dz; \V\ . :

dx dy=

^ ds | f | ' ds

dx

vdx dy = 0.

(III. 1.5)

(, ) = . (III. 1.6) , -

. -

-

(. III. 1). Y = W (, ) ,

,

.

. W (, ) .

. III. 1. .

68 . III.

= (, ). ? (, ) = const. , -

dXF = - S - d x + ^ T ^ = - (. 1.7)

(III. 1.5) (III. 1.7), , . ,

dW = ~dx + ^-dy = vdx udy = O. (III. 1. 8)

(III. 1.8) dx dy,

v (III. 1. 9) - (III. 1.1).

' '

-J = -J , -3 = -S . ( I I I . 1.10)dz ' '

(III. 1.10) .

, (, ) .

(III. 1.10), , - ,

*

' * '

,

I 1

(III. 1.10) - .

. -

z = -\- iy, i2 = 1 .

1

z + iy z.

1. 69

,

z = + iy, (, ) -j-+ i V (, ).

:

F (z) = F ( + iy)? (, ) + iN (, ),

(, ), N (, ) , z = x -\-iy. , , .

F(z) = z2 = (x + iyl)* -,

F (z) = z2 = 2 2 + i2xy. ,

(, ) = >- \ N (, ) = 2, (, ) + iN (x, ) =

2

2 + , -

, 2

2 +

z = x + iy. - ,

,

(, ) = 2 -f- 2. Mi (, ) + iN (x, ) = 2 -\-

+ 2 + 2zr/, , - z x-\-iy.

, (III. 1.10) ,

(, ) -f- i Y (, ) ( ; W ) - z = -f- iy.

, -

, , ,

z = x -f- iy. , -\- i W ,

,

(III. 1. 10). : + i W z = x -f- iy,

0. , (III. 1. 12) .

( ,

70 . III.

z = + iy), :dz .

1. 71

,

.

F (z) = (, ) +-\- i W (, ), z = + iy, ,

: , .

, ,

, , -

. .

,

, . .

(. III . 1). :

{, ) = const, W (, ) = const. |(. 1.16)

* + * * _ . * + *-. (.1.17) \--\ = kt -

\" :/= const ( I I I . 1.17):

(

72 . III.

2. . . ,

, -

, ,

. ,

(I. 2. 18):

-. (III. 2.1)

= const, = const == const.

, q -

- (-) - (-).

,

. . -

,

.

.

.

0 (. III . 2). ; , , 0 :

W = AQ + B, (III. 2. 2) .

:

-f- i =-^\nr + iAQ + iB + C. ,

--:

. I I I . 2. .

+ i = J-(1

4- i6) + const,J- (III. 2.3)

2. 73

const = iB -\- .

lnr + 9 = ln(re1 9) . z

z = -f- iy, , = cos 9, = sin 9,

z = r (cos 9 + isinS). -

cos 9 + i sin 9 = e i . ,

In ( 4 ' ) = In [r (cos 9 + i sin 9)] = Inz. (III. 2.4) , , -

,

:

F(z) = ^-\nz + C. (III. 2.5)

,

. -

, : , .

, , ,

, -

- , zo = ++ iyo.

,

, (III. 2.5) z - (z z0).

F (z) = .in (z-zo) + . (III. 2.6)

.

(. III. 3). = , = 0 --, = , = 0 -. , -

. ( )

^ ^ = -5 (. 2. 7)

74 . III. -

\ , , ;

, - \ .

( )

2 = - ^ - 1 2 , 2 = ~ ^ - 8 2 , (III. 2. 8) 2 ; 2 , 2 .

. III. 3. .

,

F(z)=^-ln^^ + C. (III. 2. 9), ,

-

. (III. 2. 9) - (III. 2.8), - :

=

+ 2 = - in - + const, (III. 2.10)W = 4'1 +

1 F 2 = ^ - ( 6 1 - 0 2 ) . (III. 2. )

2. 75

*1 = const ,

1 2 = const. (III. 2. 12), , 6i 62 , [, ], . ,

, , ,

,

92 = const. ,

. ,

6

02 - .

, ,

.

, ,

, -

, (. III . 3). -

.

, (III. 2.10) = const -, = const.

= const , -

:

.

:

{ - a f + 2 = ( + af + 2,(1 ) 2 + (1 ) 2 (1 + ) + (1 ) 2 = 0,

2 + 2 2 | ^ + 2 = 0. (III. 2.14)

(III. 2.14)

( { ^ ) ' [ ( e ) " ] ^ - (-25) -

2aj/c/(l ) (1 + )/(1 ), / = 0. , , -

- .

76 . III.

= RK ,

.

(III. 2. 9) RK. q ,

. RK -

.

RK , - '

(III. 2. ) . III. 3 :r1 = Rli-6; r2 = 2a-(RK )

.

,

.

\ =

. 2 -

-,

. 2

2

< 2 < 2 + .

2, 2.

:

= - ^ - 1 + . (III. 2.17) (III. 2.17) (III. 2.16),

^ ^ ^ _ . (.2.18) , ,

, 6. ,

' " , ,

:

2-(-6)

2. 77

2.

/ / 7? | \ I Si . / / 7? ^ |

2 RK + = 2 + ,2 2

2 = - ^ . (III. 2.19) 2

(III. 2.18). , (III. 2.18):

2 2

(III. 2.18) :

_ -. / \ 1

(III. 2.20)

|

78 . III.

F Fi . , F, Fx ().

,

z = z (), F (z) z - . , z == z (Z) z - .

-

,

,

, ,

.

-

-

, , -

.

.

. . . .

[1]. - -

. . . [2]. ,

.

[. . 2, 3, 4, 5], 3, 4. 3.

, z == -f- iy F (z). = | + i , - z z = z () = (z).

z = z (,) ,

*() = *(5 + )=*( , | ) + (.),

x = x(l,i\), y = y(l,r\),1 = 1(,), = (*.*/)

(III. 3. 1) z. , z = z (), Z, - z.

S 3. 79

. ,

, . . ,

-

. , ,

\ .

rfz,'Hz,

. I I I . 4 .

dzldt, ,

^ .

,

lim r- = lim Ax + i

|. , () z dz dt, . di,dt,2, ... z dzi, dz2, ..., z, - (. III. 4).

^- -

,

dz1 (III. 3. 2)

80 . III. ,

(III. 3. 2)

-

. arg dzx

dzx .

,

arg dzx arg dz2 = arg dx arg dt,2,

. . dzi, dzz di, dt,2 . z() (z) ,

-

.

z

.

QC,

,

(III. 3. 2)dz (III. 3.3)

, -

.

z - I, . dn dl - I z dv dX , .

| Q \ z

dn\dl\, (HI. 3.4)

wn= -j -

.

, -

, (III. 3. 2)

\dn\ =

I d / I =(.3.5)

3. 81

(III. 3.4), dz

=- ,

( -

3-

6

(III. 3. 6) (III. 3. 4) -

, - -

z. -

, -

-

F(z)=*Az. (III. 3.7) -

. -

,

F (z) = + i = { + iy),

const (L)

= , (III. 3. 8)

. I I I . 5. - -

--

-

.

,

= = const , (. III. 5), W = == const , .

, v

(III. 3. 9)

, F (z) = Az -

= .

z = In t, (III. 3.10)

82 . III.

= | +-ir\ = Q e . Q, 0 .

z = + iy = In (Q e i e) = In Q + i 0, (III.3.11), ,

3

= 1 , = 0. (III. 3.12)

= const - z In Q = const, Q = const,. .

, = const - 0 = const (. III. 5).

,

= = const, ~ = Ay = const z Q = const 0 = const, . . > 0 -

q = 2 .

-

-

.

-

-

: 1,- I /

. III . 6. 2(III. 3.13)

.

z = 0, =

,

=

,

-

=

(. I II . 6). z

.

= (z) z == z (), - ZB Q = QK , zc = ia z,

,

= 0 , .

3. 83

, ,

-

-

.

:

f l - ( in. .14), z = ia, (III. 3. 14) -

t, = 0, . . z - = 0 .

z - Q = QK %. , (III. 3. 14) z = ,

arctg _

xia l/za + a ' e x - i 2arctg

1 * - = g l ' e ' < - 3 - 1 5 > \ = .

, z = x QK , z = ia = 0. , (III. 3. 14) - .

(III. 3. 3) Qc =

( I I I . 3 . 1 4 ) (z-\-ia)(zia) I 2ia

z

= 4-^ '.' +, (III.3.17) ,

'= +-^j-InQK. (III.3.18)

2(-

)4 1 8

84 . III.

Qc (III.3.16),

2(

-)in^L In

=2(

)2 (III. 3.19)

, (III. 3.19) , .

(III. 3.14). z la* "

z-\-ia '

, z -

= 0, = , , = 0, , b =f= (. III. 6).

, z = iy, > z , - QK, Q K < i < QK, = 0. -, (III. 3. 14) z = iy,

iy~iaiy + ia

(III. 3.20)

\ - , 0 S QK ^ 5 ^ QK, = 0.

z ( = 0, = ) :

^ = 5

= Q K - ^ f ' (. 3.21). . Z, .

(III. 3. 3) QC:

Qc = dz * = 0

= QK

2ia

* = 0

(ib + ia2 Q K (III. 3.22)

t, Qc 6 (III. 3.21) b ,

QC, -

- = + ),

(III. 3.23)

3. 8S

2 Q K _

1 -QK

2 QK 1 \2

QK

. III . 7.

z , , , , , -

(III. 3. 19), - :

_ 2(

-

)In 2

(III. 3.25)

(III . 3.23) ( III . 3.24), - (III. 3.25) - Qc, - Q1{ 6 (. I I I . 6):

_ 2(

)In \

L 2 QK

- ,2:

( -

^-(1..2) 6 / Q K 2a QC

-1 inlJMJ L ec

(III. 3. 26) (III. 2. 21), .

, (III. 3. 26),

(. III . 7). z RK

Ri

86 . III.

/re-;

, -

.

-

= 2 /.

= zm. (III. 3.27)

z =

= Q ,

(III. 3.28)

, (III. 3.27) = z = 2 , . . -

z .

(III. 3.28) = Rx -

Q =i?. QC (III. 3.3)

dz (III. 3.29)

QK (III. 3. 27) = . (III. 3.30)

, Z, , QK R - 6 = R .

(III. 3.26) QC, QK,

2(

-), | (

1 \i J ^ i I ~ R2m

> 5 ~\ -" /

(III . 3.31) :

\ 2

2(-) ^ (. 3.32)

3. 87

(. III. 8) 12

= ' (III. 3.33) z = 4- iy.

( + )

.

=-QKe

8 = (III. 3.34).

. III . 8.

(III. 3. 34) , = z Q = QK .

= 2 , = L, = 0, 1, 2, ... (III. 3. 34) Z,

L

Q = QKe~ , 9 = 2 , == 0, 1 , 2 , . . . (III . 3. 35) (III . 3.3)

Qc =J t L

rc.

( I I I . 3.36) (III. 3.26), -

_

:LL. (III. 3.35) 6" = QKe a :

2(-)2 L

L

sh

US . III.

, ,

5. 89

.

-

,

,

,

, , ,

= 2

* < ^ > = , ^ t K w * ! L , (. 4.4>In

] n / aK~bK (-)

V

2 2 ,2 2 .2 =

=

.

_ 4 (

) _ 2 (

) / J J J ^

+

^ ' ' 'In v " K y K ' , : , .. In

q= 2 ( - )

t ; = + ^ ; =

+ . ( . 4.6)

, >

RK Rc, (III. 4. 6) -.

, -

,

, . . [6].

5. -

. . -

[. II. 2]. ,

- , , -

.

, -

, , -

. , , -

. .

z ABCDA, - (. III . 10, ), (z) Q = 1 . Q

90. III.

:, ABCDA ,

1

1 z1 + z

( I I I . 5.1)

L | L >

. III. 10.

= 1, = \.

= - (III. 5. 2)

Y -.

z (. III. 1, ) - .

Q < 1 - . -

, -

,

.

= t h . (III. 5.3)

,

(III. 5. 1) (III. 5. 3) . -

dz

dz r

, (III. 5. 1), dz 1 1 z2

(III. 5. 4)

(III. 5. 5)

dz

(III. 5. 1) ,

(III. 5. 6)

(III. 5. 7)

8 5. 91

Vli-(\+yl)f+4yl

[1 (*2 + 2)]2 + 4!/2- . t fl.

2

92 . III.

(III. 5. 3) ,

sh x sin l =

c h z + c o s j , ' T 1 = c h z + cosy (III. 5. 16) z

. (III. 5. 16) , (III. 5.3)

r __e

z - 1

~

2 + 1 '

2 = - ^ | - . (III. 5.17)

(III. 5.17)

2= *

, (III. 5.18)

/ ( 1 Q2)8 + 4 Q 2 sin2 61 2QC

^ ? (.5.19)

f (III.5.20) .

6. .

.

- .

QK == ), TV . .

(, -,

= const), (. . III . 6). - , , .

zc = ib -

( )

'w=itln-ii-- (-6)

6. 93

, (III. 3. 14), - z , z = ia t, 0, z = ib = 6, 6 (III. 3. 23). - .

(III. 3. 14) z ,'

.

( I I I . 6. 2)

, z ( I I I . 6. 2) 6 ( I I I . 3. 23) ( I I I . 6. 1):

& _

ie-

-

9 in

2 l

~ 6) (III . 6.3)

(III. 6.3) : / >'

(III. 6. 4)

const = -~ In

In ( S) - -, -

= 6 .

2

-

-,

t=P- ( , . I I I . 11). - : -, -

= 6 , -,

Z, = -- ( - ), [ | = QK -.

94 . III.

( I I I . 6. 4) , = Qe* = Q (COS -)-i sin 8), -:

- ^ - R e J L l ng zn Q

- Q (cos 8 + i sin6)--2.g (QCOSB ) + 2 6

| _

"to [ ?IQCOSB j^-l + Q 2 s i n a 6

6

=

Q = QK:

e

a

K + 62- 2 Q l l 6 c o s 6

(III . 6. 5), * * , 1 (Q2 + 6 2 -2Q6cose)o 2 . +

^1

eK 2Q6 COS 8

(III. 6. 6) , .

6 . ' (. III . 12)., 9 ' 0 ' = 6 . (III. 6. 6)

4 62 .

.? . 95

(III. 6. 7) , . QK . ' q\, g2,...

-

(III. 6. 7):N

^ p 2 + 6 j 2 6 ; cos ( 0 . )

' - X gj In 2 3 * . ( I I I . 6. 8)

, 2 . 2 Q 6 J c o s ( 6 { )4JT

. III . 12. . I I I . 13.

,

9. (III. 6. 8) ,

(III. 6. 8) Q = QK

(

= const) , 6.

- ~ 2 Q 6 { C O S ( 0 at

Q = Qu ( ):2

. .

_ _ 1 2 J

(,6) , , , .

(Q, 0) -

(6).

96 . III.

[ 7 ]

( 6 ) = + 2 ( cos 6 +^ sin 8), ( I I I . 6 . 11) = 1

1 2 1 ?" = _ I (8) cos 8(Q,8) Q = Q K ( I I I . 6.11)

4>(QK'9) = 2 (

6. 97

n = l

N '

2

n = l

iV (') 2 ' , i = l i=JV

i = l = /.

,

Qi, ,

( I I I . 6 . 1 5 )

(.) =

+ ^ , (Pncosra6 + P^sinn8)l-^-

n = i

V2 ' '* 206,003(8 ,)

=. (III. 6.18)

V8 . III.

( I I I . 6.16) ( I I I . 6.17)

n = l

~

6

2 kh Qc j ( I I I . 6. 19)

, , 2 4 V, Qei , -.

.

- ,

. kh/yi -

(III. 6. 18) (III. 6.19) .

-,

Q K(. III. 14). ,

.

-

, ,

QK, , , -

(9) G. (III. 6. 12) -

[7] -

'

. ,

(Q, 6) Qi, (III. 6. 18)

.

,

III . 14. .

khl\i. - Q, 6

, Q,(III . 6. 18) khl\i.

, , , -

Q, 6 khl\i. , khl\i Q = 0, .

6. 99

( I I I . 6.18)

_

2 (

- )

( i n . 6 . 2 0 )

(III. 6. 20) khl\x,

> (3. 6. 19) Q

cj.

, , -

, -

.

1. . . , . . . , 1958.

2. . . - . .- ,

. II, 1956.3. . ., . .

. , 1953.4. - . .

. - , ., 1947.5. . .

. , 1939.6. . .

, . . . . -,

1955.7. . . , . 1, 2, 3. ,

1948.

IV

1. .

III - -

.

--

. -

, , .

-

, ,

.

.

.

1. , ,

.

,

.

, ,

, -

, .

2. : , .

, .

, -

, . . ,

.

1. 101

- ,

.

.

, . . , -

: , ; , -

.

-

.

, -

,

.

,

.

, -

, . .

,

, . ,

.

-

,

.

, , ,

.

-

.

-

.

, -

, -

.

, -

. h - . -

.

,

. IV. 1, . , -

, , -

, , -

= .

102. IV.

, -

(. IV. 1, ).

.

.

, .

/. -,

-

,

-

-

.

(I. 2.18)

= - ^ 1 + const (IV. 1.1)

, -

, q = Qlh , -

.

-

.

, -

-

, -

.

-

. IV. 1. . -

. -

,

.

-

. ,

.

(. IV. 2), qi, qz, ...

, , -

2. 103

, , -

(IV. 1.1):

(IV. 1.2)

, "2, ", ... , . . ; &, , , ... (const), (IV. 1.1), - . f

M

-

. , -

.

,

1 = 1(IV. 1.3)

; * t-ro , -.

. IV. 2.

. 4) Qi t- h.

. -

.

(\ = 0) -.

2. .

(IV. 1. 3) - .

, .

, ,

.

104 . IV.

III -

.

.

,

. .

= 0

(. IV. 3).

.

. IV. 3. . IV. 4. -

.

,

(. IV. 4, ). (. IV. 4, ) ,

,

.

.

,

,

! / > 0 = 0 .

2. 105

, -

(IV. 1. 1), (IV. 1. 1) -

.

=

(IV. 1. 1) =

-

.

= 0 (IV. 1. 1) -,

(. IV. 3). , (IV. 1. 1) - ,

, -

. ,

.

, ,

: - -, . .

.

.

, -

, (IV. 1. 3), = 2, qi = q, q% = q,

n - -; - -

-.

,

(IV. 2. 1) , = .

, - -

, - .

(IV. 2. 1) = 0,

= 21 = = . (IV. 2. 2) ,

q , . .

.

= + - ^

1 , (IV. 2.4)

106 . IV.

,

, ^ 2. , 2 - -

- =

. -

=

(2

) < < (2 -)--f- r

c).

2 ^ 2 , (IV. 2. 4).

< 7 = 2 ( - ) . (IV. 2. 5)In

-

,

.

-

, -

, 2.

RK , RK - . , -

,

, , .

3. .

. -

,

.

,

. IV. 5, , , .

. - ,

, RK .

, -

.

. ,

, ,

.

.

,

.

3. 107

, -

.

, .

.

.

8 , , , . -

.

, , -

, [1 ]. (IV. 1. 3)

= - 5 2 + . (IV. 3 . 1 )

, i - 9i-

.

. (IV. 3.1)

i = " ^ ( ? 1 1 1 +? 1 2, 1 +9 I n r 3 , 1 + - + * 1 , i) + c . (IV. 3. 2)

4 ; rc i ; 2 1, 4 , . . ., rn i - * , , . . ., - .

.

.

, r 2 4, r 3 v...,rn i , , .

,

300500 , 0,1 , . :

108 . IV.

, -

.

,

, , -

.

(IV. 3. 5) ( + 1) . ,

(IV. 3. 2) (IV. 3. 5), .

, .

(IV. 3. 2) (IV. 3. 4) - (IV. 3. 5). .

(IV. 3. 2) (IV. 3. 5): R

,

^ + ft^ + ? 3 + + ffn1,2 2 , 2 , 2

_

= . l n ^ J L + ftin_?2L + ftln-^ + . . . + ? n l n - ^ - ) . ( I V . 3 . 8 )

\ ri,n 2, 3, )

: , , ,, , .

- ,

- . , -

(IV. 3. 1), - , .

. -

, -

(IV. 3. 5) . ,

, .

, -

,

-

, .

.

.

,

,

, . . . ,

(. IV. 5, ). ,

1 27-! '

2, 3, . . ., u>n , . . -,

:i. 109

, -

, ,

(. IV. 5, ), - :\ + ~w* -\- 3-*-...+

110 . IV. ,

4.

.

-

, -

, .

. -

, -

.

/ -.

-

-

,

-

.

-

. -

(. IV. 7).. IV. 7. , -

,

, , , -

.

.

, -

.

-

.

,

. .

N ( N 2, 3, 4), .

(IV. 3. 1) -

= 4 2

5. IIP

qu i = 1, 2, . . .,

2JJ (

. q -. .

112. IV.

(III. 3. 38) :

9 = L . \ . |

2 2

*ft_l. I

2

2

(IV. 5.3)

= ' . (IV. 5. 4)

(IV. 5. 1) (IV. 5. 3) :

5. 113

, , R -

, , ,

.

,

q , .

h - .

(IV. 5. 3)

1 -In

2 mh 2 mh rc

, 1 . "r In

1 m h

(IV. 5.8)2a mh 2 mh r

c

?

|(

- _

" " - - " -

. /

/ = 2 mh . (IV. 5. 8)

Q , , ;

Q' = -- ^ - 1 (IV. 5. )4 2 mh r

c

v '

,

. ,

(III. 3. 31) (III. 3. 37) (III. 3. 32) (III. 3. 38), , L .

-

- (. IV. 11, ) -- (. IV. 11, ).

txZ jib(iv. a. w)Q~ kf ~ * * '

/ ; L -; ; hCp L.

= - 4 In^r-. (IV. 5. 13)

/ (IV. 5. 11), h . , , -, .

114. IV.

v

2 , . . . 4 2

(. IV. 11).

1 >

2 - , - ,

. , ,

,

/ 2 3

, 1 I1 1

1

1

{t

1

t|

\

1

;

. IV. 11.

. . , -

. IV. 12 . . IV. 12, a Qi, Q2, Q3> 64 , : - (. IV. 11, )

3 h3 4 " 4 (IV. 5. 14)

fe1Cp. 2, /i3Cp. 4. J

^1' ^

2 l -^ ' -^4

, . IV. 11, .

, : *

10=0

. IV. 12. -.

- -

(. IV, )

Qi = ah1

- ^ . = - 4->.

= L_1 kahiCV

:/3

(IV. 5. 15)

5. 115

-

(IV. 5. 11):

2itmj/1

' 2 I

2 '

In- 0" (IV. 5. 16)

mi, m2, 3, 1, r c 2 , r c 3 , 2ai, 2"2, 2 3 , , , -

; 1, 2, h3 .

- -

. IV. 13. .

, ,

.

, .

. IV. 14. .

, . . IV. 12, - , .

pK 2i . IV. 12, , - S Q 0.

,

.

,

116 . IV.

[. II. 9, 2] , , -

-

(. IV. 13, ) -, (.. IV. 13, ).

-

,

,

I (. IV. 14). (IV. 5. 10) ( I I I . 4. 5) (III . 4. 6)

= 1

-

- ^ '

(lv-

5-

17)

4a Q' (IV. 5. 11).

. . ,

[3], , - 23%.

1. . ., . . . , , 1939.

2. . ., . ., . ., . ., . .

. , 1948.3. . .

. , 2, 1961.

V

1. .

,

.

, .

-

.

, , .

-

-

,

.

-

.

, .

,

, ,

.

,

, -

.

, . . , ,

.

, (.V. 1).

118. V.

RK - , -

.

.

. .

-

.

:

1. 119

, , -

.

, q (,) dt,, :

(V. 1.2)4

-

(V. 1. 2).

. V. 2.

, -

: , =

-

=

,

-

=

.

.

qdl, (. V. 2). -

, q dt, , . .

, .

, -

, .

120 . V.

.

qdt, - . ,

qdt, . ,

-

.

=

=

=

.

-

. -

-

-

q ().

-

q (Z),

V

Q =0.2 0,6

. V. 3.0,8

q () - ,

. V- 2, .

[. 1.11]:

(V.1.3)

g

- ln - - (V.1.4)(V.1.5)

.

q>(h) . V. 3.

1. 121

.,

-:

() = J" 4-1 e~xdx.

( = 1, 2, . . .), :

1

-

( -\- 1) = (), . - -

[1]. ,

. -

, . V. 3. q () = const

-

(. V. 2): < 2h

Q [ ]

\ \ (1 )(-

W

(2,1 - w + x) + I (2,1 +w-x)- (2,1 + w + x)] ++ (Q4) + const, (V. 1.7>

(V.I. 8>

t, (s, ) - , [2];

.> 2h

= ._ __^ _ T_L V -

(2 Q) COS (2 nw) sin (2 ;) +*- 1

+ const; (V. 1.9) In 1

-

.

122 . V.

. . [3, 4] [5, 6], -

, , -

.

(. V. 2) q () = q == const . . :

z < ,

i = l

z > b,

z h h ~ b T (r \

|? sh (ijX p / (fi.j)

ft z b . r

R RK Vi?K ^ ( V . I . 11)2 , ftOr2/4

x4 sh -- J (Hj)

y? = k/kz, kz. , JQ (-^- \. , Jx (\Xi) -

; (., /() = 0- ,

, -

. . [7; . I. 16]. ,

, [8, 9]. .

. -

, . -

, -

.

; - .

, . . , -

,

1. 123

, -

.

. . [10], - -

. . . ,

, -

.

-

. .

.

. -

.

, , . . / 0., :

,

.

.

. . , -

.

, ,

.

, -

,

3. . . , -

.

, -

, -

, ,

, .

. (V. 1. 3) ,

h1. , , RK >

xUh, - .

. . [11] - (. V. 4):

, 1,6 bIn

1 .

124 . V.

. V. 4. - -

.

-

, -

(V. 1.2),

.

(V. 1. 12) -

,

q () = const, .

(V. 1. 12) >

.

,

( , ) -

-

,

( ) [12, 13, 14].

2. .

-

-

.

. .

115, 16]. . .

,

[. II. 9], .

-

. , .

V. 5.

.

-

Ro, : > h. ; . R . . -

-

Ro, .

2. 125

, -

(. V. 6).

. V. 5. - .

vrv

. ,

.

.

-

-

-

Ro, -

-

-

. -

-

-

-

. -

-

- . V. 6. .

(IV. 3. 6) (IV. 3. 8),

2(-0)< ? = (V.2.1)

126 . V.

, , -

.

,

:

0 (V. 1.4) , RK = R0^h. (V. 2.1) (V. 2. 2.),

_

2(

) ...

.

, -

Ro -,

, | 0 . (V. 2. 3) - 0 :

lo = \n^- + l

o-ln^- = ln^ + C, (V.2.4)

' ' '

C = go- l n - ^ - (V.2.5>

, -

.

(V. 1.4),

2 ( ) i n .

, , In Ro

:

-&'

, . .

, [. IV. 2; . I. 8. I. 16).

, . . -

, ROr

2. 127

, , Ro > h

Ro>i-h. (V. 2. 4), -

(V. 2. 3)

) 2 ft (

) (V. 2. 7)

(V. 2. 3) (V. 2. 7)

.

-

,

, -

(V. 2. 6) - .

(V. 2. 6) . V. 7 - = (h).

"(h)

16

12

4

\\

1

\>

\

0.2

\

\

0,6,

.

0.8-

h

. V. 7.

Q . . '^ - -

= 100. .

, ,

(-L l) In '01 h .\ ft j rc

. .

[7, . I. 16; . I. 8] , , , , -

. 4, 5. (V. 2 . 7 ) . :

~

= . (V.2.8)

~ =

. ,

128 . V.

.

In \- = In .

, 6

, -

'

.

-

, , .

. . -

, .

,

.

i?o . , ,

Q= 2",-) . ( V . 2 < 9 )

ln^JL +e

Ro , -

, , Ro ^> ir-h, .

QCOB= 2 "*( - > . (V.2.10)

-

= - # - - , (V.2. )VCOB

. V. 8.

Q (? .

,

Ro/rc

,

Ro/rc .

S. 129

, ), .

(V. 2. 8), (V. 2. 9) (V. 2. 10)

) =

,

(V.2. 12)

(V.2.13) -

) , - R

o

, -

.

-

,

-

, , -

'

,

,

,

.

( ,

[17]), .

. . [18] . . [19].

3. ,

-

,

-

.

- , ; - w :

0,2

. V. 8. -.

=

13Q . V.

kr ; kz -

z . ,

d u . d v . d w

-bj + -dj + ~ = 0

+ 0-)+^S = O. (V.3.2) , -

. (V. 3. 2)

xz = z' (V. 3.3)

' ^ dz't ~ U - (V. 6. )* '

.

-

h, , .

= 0, z = h, ( rc< r < i ? 0 ) , - - ^ = 0; (V.3.5)

=

; (V.3.6) =

-:

(V.3.7) g (z)

, q (z) [.. 7].

(V. 3. 4) - . -

, = 1, z = z'. -

:

0.

3. 131

(V.3.8) O = i?(r)Z(z), (V.3.9)

R (), Z (z) , - .

(V. 3.9) (V. 3.8),

Z (R' + - ') + RZ" =

^ ^ ( ) 2 . (V.3.10)

(V. 3. 10) z, r, (V. 3.10) , -

X2, .

(V. 3. 10) :Z"X*Z = 0, (V-3.ll)

R"+1R' + X2R =0. (V.3.12)

(V. 3.10) X2 , - (V. 3. ) (V. 3.12) :

Z = e~Xz, e*z; R = J0(Kr), Y0(Xr), (V.3.13) J

o, Y

o

.

(V. 3.10) X2 , - (V. 3.11) (V.3.12)

Z = sinXz,coslz; R = I0(Xr), K0{Xr). (V.3.14) /0, Ko [20].

X = 0Z = C!Z + c2, R = 3 In + 4. (V. 3 5)

z = 0 -^- = 0, (V. 3.13), , -. (V. 3.14) - cos X z.

132 . V.

(-^- = 0 z = h) , ,sin h= 0,

= 0 + In +

+ 2j [ \~~h~=1

^ 1

C 0 S ~

= 0 + Cj In +

)]

h' = nh; (V. 3.18)

,

,

, -

=

, Ro.

q(z) 0 < z < f t :

q(z) = qo+ V 9 n C o s - ^ - , (V. 3. 19)

() ^ j ^ - d z . (V.3.20)

,

, :

Rn , Xh \ . \ / _ ( 3 211

n = l

- / . ( ^ (^1), (V.3.22)

(V.3.23)

3. 133

, . .

,

. ,

.

(V. 3. 16) .

. . [10], 10 -, .

-

.

,

, -

,

.

q(z) :q(z) = -|- = const, 0 < z < ; q (z) = 0, < z < h. (V. 3. 24)

Q , . . (V. 3-20) -

(V. 3, 21) :

(V. 3. 26)

n = i

0 < z < 6 1 , , = 6, =:

in ILJlh.. (V. 3. 27)

n = l

134 . V.

:

n = l

,X Sin Sin -^-

(V.3.28)

(V. 3.29)

U

n = l

\ Y.h

sin re sin

n = l

(V.3. 28)

,

, ,

.

= 1, =

(V. 3.30)

\1 ( V ; (V.3.32)

.

1.

, -*0. (V. 3. 30)

"

(.3.33)

$ 3. 135

2. = bv

)~) sin2 n

451 ""' J?- (V.3.34)

q>x = -j-^ - .

,

( = 0) (b = bi) - ,

bi . ,

bi Q, -

bi

-

. -

. .

[21], -

q (z), . . - . V. 9. [45]. - ,

, [22, 23], . . -

(. V. 9). -

, -

, ,

5 VI:Q = 5 - c s 1 - . (V. . 35)

; s - (. V. 9); | (V. 1. 4).

. .

. . . -

. 1. . . h = 12 , Ro = 30 .

. 1 -

.

136 . V.

1

,

0,764

0,56

0,33

,

9,67,24,89,67,29,69,67,24,89,67,29,69,67,24,89,67,29,6

h

0,80,60,40,80,60,80,80,60.40,80,60,80.80,60,40,80,60,8

S,

2,42.42,44,84,87,22,42,42,44,84,87,22,42,42,44,84,87,2

Qlc

-

39,335,631,072,658,792.438,432,724,565,452,885,033,229,121,558,747,573,0

2

-

(V. 3. 35)

44,137,727,275,860,194,540,133,623,768,753,686,034,828,419,659,645,474,5

% --

12,25,9

12,254,32,382,34,32,3

-3,35,01,51,187,84

2,36,53

1,534.322,061,82%

, kz = 0, = \ (V. 3. 31), , -

.

' nnRK\ . *

\ 1

. ) ~* 2 %h

. \ / , ,

\

~ith~

= 0,577. . . .

S 3. 137

(V. 3.22) (V. 3. 23) ->

\ , I , ,

\

.

2 xfc

(V. 3. 34) 00

_ 2x/i

,

V l n s i n ! ! "

= 1

(V. 3. 37) [24]

V s i n 2

2

sin2 12 2

I cos2rc(p 122

1"

2"

cos 2

, (V. 3. 37) (V. 3. 31), (V. 3. 29), = 2In . | ( - i) = / _

^L , 2 \ j \

'

=

+ f i2(

In ^ 2 -

(V. 3. 39)

.

-

- -

, h h' = % h. (V. 3. 34), -

(V. 3. 22) (V. 3. 23) Ro > 0,5 h, - R

o .

(V. 3. 34) . . [25], , - . 2 h = 10 ,

= 0,1 , xh/rP == 100.

-> (V. 3. 39) = ( 4 l) In -^ 2- . (V. 3. 40)

, . 2, - , -

138. V. ,

2

0 ,

10510,50,2

100501052

0,125

19,3619,1114,0710,4034,500

h =

0,25

9,3619,1656,4824,6032,642

b/h

0,5

3,3183,2282,1701,5500.6682

0,75

1,0401,0190,72030,51160,2936

. = 588,11 ~ 590 > 10 ,h = 0,0032.

, . /0 100, (V. 3. 34), . 2, - .

-

h 0, = 100.

, ,

li, - 0 -,

(V. 3. 39), 1

. -

,

. 2, /, | (% rjj) |, (V. 3. 40)

fi-lW . (V.3. 41)h j r

c

:

r0 x

= i - 1 Inu ) 0,01 (V.3.42) , =f= 100

'

. 2 (V.3.42).

. 2 ,nb -

= j h .

4. 139

(V. 3. 34) :

2r (h) = ''"" ^ ' v 5 * . . _ 1 _ s i n 2 [ ( ) ] ( (^ J I xAn=i \

(V.3.43)

(h), (I h) b b' = h b. (1 h) h -

. 2, (1) = 0. -

. -

, , -

, , -

.

[26, 27, 28, 29 .]. , - ,

[8, 9]. , - -

, . , -

. , -

, , -

. -

,

.

-

[30, 31], -, [32].

, , ,

-

10%.

4. -

.

140 . V.

,

.

-

, . .

(. V. 10).

(V. 1.4) , - .

.

,

. V. 11. , - q

-

. V. 10. - . V. 11. . .

,

; , -

.

. -

.

, -

: /0 = 2 - 3. -

,

(. V. 12). '

.

.

. -

(V. 1. 4).

4. 141

,

.

,

-

-, . .

.

, 5, 6, , -

.

-

\ \2rc

: // // / /Jj s/s////// ///////. /////// //////////////J J

UL :_-^' !

//////////////////////////////////////////''//7

, -

.

-

,

-

,

,

.

-

[. I. 8, 16; . IV. 2, 33]. ,

b h. b^=h (V. 4. 1)

,

, hlb. , , h,

. V. 12.

/it =

~~'

(V. 4. 2)

-\- . . - -

.

(V. 1. 4) , " ,

. . [34]:C'~=f, (V.4.3,

D ; 1 ; h = blh; -.

142 . V.

. . =s 0,4 .

-

, 23 - ^ 0,15. -

.

[34, 35, 36, 37].

5. ,

-

.

- z' =

= z = -1- z, . . kz , ,

. , .

'

Q = , Q -- ; Q' . -,

Q=,2n }*=**. Cr^dz> = ^ . (V.5.1)

J J v 'J J0

(V. 3. 3).

In il-(V.5.2)

, -

;

,

-

= Ro . (V. 5. 2)

, .

. z' == xz . - -

, -

, , -

.

5. 143

-

. -

.

,

[12, 38]. , ai, ,

as,

(V.5.4)

(V. 5. 4) - . -

,

,

, = 0. ,

,

Q :

Q

4 J

--

(+!)(V. 5. 5)

. V. 13. -. -

a=Yaia2 - - ,

= 14 = _L, (v.5.6)t ia (V.5.5) (V. 5.6) -

:

f- =

(

) , = ^ ,Qo 2

(V.5.7)

(V. 5. 7) . () (V. 5. 7) . V. 13,

1

144 . V.

, (V. 5. 4)

0 = 4 ( 0 - ) ] / ^ (V. 5. 9)

-

h, , d, - .

RR > h . -, RK ^> ^>Ro -, R *= h.

Q' - ' = h. r

c 1.

(V. 5. 10) =

^ ^

N 2dYx 2 h' NdVv. (V. 5. 10) (V. 5. 11)

=R

o

= -%-f In ^ + % 1

(-1) - In^s- l . (V. 5. 12)2 h I r

c Nd r

c \

lni?0/rc

(V. 5.12)

{) (V.5.13), ,

. . -

, ( 2,53 ) . -

6. 14.4

, , , -

(V. 5. 13) 3 h ( 1 (V.5.14)

6.

.

, -

, , -

.

. V. 14.

.

. V. 15. -

,

.

,

, , . .

Q , (. V. 14):= C0Ap, (V. 6.1)

.

-

2nkh

'"

(V.6.2)

,

(. V. 15).

146 . V. ,

-

2 = % \. ,

~-

2 G.

2

(?, - ,

.

, (?

= (&2), ,

:

6. 147

2 =

148 . V.

.

.

(. . V. 6). -

300500 .

. V. 10 , - ,

.

, , -

. .

( 2, . V), > /, , , -

(. . V. 12). , :

R ( - ) , ,

-

.

.

MN, - - .

.

,

.

s . (V. 6. 5)

dp = -^ - w ds + Q w2 ds.

.

,

i i

\

(V. 6. 9)

I . (V. 6. 9),

.

' -

.

.

6. 149"

, . .

i

(V.6.10)

,

,

,

.

,

,

.

^ ^ 8 =

1 7 ' (V-6-12)

-

(V. 6.5), =

-

:i

- = - ^ In - ^ + Q fw* ds. (V. 6. 13)2 J

, Q = Q (} (V. 6. 13).

, ,

, .

(V. 6. 9), .

, -

,

, -

(V. 6. 9) ., , ,

.

: 1) ; 2) ; 3) .

150 . V.

1.

-

-.

-

/

= 2 - i- , - -

, . . -

:

< < 0 , (V.6.14)

wc .

(V. 6. 13)

0,

0 .

,

1 1

,- 1 1 -

6. 151

2, , /2, /3,

(V. 6. 16) :

.

2.

.

D. -

- .

,

.

-

:

.

< <

+ nD, = 2-=-4.

, . . -

, 6 ^ 0 , 4 / ) [43]. (V. 6. 13) :

i rn + nD 2

1 ) I J -

.

j ^ - (V'6-20> / .

(V. 6.13), = AQ + BQ2.

152 . V.

(V. 6. 8)

= 1

-^' (V-6.21)

=

4 0 / ^ \2 D

\ V ,

, 0,15 < < 0,40. ess0,4 .

3.

-

w = -^ , (V.6.22)

, t dz^et, 0,25 < < 0,50.

, ,

1 1- 2 ;

120 , 1

nkh

1 rfa

6. 153

.

. . .

[. I. 20; 44]; (V. 6. 6) (V.6. 25)

-?, Q, (V. 6. 25) (. V. 16).

, - /Q ^~,

Q . .

.

-

-

(V. 6. 26)

. V. 16.

"

154 . V.

, ,

. IV. 12 , - / / + Q" ( 0 , Q" ((?) = BQ . , , , -

, -

, -

. -

.

1. . ., . . - . . , 1948.

2. w 11 . . A table of the generalized Riemann zeta function in a par-ticular case. Quarterly Journal of Mechanics and Applied Mathematics (Oxford),vol. 5, No. 1, 1952, pp. 116123.

3. . ., . . - . . . ,

. . . ., 5, 1961.4. . . ,- - -

. . . 1962 1963.

5. . . . , 1956.

6. . . , 1955.7. -

. , 1954.8. i n e R. L. Well Productivity increase from Drain Holes as measu-

red by Model Studies. Petroleum Transactions AIME, vol. 204, 1955.9. L a n d r u m R . L., C r a w f o r d P. B. Effect of Drain Holle Dril-

ling on Production Capasity. J. Petroleum Technology, Febr., 1955.10. . . ,

. . , . 11, 1951.11. . . .

, 1950.12. . . . . ,

1954.13. . . . , 1943.14. . .

. . , 1948.15. . . -

. . , . ., 10, 1946.16. . . . .

, . ., 16, 1952.17. . .

. , 1961.18. . . -

,

-

. . , . 62, 1959.19. . . .

. , 1957.20. . ., . . -

. , 1953.

6. 155

21. . . - . . .-. -

. , 1955.22. . . -

. . . , . XVII, 1953.23. . . -

. . , , 2,1953.

24. . ., . . ,, . , 1951.

25. . . . . -

, 1955.26. . .

. . , , 3, 1957.27. . . -

. . , , 7, 1958.28. . , . ., . ., -

. . -

. . , . .-. .

, 5, 1954.29. . ., . . -

. ,

, 1960.30. . .

. . , , 17, 1950.31. . .

. . . . , . 12,1953.

32. . ., . . . . ., 9, 1955.

33. . . . -, , 1956.

34. . . - . .

, , 6, 1950.35. . . .

. .

. , 1953.36. . .

. .

. . , 1954.37. . . -

. -

- .

. . , , 1953.38. . . , . 1. , 1951.39. . ., . . -

. . ., 23, 1945.40. . -

. . , 1961.41. . . , . .

. . ,

, , 1, 1962.42. . , . , . .

. . .

, . . . ., 3, 1961.

156 . V.

43. . . . . , , 2, 1955.

44. . . , . ., . ., - . ., . ., . ., . .,

. X . . ,1955.

45. . . - , . -

, , 8, 1957.

VI

1. .

, -

-

, .

, . . -

.

. -

, ,

.

,

, -

, .

, ,

.

, , , -

. -

-

-

. , ,

,

.

.

-

,

158 . VI.

, -

.

-

. ,

.

-

(-), . VI.1.

-

,

-

.

-

.

Hi ,

. VI. 1. -

.

.

,

, ( ABC). -

.

-

-

. -

-

-

.

-

.

. VI. 2.

-

.

,

.

''', RK , .

. VI. 2.

- .

, -

1. 159

,

,

.

-

-

, .

, -

-

,

-

.

-

,

-

, -

.

-

-

.

. VI. 3. ,

, . -

,

.

. . [. . 2] ,

.

.

-

.

.

h, - i, i = sin (. VI. 3). - :

1) -;

2) , . . = z -{- = (, ). , ,

, , .

[1], , 2

160 . VI.

-

, -

.

: -

,

. . . -

[2].,

-

,

.

, -

, -

. ,

, -

.

( ,) - , - , , ,

.

, ,

-

.

.

dh / \>= , ( V I . 1.1)

; ds - .

# = z + ^ - . (VI. 1.2)

, , , . . -

. ,

, h:

H = h, ( V I . 1 .3) ( V I . 1 . 1 ) .

2. 161

(VI. 1. 2) , , = ,

,

z. z .

=- ( V I . 1 . 4 ) , -

. -

, . . q - h

q = uh-l = ch-^. (VI. 1.5)

2.

,

t. (VI. 1. 5) .

,

qdx = chdh,

qx = ~ + const. (VT. 2.1) (const) (VI. 2.1)

.

-

(. . VI. 1):

i = 0 (VI. 2.1), ~

const = ,

qx = (

' ~

. (VI. 2.2)

(VI. 2.2) . .

162 . VI.

- , -

/, 2 . - (VI. 2. 2)

ql = - |- {\ \) (VI. 2.3)

9="^7"(.-"i ")- (VI.^.4)

(VI. 2. 2)

(\ ^ -. (VI. 2. 5) q

(VI. 2. 4), -

' ~

* . (VI. 2. 6) ,

,

. VI. 1 ( ). (VI. 2. 5) (VI. 2. 6), . .

", , ,

.

. (VI. 2. 6) % = ( = /) h = 0 , , q/h, . , &*=;> Hz,. . .

(VI. 2. 4), , ,

.

3.

-

(. . VI. 2). RK . -

.

, h.

, (VI. 1. 4) - :

dhw c

S 4. 1 163

.

,

-:

Q = \wr\2arh = c~2nrh. (VI. 3.1) ,

h h () ,, , .

Q, h(r) . (VI. 3. 1) :

Qy- = 2nchdh.,

Q In = ch2 + const. (VI. 3. 2) (const)

:

Q In i?K = -\- const,

Q\n^ = nc(Hl h\ (VI. 3.3) ,

( '').

(1 Hi)Q > . (VI. 3.4)In -

(VI. 2. 4) (VI. 3. 4) . ( 7, . VI), -

.

. . .

4.

, (VI. 2. 4) (VI. 3. 4) - [. I. 111.

(VI. 3. 3) (VI. 2. 5)

. -

.

1U . VI.

(VI. 2. 4) (VI. 3. 4) .

1951 . [3]. .

-

h, . z -

dz (. VI. 4). - -

dz

. VI. 4. - () -

().

(VI. 4.1)

-

-

. -

h:h

g=fudz. (VI. 4.2)

-

= z + ~ .

,

=

(VI. 4.3)

(VI.4.4,

.

; .

[. I I I . 7] :() (

J f{z, a)dz= J1 () 1 ()

# 4. 16

() 2 ()

^ 1 / (J(J /1 ( ) >1 ( )+ /( ) - ^ - . (VI. 4. 5)

(VI. 4.4) (VI. 4.5). , h = h(x) (VI. 4.4) ; -, (VI. 4. 5) = ,

166 . VI.

,

(VI. 4. 8) . , -

.

, q . (VI. 4. 9),

g dx = dP,

qx = + const. (VI. 4. 10)

const =

= P-L = 0.

Y

q = C ~ ) . (VI. 4. 11) 2 = I,

q = ( 7 ) . (VI. 4.12) ,

:

(VI. 4.13)# 2 - 1 =

- z 2 - - 2

1 2 (VI. 4. 12)= _ {\-\)

= ^_

( 2 _ 2 )

(VI. 2. 4), , , .

(VI. 3. 4), - ,

.

, - , -

:h

+ z]dz, (VI. 4.14)

4. 167

,

: rc

168 . VI.

hB , . . [. II. 2]:

df- = 1 > 3 5 i ( V I - 4> 1 7 > , = h (. VI. 4),

, -

(VI. 2. 2) (VI. 3. 3).

[. I. ; . .