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dC
'
VGCCCG
U
ɫɦ ɫɦ ɫɦ ɫɦ Ⱥ ɫɦ Ⱥ
dt
000
ɫɦ
' '
()
. (13)
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ ɫ ɛɟɡɪɚɡɦɟɪɧɵɦɢ ɩɟɪɟɦɟɧɧɵɦɢ:
ɛ
()
dC t
000ɛ 000ɛ
U
V ɋ G ɋ Ct C ɋ GG t
ɫɦ ɫɦ ɫɦ ɫɦ ɫɦ ɫɦ Ⱥ ɫɦ Ⱥ Ⱥ
ɫɦ
. (14)
dt
() ()
ɇɨɪɦɚɥɢɡɨɜɚɧɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ ɨɛɴɟɤɬɚ ɜɨ ɜɪɟɦɟɧɧɨɣ ɨɛɥɚɫɬɢ ɛɟɡ
ɭɱɟɬɚ ɬɪɚɧɫɩɨɪɬɧɨɝɨ ɡɚɩɚɡɞɵɜɚɧɢɹ:
ɛ
()
dC t
ɫɦ
TCtɄ Gt
ɨɛ ɫɦ ɫɦ A
dt
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ ɩɨ ɤɚɧɚɥɭ ɭɩɪɚɜɥɟɧɢɹ
ɛɛ
() ()
. (15)
GC ɜɨ ɜɪɟɦɟɧɧɨɣ ɨɛɥɚ-
A ɫɦ
ɫɬɢ ɫ ɭɱɟɬɨɦ ɬɪɚɧɫɩɨɪɬɧɨɝɨ ɡɚɩɚɡɞɵɜɚɧɢɹ:
ɛ
()
dC t
ɫɦ
TCtɄ Gt
ɨɛ ɫɦ ɨɛ A
dt
ɉɟɪɟɞɚɬɨɱɧɚɹ ɮɭɧɤɰɢɹ ɨɛɴɟɤɬɚ ɩɨ ɤɚɧɚɥɭ ɭɩɪɚɜɥɟɧɢɹ
ɛɛ
. (16)
() ( )
pW
K
)(
ɨɛ
ɨɛ
e
pT
1
W
GC :
A ɫɦ
W
p
, (17)
ɝɞɟ
000
VCCG
U
ɬɪɭɛ – ɨɛɴɟɦ ɬɪɭɛɨɩɪɨɜɨɞɚ ɨɬ Ɋ.Ɉ. ɞɨ ɜɯɨɞɚ ɜ ɚɩɩɚɪɚɬ.
ɝɞɟ V
ɫɦ ɫɦ Ⱥ ɫɦ A
T Ʉ
,
ɨɛ ɨɛ
;
000
GGC
ɫɦ ɫɦ ɫɦ
W
ɨɛ
()
ȡ V
A ɬɪɭɛ
, (18)
G
A
Ⱥɧɚɥɢɡ ɭɪɚɜɧɟɧɢɹ ɞɢɧɚɦɢɤɢ ɧɚ ɨɫɧɨɜɟ ɦɚɬɟɪɢɚɥɶɧɨɝɨ ɛɚɥɚɧɫɚ ɩɨ ɜɫɟɦɭ ɜɟɳɟɫɬɜɭ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
dh
ɫɦ
SGGG
U
ɫɦ ɚɩɩ A Ȼɫɦ
. (19)
dt
ɇɚɱɚɥɶɧɵɟ ɭɫɥɨɜɢɹ ɞɥɹ ɜɵɜɨɞɚ ɩɟɪɟɞɚɬɨɱɧɨɣ ɮɭɧɤɰɢɢ ɩɨ ɤɚɧɚɥɭ ɭɩɪɚɜɥɟɧɢɹ G
– hɫɦ:
Ȼ
hh h ';
0
GG G ';
ȻȻ Ȼ
0
ɫɦ ɫɦ ɫɦ
0
GG ;
AA
ɫɦ ɫɦ
11
0
GG .
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ:
p
U
000
GGG . (20)
ɫɦ Ⱥ Ȼ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ ɜ ɩɪɢɪɚɳɟɧɢɹɯ (ɩɨɫɥɟ ɩɨɞɫɬɚɧɨɜɤɢ ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɣ ɜ ɜɵɪɚɠɟɧɢɟ (19), ɜɵɱɢɬɚɧɢɹ ɭɪɚɜɧɟɧɢɹ ɫɬɚɬɢɤɢ ɢ ɩɪɢɜɟɞɟɧɢɹ ɩɨɞɨɛɧɵɯ
ɱɥɟɧɨɜ):
dh
'
SG
U
ɫɦ ɚɩɩ Ȼ
ɫɦ
' . (21)
dt
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ ɫ ɛɟɡɪɚɡɦɟɪɧɵɦɢ ɩɟɪɟɦɟɧɧɵɦɢ:
ɛ
()
dh t
00ɛ
Sh GGt
U
ɫɦ ɚɩɩ ɫɦ Ȼ Ȼ
ɫɦ
. (22)
dt
()
ɇɨɪɦɚɥɢɡɨɜɚɧɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ ɨɛɴɟɤɬɚ ɜɨ ɜɪɟɦɟɧɧɨɣ ɨɛɥɚɫɬɢ:
ɛ
()
dh t
ɫɦ
TGt
ɨɛ Ȼ
dt
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ ɩɨ ɤɚɧɚɥɭ ɭɩɪɚɜɥɟɧɢɹ
ɛ
()
. (23)
Gh ɜɨ ɜɪɟɦɟɧɧɨɣ ɨɛɥɚɫɬɢ
Ȼɫɦ
ɫ ɭɱɟɬɨɦ ɬɪɚɧɫɩɨɪɬɧɨɝɨ ɡɚɩɚɡɞɵɜɚɧɢɹ:
ɛ
()
dh t
ɫɦ
TGt
ɨɛ Ȼ
dt
ɉɟɪɟɞɚɬɨɱɧɚɹ ɮɭɧɤɰɢɹ ɨɛɴɟɤɬɚ ɩɨ ɤɚɧɚɥɭ ɭɩɪɚɜɥɟɧɢɹ
()
Wp e
ɛ
()
. (24)
1
, (25)
Tp
ɨɛ
W
Gh :
Ȼɫɦ
W
ɝɞɟ
ɝɞɟ V
– ɨɛɴɟɦ ɬɪɭɛɨɩɪɨɜɨɞɚ ɨɬ Ɋ.Ɉ. ɞɨ ɜɯɨɞɚ ɜ ɚɩɩɚɪɚɬ.
ɬɪɭɛ
Ɍ
ɫɦ ɚɩɩ ɫɦ
;
ɨɛ
0
G
Ȼ
W
0
Sh
U
V
Ȼɬɪɭɛ
, (26)
G
Ȼ
Ⱥɧɚɥɢɡ ɫɬɚɬɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɨɛɴɟɤɬɚ
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ ɧɚ ɨɫɧɨɜɟ ɦɚɬɟɪɢɚɥɶɧɨɝɨ ɛɚɥɚɧɫɚ ɩɨ ɰɟɥɟɜɨɦɭ ɤɨɦɩɨɧɟɧɬɭ:
ɂɡ ɭɪɚɜɧɟɧɢɹ (27) ɜɵɪɚɡɢɦ
000 0000
()GGC Gɋ G ɋ . (27)
ȺȻɫɦȺȺȻȻ
0
ɜ ɹɜɧɨɦ ɜɢɞɟ:
C
ɫɦ
00 00
G ɋ G ɋ
0
C
ȺȺ ȻȻ
ɫɦ
0000
GGGG
ȺȻ ȺȻ
. (28)
Ⱥɧɚɥɢɡ ɜɵɪɚɠɟɧɢɹ (28) ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ:
ɫɬɚɬɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɥɢɧɟɣɧɚ ɩɨ ɤɚɧɚɥɚɦ
ɫɬɚɬɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɧɟɥɢɧɟɣɧɚ ɩɨ ɤɚɧɚɥɚɦ
12
; CC CC;
A ɫɦ Ȼ ɫɦ
; GC GC
A ɫɦ Ȼ ɫɦ
.
Ʌɢɧɟɚɪɢɡɨɜɚɧɧɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɫɬɚɬɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɧɚ ɨɫɧɨɜɟ
J
J
J
ɫɬɚɛɢɥɢɡɚɰɢɢ ɫɨɨɬɧɨɲɟɧɢɹ ɪɚɫɯɨɞɨɜ:
00 00 0 0
G ɋ G ɋɋ ɋ
0
C
ɫɦ
ȺȺ ȺȻ Ⱥ Ȼ
00
GG
(1 ) (1 )
ȺȺ
JJ
JJ
(ɢɥɢ
ȻȺ
GG
):
ȺȻ
(1 ) (1 )
J
. (29)
GG
Ʌɢɧɟɚɪɢɡɨɜɚɧɧɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɫɬɚɬɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɱɟɪɟɡ ɪɚɡɥɨɠɟɧɢɟ ɜ ɪɹɞ Ɍɟɣɥɨɪɚ:
' ' '
¨¸ ¨¸
ɫɦ Ⱥ Ⱥ
©¹ ©¹
''
§· §·
CGɋ
00
CC
ww
ɫɦ ɫɦ
G ɋ
ww
ȺȺ
§· §·
¨¸ ¨¸
©¹ ©¹
00
CC
ww
ɫɦ ɫɦ
G ɋ
G ɋ
ww
ȻȻ
ȻȻ
. (30)
Ɉɛɨɡɧɚɱɢɦ:
§· §· §· §·
KKKK
¨¸ ¨¸ ¨¸ ¨¸
1234
©¹ ©¹ ©¹ ©¹
0000
CCCC
wwww
ɫɦ ɫɦ ɫɦ ɫɦ
; ; ;
wwww
G ɋ G ɋ
ȺȺȻȻ
Ʌɢɧɟɚɪɢɡɨɜɚɧɧɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɩɪɢɪɚɳɟɧɢɹ ɜɵɯɨɞɧɨɣ ɩɟɪɟɦɟɧɧɨɣ ɱɟɪɟɡ
ɩɪɢɪɚɳɟɧɢɹ ɜɫɟɯ ɜɨɡɦɨɠɧɵɯ ɜɯɨɞɧɵɯ ɩɟɪɟɦɟɧɧɵɯ:
CKGKɋ KG Kɋ' ''''. (31)
ɫɦ 1 Ⱥ 2 Ⱥ 3 Ȼ 4 Ȼ
Ɍɢɩɨɜɚɹ ɫɯɟɦɚ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ ɩɟɪɟɦɟɲɢɜɚɧɢɹ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ
ɪɢɫ. 14.
.
Ɋɢɫ. 4. Ɍɢɩɨɜɚɹ ɫɯɟɦɚ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ ɩɟɪɟɦɟɲɢɜɚɧɢɹ
13
Ɍɢɩɨɜɨɟ ɪɟɲɟɧɢɟ ɚɜɬɨɦɚɬɢɡɚɰɢɢ
Ɋɟɝɭɥɢɪɨɜɚɧɢɟ:
ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɤɨɧɰɟɧɬɪɚɰɢɢ Cɫɦ ɩɨ ɩɨɞɚɱɟ ɪɟɚɝɟɧɬɚ GȺ – ɤɚɤ ɩɨɤɚ-
ɡɚɬɟɥɹ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɩɪɨɰɟɫɫɚ ɩɟɪɟɦɟɲɢɜɚɧɢɹ ɫ ɰɟɥɶɸ ɩɨɥɭɱɟɧɢɹ ɝɨɦɨɝɟɧɢɡɢɪɨɜɚɧɧɨɝɨ ɪɚɫɬɜɨɪɚ;
ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɭɪɨɜɧɹ ɜ ɚɩɩɚɪɚɬɟ h
ɩɨ ɩɨɞɚɱɟ ɪɟɚɝɟɧɬɚ GȻ – ɞɥɹ
ɫɦ
ɨɛɟɫɩɟɱɟɧɢɹ ɦɚɬɟɪɢɚɥɶɧɨɝɨ ɛɚɥɚɧɫɚ ɩɨ ɠɢɞɤɨɣ ɮɚɡɟ.
Ʉɨɧɬɪɨɥɶ:
ɪɚɫɯɨɞɵ – G
ɤɨɧɰɟɧɬɪɚɰɢɹ – ɋ
ɭɪɨɜɟɧɶ – h
, GȻ, Gɫɦ;
Ⱥ
.
ɫɦ
;
ɫɦ
ɋɢɝɧɚɥɢɡɚɰɢɹ:
ɫɭɳɟɫɬɜɟɧɧɵɟ ɨɬɤɥɨɧɟɧɢɹ ɋ
ɪɟɡɤɨɟ ɩɚɞɟɧɢɟ ɪɚɫɯɨɞɨɜ ɢɫɯɨɞɧɵɯ ɪɟɚɝɟɧɬɨɜ G
ɢ hɫɦ ɨɬ ɡɚɞɚɧɢɹ;
ɫɦ
p ɢɥɢ GȻ p, ɩɪɢ ɷɬɨɦ
Ⱥ
ɮɨɪɦɢɪɭɟɬɫɹ ɫɢɝɧɚɥ «ȼ ɫɯɟɦɭ ɡɚɳɢɬɵ».
ɋɢɫɬɟɦɚ ɡɚɳɢɬɵ.
ɉɨ ɫɢɝɧɚɥɭ «ȼ ɫɯɟɦɭ ɡɚɳɢɬɵ» ɨɬɤɥɸɱɚɸɬɫɹ ɦɚɝɢɫɬɪɚɥɢ ɩɨɞɚɱɢ ɢɫɯɨɞɧɵɯ
ɪɟɚɝɟɧɬɨɜ G
, GȻ ɢ ɨɬɛɨɪɚ ɫɦɟɫɢ ɋɫɦ.
Ⱥ
Ɍɪɭɛɨɩɪɨɜɨɞ ɤɚɤ ɨɛɴɟɤɬ ɭɩɪɚɜɥɟɧɢɹ
Ɍɢɩɨɜɚɹ ɫɯɟɦɚ ɩɪɨɰɟɫɫɚ ɩɟɪɟɦɟɳɟɧɢɹ ɠɢɞɤɨɫɬɢ (ɢɡɨɛɪɚɠɟɧɚ ɧɚ ɪɢɫ. 5).
Ɋɢɫ. 5. Ɍɢɩɨɜɚɹ ɫɯɟɦɚ ɩɪɨɰɟɫɫɚ ɩɟɪɟɦɟɳɟɧɢɹ ɠɢɞɤɨɫɬɢ
1. Ɉɛɴɟɤɬ ɭɩɪɚɜɥɟɧɢɹ – ɫɯɟɦɚ, ɩɪɢɜɟɞɟɧɧɚɹ ɧɚ ɪɢɫ. 5.
ɂɡ ɟɦɤɨɫɬɢ 1 ɧɚɫɨɫɨɦ 2 ɩɨ ɬɪɭɛɨɩɪɨɜɨɞɭ 3 ɠɢɞɤɨɫɬɶ ɩɟɪɟɤɚɱɢɜɚɟɬɫɹ ɜ ɟɦɤɨɫɬɶ 4.
2. ɉɨɤɚɡɚɬɟɥɶ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɩɪɨɰɟɫɫɚ – ɪɚɫɯɨɞ Q.
3. ɐɟɥɶ ɭɩɪɚɜɥɟɧɢɹ ɩɪɨɰɟɫɫɨɦ Q = Q
.
ɡɞ
4. Ⱥɧɚɥɢɡ ɬɢɩɨɜɨɣ ɫɯɟɦɵ ɤɚɤ ɨɛɴɟɤɬɚ ɭɩɪɚɜɥɟɧɢɹ.
Ɉɫɧɨɜɧɵɟ ɷɥɟɦɟɧɬɵ, ɩɨɞɥɟɠɚɳɢɟ ɚɧɚɥɢɡɭ – ɬɪɭɛɨɩɪɨɜɨɞ 3 ɢ ɧɚɫɨɫ 2.
14
Ɉɫɧɨɜɧɵɟ ɩɚɪɚɦɟɬɪɵ ɬɪɭɛɨɩɪɨɜɨɞɚ ɤɚɤ ɨɛɴɟɤɬɚ ɭɩɪɚɜɥɟɧɢɹ:
U
p
p
ɜɧɭɬɪɟɧɧɢɣ ɞɢɚɦɟɬɪ d:
ɝɞɟ Q – ɪɚɫɯɨɞ, ɦ
3
dv ,
/ɫ;
Q
0,785
v – ɫɤɨɪɨɫɬɶ ɩɨɬɨɤɚ, ɦ/ɫ.
ɋɤɨɪɨɫɬɶ ɩɨɬɨɤɚ v = 0,5–2,5ɦ/ɫ;
ɝɢɞɪɚɜɥɢɱɟɫɤɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɬɪɭɛɨɩɪɨɜɨɞɚ:
= 'p
'p
ɩɨɬɟɪɢ ɞɚɜɥɟɧɢɹ ɧɚ ɫɨɨɛɳɟɧɢɟ ɩɨɬɨɤɭ ɫɤɨɪɨɫɬɢ:
ɝɫ
ɩɨɬɟɪɢ ɞɚɜɥɟɧɢɹ ɧɚ ɩɪɟɨɞɨɥɟɧɢɟ ɬɪɟɧɢɹ ɩɨɬɨɤɚ ɨ ɫɬɟɧɤɢ ɬɪɭɛɨɩɪɨɜɨɞɚ:
ɝɞɟ
O
= f (Re, l) – ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ;
ɩɨɬɟɪɢ ɞɚɜɥɟɧɢɹ ɧɚ ɩɪɟɨɞɨɥɟɧɢɟ ɦɟɫɬɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ:
'p
ɝɞɟ
[
– ɤɨɷɮɮɢɰɢɟɧɬ ɦɟɫɬɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ;
ɦɫ
ɫɨɩɪɨɬɢɜɥɟɧɢɟ, ɡɚɬɪɚɱɢɜɚɟɦɨɟ ɧɚ ɩɨɞɴɟɦ ɠɢɞɤɨɫɬɢ ɧɚ ɜɵɫɨɬɭ h:
'p
ɞɨɩɨɥɧɢɬɟɥɶɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ:
'p
ɩɨɥɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ:
2
ɦɨɳɧɨɫɬɶ, ɤɨɬɨɪɭɸ ɧɟɨɛɯɨɞɢɦɨ ɡɚɬɪɚɬɢɬɶ ɧɚ ɩɟɪɟɤɚɱɢɜɚɧɢɟ:
' ¦;
UZ
ɨɛɳ ɦɫ 21
(1 ) ( )
2
N = 'p
ɝɞɟ
K
– ɩɨɥɧɵɣ ɄɉȾ ɧɚɫɨɫɚ;
K
– ɄɉȾ ɧɚɫɨɫɚ;
ɧ
K
– ɄɉȾ ɩɟɪɟɞɚɱɢ;
ɩ
K
– ɄɉȾ ɞɜɢɝɚɬɟɥɹ.
ɞ
+ 'pɬɪ + 'pɦɫ;
ɫɤ
2
' ;
p
' ',
ɬɪ ɫɤ
ɦɫ
ɞɨɩ
l
O]U
d
K
=
v
ɋɄ
2
l
p
O
d
= ¦
[
,
ɦɫ'pɫɤ
= Ugh;
ɩɨɞ
= p2 – p1;
gh p p
3
Q/(10
K
ɨɛɳ
K
K
ɧ
),
K
,
ɩ
ɞ
ɋɯɟɦɚ ɬɪɭɛɨɩɪɨɜɨɞɚ ɤɚɤ ɨɛɴɟɤɬɚ ɭɩɪɚɜɥɟɧɢɹ ɞɥɹ ɬɢɩɨɜɨɣ ɫɯɟɦɵ ɩɪɨɰɟɫɫɚ
ɩɟɪɟɦɟɳɟɧɢɹ ɠɢɞɤɨɫɬɢ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 6.
15
Ɋɢɫ. 6. ɋɯɟɦɚ ɬɪɭɛɨɩɪɨɜɨɞɚ ɤɚɤ ɨɛɴɟɤɬɚ ɭɩɪɚɜɥɟɧɢɹ ɞɥɹ ɬɢɩɨɜɨɣ ɫɯɟɦɵ ɩɪɨɰɟɫɫɚ
ɩɟɪɟɦɟɳɟɧɢɹ ɠɢɞɤɨɫɬɢ
Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɩɢɫɚɧɢɟ ɫɬɚɬɢɤɢ ɨɛɴɟɤɬɚ
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɞɥɹ ɬɪɭɛɨɩɪɨɜɨɞɚ (ɪɢɫ. 6) ɧɚ ɨɫɧɨɜɚɧɢɢ ɭɫɥɨɜɢɹ ɧɟɪɚɡɪɵɜɧɨɫɬɢ ɫɬɪɭɢ:
S
= Sb vb. (32)
a va
ɂɡ (32) ɩɨɥɭɱɢɦ:
v
= Sb vb / Sa. (33)
a
Ɉɛɨɡɧɚɱɢɦ
S
/ Sa = m. (34)
b
ɗɧɟɪɝɟɬɢɱɟɫɤɢɣ ɛɚɥɚɧɫ – ɭɪɚɜɧɟɧɢɟ Ȼɟɪɧɭɥɥɢ:
gh P gh X P
UUO]]
aa b ɪɨ ɪɨ b
22
vvl
UU
ab
22
§·
1()
¨¸
©¹
d
D
. (35)
ɉɨɞɫɬɚɜɢɦ ɜ (35) ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɫɤɨɪɨɫɬɢ ɩɨɬɨɤɚ ɜ ɫɟɱɟɧɢɢ «ɚ»:
22
§·
vSl
U
bb
gh h P P
ɉɨɞɫɬɚɜɢɦ ɜ (36) ɜɦɟɫɬɨ v
ɪɚɫɯɨɞɚ ɜ ɫɟɱɟɧɢɢ «b»:
Q
ɨɬɤɭɞɚ
UO]]
ab a b d ɪɨ
ɟɝɨ ɜɵɪɚɠɟɧɢɟ ɢɡ ɫɨɨɬɧɨɲɟɧɢɹ ɞɥɹ ɨɛɴɟɦɧɨɝɨ
b
v
UO]]
gh h P P m
ab a b d ɪɨ
1
¨¸
2
= vb Sb,
b
= Qb / Sb,
b
2
U
Ql
b
2
2
S
b
2
D
S
a
©¹
§·
2
1
¨¸
©¹
D
. (36)
. (37)
ɉɪɟɨɛɪɚɡɭɟɦ ɜɵɪɚɠɟɧɢɟ (37) ɫ ɭɱɟɬɨɦ (33) ɤ ɜɢɞɭ:
222
ªº
21
SghhPP Qm
UUO]]
bababb dɪɨ
¬¼
§·
¨¸
©¹
l
D
. (38)
16
Ɋɟɲɢɦ ɜɵɪɚɠɟɧɢɟ (38) ɨɬɧɨɫɢɬɟɥɶɧɨ Qb:
b
Sg
QhhPP
1
m
b
l
2
O]]
d ɪɨ
D
22
U
()()
UU
ab ab
Ʌɢɧɟɚɪɢɡɨɜɚɧɧɵɟ ɜɵɪɚɠɟɧɢɹ ɦɚɬ. ɦɨɞɟɥɢ ɫɬɚɬɢɤɢ ɧɚ ɨɫɧɨɜɚɧɢɢ ɪɚɡɥɨɠɟɧɢɹ ɜ ɪɹɞ Ɍɟɣɥɨɪɚ:
1.
ɑɟɪɟɡ ɩɪɢɪɚɳɟɧɢɹ ɢ ɱɚɫɬɧɵɟ ɩɪɨɢɡɜɨɞɧɵɟ:
§· §· §· §·
QQQQ Q
wwww w
QP P h h X
' '''' '
¨¸ ¨¸ ¨¸ ¨¸
wwwww
2. ɑɟɪɟɡ ɩɪɢɪɚɳɟɧɢɹ ɢ ɤɨɷɮɮɢɰɢɟɧɬɵ ɭɫɢɥɟɧɢɹ:
©¹ ©¹ ©¹ ©¹
abab po
PPh h X
abab po
QK P K P K h K h K X' ' ' ' ' ' .
1a 2 b 3a 4 b 5 ɪɨ
§·
¨¸
¨¸
©¹
ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɨɛɴɟɤɬɚ ɭɩɪɚɜɥɟɧɢɹ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 7.
(39)
.
Ɋɢɫ. 7. ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɨɛɴɟɤɬɚ ɭɩɪɚɜɥɟɧɢɹ:
ɏɪɨ – ɜɨɡɦɨɠɧɨɟ ɪɟɝɭɥɢɪɭɸɳɟɟ ɜɨɡɞɟɣɫɬɜɢɟ, Ɋa, ha, Pb, hb – ɜɨɡɦɨɠɧɵɟ
ɤɨɧɬɪɨɥɢɪɭɟɦɵɟ ɜɨɡɦɭɳɚɸɳɢɟ ɜɨɡɞɟɣɫɬɜɢɹ,
Z – ɜɨɡɦɨɠɧɵɟ ɧɟɤɨɧɬɪɨɥɢɪɭɟɦɵɟ ɜɨɡɦɭɳɚɸɳɢɟ ɜɨɡɞɟɣɫɬɜɢɹ
Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɩɢɫɚɧɢɟ ɞɢɧɚɦɢɤɢ ɨɛɴɟɤɬɚ
ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɨɛɴɟɤɬɚ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 8.
Ɋɢɫ. 8. ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɨɛɴɟɤɬɚ
17
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
VdQ
ɬɪ ɫɭ
Qdt
ɫɭ
QQ
ɪɨ ɫɭ
. (40)
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ:
QQ . (41)
ɪɨ ɫɭ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ ɜɨ ɜɪɟɦɟɧɧɨɣ ɨɛɥɚɫɬɢ ɧɚ ɨɫɧɨɜɟ ɦɟɬɨɞɚ ɛɟɡɪɚɡɦɟɪɧɵɯ ɩɟɪɟɦɟɧɧɵɯ:
VdQt Q
QQ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ ɫ ɭɱɟɬɨɦ ɡɚɩɚɡɞɵɜɚɧɢɹ:
ɉɟɪɟɞɚɬɨɱɧɚɹ ɮɭɧɤɰɢɹ ɛɭɞɟɬ ɢɦɟɬɶ ɜɢɞ:
TQtɄ Qt
ɨɛ ɫɭ ɨɛ ɪɨ
ɛ 0
ɬɪ ɫɭ ɪɨ
00
ɫɭ ɫɭ
. (43)
()
ɛɛ
() ()
ɛ
dQ t
ɫɭ
dt
()
Wp e
Qt Qt
dt
()
ɫɭ ɪɨ
ɛɛ
() ( )
K
Tp
ɨɛ
ɨɛ
1
p
W
ɨɛ
, (44)
. (42)
W
ɝɞɟ
TQ
ɨɛ
V
ɬɪ
,
0
ɫɭ
W
.
ɨɛ
V
ɬɪ
0
Q
ɪɨ
Ⱥɜɬɨɦɚɬɢɡɚɰɢɹ ɰɟɧɬɪɨɛɟɠɧɵɯ ɧɚɫɨɫɨɜ
Ɉɫɧɨɜɧɵɟ ɩɨɤɚɡɚɬɟɥɢ ɪɚɛɨɬɵ ɧɚɫɨɫɨɜ
ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ, ɢɥɢ ɩɨɞɚɱɚ, Q (ɦ3/c) – ɨɛɴɟɦ ɠɢɞɤɨɫɬɢ, ɩɨɞɚɜɚɟ-
ɦɨɣ ɧɚɫɨɫɨɦ ɜ ɧɚɝɧɟɬɚɬɟɥɶɧɵɣ ɬɪɭɛɨɩɪɨɜɨɞ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ;
ɧɚɩɨɪ ɇ (ɦ) – ɭɞɟɥɶɧɚɹ ɷɧɟɪɝɢɹ, ɫɨɨɛɳɚɟɦɚɹ ɧɚɫɨɫɨɦ ɟɞɢɧɢɰɟ ɜɟɫɚ
ɩɟɪɟɤɚɱɢɜɚɟɦɨɣ ɠɢɞɤɨɫɬɢ:
PP v v
Hh
ɧɜɫ ɧɜɫ
U
22
2
gg
, (45)
ɱɥ. 1 ɱɥ. 2 ɱɥ. 3
ɝɞɟ ɱɥ. 1 – ɜɵɫɨɬɚ ɩɨɞɴɟɦɚ ɠɢɞɤɨɫɬɢ ɜ ɧɚɫɨɫɟ;
ɱɥ. 2 – ɪɚɡɧɨɫɬɶ ɩɶɟɡɨɦɟɬɪɢɱɟɫɤɢɯ ɧɚɩɨɪɨɜ;
ɱɥ. 3 – ɪɚɡɧɨɫɬɶ ɞɢɧɚɦɢɱɟɫɤɢɯ ɧɚɩɨɪɨɜ;
ɩɨɥɟɡɧɚɹ ɦɨɳɧɨɫɬɶ N
– ɷɬɨ ɦɨɳɧɨɫɬɶ, ɡɚɬɪɚɱɢɜɚɟɦɚɹ ɧɚɫɨɫɨɦ ɧɚ ɫɨ-
n
ɨɛɳɟɧɢɟ ɠɢɞɤɨɫɬɢ ɷɧɟɪɝɢɢ:
18
J
U
K
NQHgQH
n
; (46)
U
ɦɨɳɧɨɫɬɶ ɧɚ ɜɚɥɭ ɧɚɫɨɫɚ Ne – ɷɬɨ ɨɬɧɨɲɟɧɢɟ ɩɨɥɟɡɧɨɣ ɦɨɳɧɨɫɬɢ N
ɤ ɄɉȾ ɧɚɫɨɫɚ:
ɤɨɷɮɮɢɰɢɟɧɬ ɩɨɥɟɡɧɨɝɨ ɞɟɣɫɬɜɢɹ ɧɚɫɨɫɚ Ș
ɝɞɟ Ș
= Q/Qɬ – ɨɛɴɟɦɧɵɣ ɄɉȾ;
v
H
K
ɝ
Ș
ɦɟɯ
– ɝɢɞɪɚɜɥɢɱɟɫɤɢɣ ɄɉȾ;
H
ɬ
– ɦɟɯɚɧɢɱɟɫɤɢɣ ɄɉȾ.
N
e
KK
ɧɧ
KKK
, (48)
ɧɝɦɟɯv
; (47)
:
ɧ
NgQH
ɩ
Ɉɫɧɨɜɧɚɹ ɰɟɥɶ ɭɩɪɚɜɥɟɧɢɹ ɧɚɫɨɫɚɦɢ – ɨɛɟɫɩɟɱɢɬɶ ɷɮɮɟɤɬɢɜɧɭɸ ɪɚɛɨɬɭ
ɧɚɫɨɫɚ ɧɚ ɫɟɬɶ.
ɇɚɫɨɫɵ ɤɚɤ ɨɛɴɟɤɬɵ ɭɩɪɚɜɥɟɧɢɹ ɤɥɚɫɫɢɮɢɰɢɪɭɸɬɫɹ ɩɨ ɩɪɢɧɰɢɩɭ ɞɟɣɫɬɜɢɹ ɧɚ:
ɰɟɧɬɪɨɛɟɠɧɵɟ;
ɩɨɪɲɧɟɜɵɟ.
ɋɯɟɦɚ ɰɟɧɬɪɨɛɟɠɧɨɝɨ ɧɚɫɨɫɚ ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 9.
n
Ɋɢɫ. 9. ɋɯɟɦɚ ɰɟɧɬɪɨɛɟɠɧɨɝɨ ɧɚɫɨɫɚ:
1 – ɤɨɪɩɭɫ, 2 – ɪɚɛɨɱɟɟ ɤɨɥɟɫɨ, 3 – ɩɪɢɜɨɞ ɧɚɫɨɫɚ, 4 – ɥɢɧɢɹ ɜɫɚɫɵɜɚɧɢɹ,
5 – ɩɚɬɪɭɛɨɤ ɧɚɝɧɟɬɚɧɢɹ
ɉɪɢɧɰɢɩ ɞɟɣɫɬɜɢɹ ɰɟɧɬɪɨɛɟɠɧɵɯ ɧɚɫɨɫɨɜ ɨɫɧɨɜɚɧ ɧɚ ɫɨɡɞɚɧɢɢ ɰɟɧɬɪɨɛɟɠɧɵɯ ɩɨɥɟɣ ɞɚɜɥɟɧɢɹ ɩɪɢ ɜɪɚɳɟɧɢɢ ɪɚɛɨɱɟɝɨ ɤɨɥɟɫɚ ɜ ɠɢɞɤɨɫɬɢ.
19
Ɋɚɛɨɬɚ ɫɯɟɦɵ
ȼ ɤɨɪɩɭɫɟ 1 ɜɪɚɳɚɟɬɫɹ ɪɚɛɨɱɟɟ ɤɨɥɟɫɨ 2 ɨɬ ɩɪɢɜɨɞɚ 3. ɉɪɢ ɷɬɨɦ ɡɚɥɢɬɚɹ ɜ
ɤɨɪɩɭɫ ɠɢɞɤɨɫɬɶ ɬɚɤɠɟ ɜɪɚɳɚɟɬɫɹ, ɢ ɜɨɡɧɢɤɚɟɬ ɰɟɧɬɪɨɛɟɠɧɨɟ ɩɨɥɟ ɞɚɜɥɟɧɢɣ ɫ
ɦɚɤɫɢɦɚɥɶɧɵɦ ɞɚɜɥɟɧɢɟɦ ɧɚ ɩɟɪɢɮɟɪɢɢ (ɞɚɜɥɟɧɢɟ Ɋ
ɧɢɟɦ ɩɨ ɨɫɢ ɩɨɬɨɤɚ (ɞɚɜɥɟɧɢɟ Ɋ
) ɬ. ɟ. ɫɨɡɞɚɟɬɫɹ Ɋ4 << Ɋ5. ɉɨɷɬɨɦɭ ɩɨɞɚɱɚ ɠɢɞ-
4
) ɢ ɦɢɧɢɦɚɥɶɧɵɦ ɞɚɜɥɟ-
5
ɤɨɫɬɢ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɱɟɪɟɡ ɩɚɬɪɭɛɨɤ 4, ɚ ɧɚɝɧɟɬɚɧɢɟ – ɱɟɪɟɡ ɩɚɬɪɭɛɨɤ 5.
Ɋɢɫ. 10. Ɉɫɧɨɜɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɰɟɧɬɪɨɛɟɠɧɵɯ ɧɚɫɨɫɨɜ
Ɉɫɧɨɜɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɰɟɧɬɪɨɛɟɠɧɵɯ ɧɚɫɨɫɨɜ (ɪɢɫ. 10):
ɡɚɜɢɫɢɦɨɫɬɶ ɧɚɩɨɪɚ ɨɬ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ
ɇ = f1(Q);
ɡɚɜɢɫɢɦɨɫɬɶ ɦɨɳɧɨɫɬɢ ɧɚ ɜɚɥɭ ɧɚɫɨɫɚ ɨɬ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ
Nɟ = f2(Q);
ɡɚɜɢɫɢɦɨɫɬɶ ɄɉȾ ɧɚɫɨɫɚ ɨɬ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ
K
= f(Q).
ɧ
ɏɚɪɚɤɬɟɪɢɫɬɢɤɢ ɧɚɫɨɫɚ ɩɨɥɭɱɚɸɬ ɜ ɯɨɞɟ ɫɩɟɰɢɚɥɶɧɨɝɨ ɷɤɫɩɟɪɢɦɟɧɬɚ ɢɥɢ
ɧɚ ɨɫɧɨɜɟ ɨɫɧɨɜɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɗɣɥɟɪɚ ɞɥɹ ɰɟɧɬɪɨɛɟɠɧɵɯ ɦɚɲɢɧ.
Ⱥɧɚɥɢɬɢɱɟɫɤɨɟ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɧɚɩɨɪɚ ɜ ɫɟɬɢ
ɇɫ = ɇɝ + k Q2,
ɝɞɟ ɇɝ – ɝɟɨɦɟɬɪɢɱɟɫɤɚɹ ɜɵɫɨɬɚ ɩɨɞɚɱɢ;
k Q
= hɩ – ɩɨɬɟɪɢ ɧɚɩɨɪɚ ɜ ɫɟɬɢ;
2
(x)Ⱥ – ɪɚɛɨɱɚɹ ɬɨɱɤɚ, ɨɛɟɫɩɟɱɢɜɚɸɳɚɹ ɦɚɤɫɢɦɚɥɶɧɭɸ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ
ɧɚɫɨɫɚ Q
ɩɪɢ ɪɚɛɨɬɟ ɧɚ ɞɚɧɧɭɸ ɫɟɬɶ (ɪɢɫ. 11).
1
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