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Файл:Автоматизация процессов химических производств. Учебное пособие
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ɜɵɯ
f
T
d
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ ɩɪɢ
Gc Gc Gr
ɇɚ ɨɫɧɨɜɚɧɢɢ (137) ɢ (138) ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ:
ɝɞɟ
()rfP , ɬɚɤ ɤɚɤ ɩɪɢ Pɩ n
ɩɩ
ɠɪɠ ɠ ɠ ɩɪɩ ɩ ɧ ɩɩ
ɜɵɯ ɜɯ
TTTT
ɠɩɠɩɤɠɩɤpi
ɠ
0
:
dt
ɜɵɯ ɜɯ
()()
TT TT
. (138)
()
Gc
(, ,,, ,,,)
GG rhc
, (139)
T
ɤɢɩ
TT
ɤɪɤ ɧ ɤ
norɩ p.
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɠɢɞɤɨɣ ɮɚɡɟ ɞɥɹ ɦɟɠɬɪɭɛɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
dh
ɤ
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ ɩɪɢ
ɇɚ ɨɫɧɨɜɚɧɢɢ (141) ɢ (142)
ɳɟɟ ɜɨɡɞɟɣɫɬɜɢɟ – G
ɤ.
SGG
U
ɤɦɬɪ ɩ ɤ
dh
ɤ
:
dt
. (140)
dt
0
GG . (141)
ɩɤ
(,)hfGG ɢ ɩɪɟɞɩɨɱɬɢɬɟɥɶɧɨɟ ɭɩɪɚɜɥɹɸ-
ɤɩɤ
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɩɚɪɨɜɨɣ ɮɚɡɟ ɞɥɹ ɦɟɠɬɪɭɛɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
VM dP
ɝɞɟ Ɇ
– ɦɨɥɶɧɚɹ ɦɚɫɫɚ ɩɚɪɨɜɨɣ ɮɚɡɵ ɬɟɩɥɨɧɨɫɢɬɟɥɹ, ɤɝ/ɦɨɥɶ;
ɩ
– ɞɚɜɥɟɧɢɟ ɩɚɪɨɜɨɣ ɮɚɡɵ ɬɟɩɥɨɧɨɫɢɬɟɥɹ, ɉɚ;
Ɋ
ɩ
T
– ɬɟɦɩɟɪɚɬɭɪɚ ɩɚɪɨɜɨɣ ɮɚɡɵ ɬɟɩɥɨɧɨɫɢɬɟɥɹ, Ʉ;
ɩ
V
– ɨɛɴɟɦ ɩɚɪɨɜɨɣ ɮɚɡɵ ɬɟɩɥɨɧɨɫɢɬɟɥɹ, ɦ3.
ɩ
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ ɩɪɢ
ɇɚ ɨɫɧɨɜɚɧɢɢ (142) ɢ (143)
ɳɟɟ ɜɨɡɞɟɣɫɬɜɢɟ – G
ɩ.
ɩɩ ɩ
R
T
ɩ
dP
dt
, (142)
GG
ɩɤ
dt
0ɩ
:
GG . (143)
ɩɤ
(,)PfGG ɢ ɩɪɟɞɩɨɱɬɢɬɟɥɶɧɨɟ ɭɩɪɚɜɥɹɸ-
ɩɩɤ
51
ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɨɛɴɟɤɬɚ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 44.
U
U
Ɋɢɫ. 44. ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɨɛɴɟɤɬɚ
ȼɨɡɦɨɠɧɵɟ ɭɩɪɚɜɥɹɸɳɢɟ ɜɨɡɞɟɣɫɬɜɢɹ:
ȼɨɡɦɨɠɧɵɟ ɤɨɧɬɪɨɥɢɪɭɟɦɵɟ ɜɨɡɦɭɳɟɧɢɹ:
ȼɨɡɦɨɠɧɵɟ ɧɟɤɨɧɬɪɨɥɢɪɭɟɦɵɟ ɜɨɡɦɭɳɟɧɢɹ:
ȼɨɡɦɨɠɧɵɟ ɭɩɪɚɜɥɹɟɦɵɟ ɩɟɪɟɦɟɧɧɵɟ:
ɇɚɢɛɨɥɟɟ ɷɮɮɟɤɬɢɜɧɵɟ ɤɚɧɚɥɵ ɭɩɪɚɜɥɟɧɢɹ:
ɜɵɯ
;;GGhGP
T
.
ɩɠ ɤ ɩɩ
,,GGG.
ɠɩɤ
ɜɯ
,,
TTT
ɠɩɤ
,()
ɫ rP.
ɩɩ
ɪi
ɜɵɯ
,,PhT.
ɠɤɩ
.
Ⱥɧɚɥɢɡ ɞɢɧɚɦɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɚɪɨɠɢɞɤɨɫɬɧɨɝɨ ɬɟɩɥɨɨɛɦɟɧɧɢɤɚ
ɤɚɤ ɨɛɴɟɤɬɚ ɭɩɪɚɜɥɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɨɣ
TTT
ɂɫɯɨɞɧɵɟ ɭɫɥɨɜɢɹ:
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ ɜ ɧɨɪɦɚɥɢɡɨɜɚɧɧɨɦ ɜɢɞɟ.
Vc Gc G r G c
ɠɠ ɠɪɠ ɠ ɩ ɩ ɠ ɪɠ ɠ
.
ɩɧɤ ɩɩɩ
ɜɵɯ
d
T
ɠ
ɪɠ
dt
ɇɚ ɨɫɧɨɜɟ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ ɞɢɧɚɦɢɤɢ ɨɛɴɟɤɬ ɩɨ ɤɚɧɚɥɭ
ɟɬɫɹ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɶɸ ɚɩɟɪɢɨɞɢɱɟɫɤɨɝɨ ɡɜɟɧɚ 1-ɝɨ ɩɨɪɹɞɤɚ:
ɢ QrG
ɜɵɯ ɜɯ
. (144)
Wp
TT
ɜɵɯ
GT ɨɩɢɫɵɜɚ-
ɩɠ
K
ɨɛ
()
Tp
, (145)
1
ɨɛ
ɝɞɟ
V
;
ɨɛ
ɠɠ
0
G
ɠ
K
.
ɨɛ
Ɍ
0
Gr
ɩɩ
0 ɜɵɯ0
Gc
ɠɪɠ ɠ
T
52
Ɉɛɴɟɤɬ ɢɦɟɟɬ ɬɪɚɧɫɩɨɪɬɧɨɟ ɡɚɩɚɡɞɵɜɚɧɢɟ:
U
J
J
V
ɩɬɪɭɛ
WW
, (146)
ɬɪ ɨɛ
0
G
ɩ
ɝɞɟ V
– ɨɛɴɟɦ ɬɪɭɛɨɩɪɨɜɨɞɚ ɩɨɞɚɱɢ ɩɚɪɚ ɨɬ Ɋ.Ɉ. ɞɨ ɜɯɨɞɚ ɜ ɚɩɩɚɪɚɬ.
ɬɪɭɛ
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɰɟɥɨɦ ɞɢɧɚɦɢɤɚ ɨɛɴɟɤɬɚ ɩɨ ɤɚɧɚɥɭ ɭɩɪɚɜɥɟɧɢɹ ɨɩɢɫɵɜɚɟɬɫɹ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɶɸ ɚɩɟɪɢɨɞɢɱɟɫɤɨɝɨ ɡɜɟɧɚ 1-ɝɨ ɩɨɪɹɞɤɚ ɫ ɡɚɩɚɡɞɵɜɚɧɢɟɦ:
Tp
ɨɛ
K
Wp e
()
p
W
ɨɛ
ɨɛ
1
. (147)
Ⱥɧɚɥɢɡ ɫɬɚɬɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɨɛɴɟɤɬɚ
ɜɵɯ
T
ɂɡ ɭɪɚɜɧɟɧɢɹ ɫɬɚɬɢɤɢ ɜɵɪɚɡɢɦ
ɜɵɯ ɜɯ
TT
ɠɠ
ɜ ɹɜɧɨɦ ɜɢɞɟ:
ɠ
Gr
ɩɩ
Gc
ɠɪɠ
. (148)
ɋɬɚɬɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɥɢɧɟɣɧɚ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɜɨɡɞɟɣɫɬɜɢɹɦ
ɩɨ:
ɜɯ
,,Gr
T
ɩɩ ɠ
.
ɋɬɚɬɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɧɟɥɢɧɟɣɧɚ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɜɨɡɞɟɣɫɬɜɢɸ ɩɨ G
.
ɠ
ɋɬɚɬɢɱɟɫɤɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɦɨɠɧɨ ɥɢɧɟɚɪɢɡɨɜɚɬɶ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ G
ɜɜɟɞɟɧɢɟɦ ɫɬɚɛɢɥɢɡɚɰɢɢ ɫɨɨɬɧɨɲɟɧɢɹ ɪɚɫɯɨɞɨɜ:
Gr
ɜɵɯ ɜɯ
TT
ɠɠ
ɠɩ
Gc
ɠɪɠ
GG
, ɬɨɝɞɚ ɩɨɥɭɱɢɦ:
ɩɠ
. (149)
Ʌɢɧɟɚɪɢɡɨɜɚɧɧɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɫɬɚɬɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɱɟɪɟɡ ɪɚɡɥɨɠɟɧɢɟ ɜ ɪɹɞ Ɍɟɣɥɨɪɚ:
§· §· §· §·
ɜɵɯ ɜɯ
' ' ' ' '
TT
¨¸ ¨¸ ¨¸ ¨¸
ɠɩɠɩɠ
ɇɚ ɨɫɧɨɜɚɧɢɢ (150) ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ:
©¹ ©¹ ©¹ ©¹
00 00
ɜɵɯ ɜɵɯ ɜɵɯ ɜɵɯ
wwww
TTTT
ɠɠ ɠɠ
ww
GG
GG r
ɩɠ
ɜɵɯ ɜɯ
KG K G K r K
TT
' ''''. (151)
ɠ 1 ɩ 2 ɠ 3 ɩ 4 ɠ
r
ww
ɩɠ
ɜɯ
T
. (150)
ɋɯɟɦɚ ɢɫɩɚɪɢɬɟɥɹ (ɤɨɠɭɯɨɬɪɭɛɧɨɝɨ ɬɟɩɥɨɨɛɦɟɧɧɢɤɚ ɫ ɢɡɦɟɧɹɸɳɢɦɫɹ ɚɝɪɟɝɚɬɧɵɦ ɫɨɫɬɨɹɧɢɟɦ ɬɟɩɥɨɧɨɫɢɬɟɥɹ ɢ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɩɨɬɨɤɚ) ɩɪɟɞɫɬɚɜɥɟɧɚ
ɧɚ ɪɢɫ. 45.
ɉɨɤɚɡɚɬɟɥɶ ɷɮɮɟɤɬɢɜɧɨɫɬɢ: h
ɐɟɥɶ ɭɩɪɚɜɥɟɧɢɹ: ɩɨɞɞɟɪɠɚɧɢɟ
– ɭɪɨɜɟɧɶ ɠɢɞɤɨɣ ɮɚɡɵ ɜ ɬɪɭɛɤɚɯ ɢɫɩɚɪɢɬɟɥɹ.
ɠ
ɡɞ
hh .
ɠɠ
53
ɠ
Ɋɢɫ. 45. ɋɯɟɦɚ ɢɫɩɚɪɢɬɟɥɹ (ɤɨɠɭɯɨɬɪɭɛɧɨɝɨ ɬɟɩɥɨɨɛɦɟɧɧɢɤɚ ɫ ɢɡɦɟɧɹɸɳɢɦɫɹ ɚɝɪɟɝɚɬɧɵɦ
ɫɨɫɬɨɹɧɢɟɦ ɬɟɩɥɨɧɨɫɢɬɟɥɹ ɢ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɩɨɬɨɤɚ)
Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɩɢɫɚɧɢɟ ɧɚ ɨɫɧɨɜɟ ɮɢɡɢɤɢ ɩɪɨɰɟɫɫɚ
Ɉɛɳɚɹ ɬɟɩɥɨɜɚɹ ɧɚɝɪɭɡɤɚ ɢɫɩɚɪɢɬɟɥɹ Q:
QQ Q . (152)
ɝɪ ɤ
ɇɚ ɨɫɧɨɜɚɧɢɢ ɭɪɚɜɧɟɧɢɹ ɬɟɩɥɨɩɟɪɟɞɚɱɢ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ:
()QfF ɢ
ɝɪ ɝɪ
()QfF . (153)
ɤɤ
ɉɪɢ ɬɟɩɥɨɩɟɪɟɞɚɱɟ ɨɬ ɝɪɟɸɳɟɝɨ ɩɚɪɚ ɢ ɤɨɧɞɟɧɫɚɬɚ ɱɟɪɟɡ ɬɪɭɛɤɢ ɫɩɪɚɜɟɞɥɢɜɵ ɫɨɨɬɧɨɲɟɧɢɹ:
Ɉɛɳɚɹ ɩɨɜɟɪɯɧɨɫɬɶ ɬɟɩɥɨɩɟɪɟɞɚɱɢ F
ɨɩɪɟɞɟɥɢɬɫɹ ɤɚɤ:
F
ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɧɚ ɨɫɧɨɜɚɧɢɢ (154) ɢ (155) ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ:
Ɉɩɪɟɞɟɥɟɧɢɟ
ɷɮɮ
G ɧɚ ɨɫɧɨɜɚɧɢɢ ɬɟɩɥɨɜɨɝɨ ɛɚɥɚɧɫɚ ɩɨ ɝɪɟɸɳɟɦɭ ɩɚɪɭ:
ɝɪ
()FfH h ɢ
ɝɪ ɬɪɭɛ ɤ
ɬ ɩɪɢ ɤɨɧɞɟɧɫɚɰɢɢ ɝɪɟɸɳɟɝɨ ɩɚɪɚ
= Fɩ + Fɤ, (155)
ɬ
()Ffh . (156)
ɬɤ
; (157)
G
TT
ɝɪ ɪɝɪ ɝɪ ɤ ɪɤ ɤ ɝɪ ɝɪ
QGc
ɷɮɮ
ɝɪ
c
ɪɝɪ ɝɪ
ɤɪɤɤ
T
54
T
()Ffh . (154)
ɤɤ
rQGc Gc G
Q
. (158)
r
ɝɪ
Ɉɩɪɟɞɟɥɟɧɢɟ
ɷɮɮ
G ɧɚ ɨɫɧɨɜɚɧɢɢ ɬɟɩɥɨɜɨɝɨ ɛɚɥɚɧɫɚ ɩɨ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɦɭ
ɠ
ɩɨɬɨɤɭ:
QGc Gc
; (159)
ɷɮɮ
G
.
ɠ
ɜɯ
TT
ɠɪɠ ɠ ɩɪɩɩ
QGc
c
ɪɠ ɠ
T
ɩɪɩɩ
ɜɯ
T
(160)
ȼɵɜɨɞɵ ɢɡ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɨɩɢɫɚɧɢɹ ɮɢɡɢɤɢ ɩɪɨɰɟɫɫɚ:
ɨɛɳɚɹ ɬɟɩɥɨɜɚɹ ɧɚɝɪɭɡɤɚ, ɨɬɞɚɜɚɟɦɚɹ ɝɪɟɸɳɢɦ ɩɚɪɨɦ, ɡɚɜɢɫɢɬ ɫɥɟ-
ɞɭɸɳɢɯ ɟɝɨ ɩɚɪɚɦɟɬɪɨɜ:
{,(),,()}QfGrP Fh
; (161)
ɝɪ ɝɪ ɝɪ ɝɪ ɬ ɤ
T
ɨɛɳɚɹ ɬɟɩɥɨɜɚɹ ɧɚɝɪɭɡɤɚ, ɩɨɥɭɱɚɟɦɚɹ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɦ ɩɨɬɨɤɨɦ,
ɨɩɪɟɞɟɥɹɟɬ ɫɥɟɞɭɸɳɢɟ ɟɝɨ ɩɚɪɚɦɟɬɪɵ:
()PfQ ɢ
ɩ
ɠ
()rfP ; (162)
ɠɩ
()hfQ . (163)
Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɩɢɫɚɧɢɟ ɧɚ ɨɫɧɨɜɟ ɬɟɩɥɨɜɨɝɨ ɢ ɦɚɬɟɪɢɚɥɶɧɵɯ ɛɚɥɚɧɫɨɜ
ɩɪɨɰɟɫɫɚ
Ɍɟɩɥɨɜɨɣ ɛɚɥɚɧɫ ɢɫɩɚɪɢɬɟɥɹ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ.
ȼ ɪɚɡɜɟɪɧɭɬɨɦ ɜɢɞɟ ɩɪɢ ɭɫɥɨɜɢɢ
Mc Mc Gc Gr
()()
ɠɪɠ ɩɪɩ ɝɪɪɝɪ ɝɪ ɝɪ ɝɪɝɪ
Gc G c G r Gc
ɧɧ
() () ,
TT TT T
ɤɪɤ ɝɪ ɤ ɠɪɠ ɩ ɠ ɠɠ ɩɪɩɩ
ɬ. ɟ. ɬɟɩɥɨ ɜɵɞɟɥɹɟɬɫɹ ɡɚ ɫɱɟɬ ɨɯɥɚɠɞɟɧɢɹ G
T
ɞɨ ɬɟɦɩɟɪɚɬɭɪɵ ɧɚɫɵɳɟɧɧɨɝɨ ɩɚɪɚ
ɪɵ
ɝɪ
ɝɨ ɨɯɥɚɠɞɟɧɢɹ ɤɨɧɞɟɧɫɚɬɚ ɞɨ
ɬɟɩɥɨ ɪɚɫɯɨɞɭɟɬɫɹ ɧɚ ɧɚɝɪɟɜɚɧɢɟ G
ɝɪ
TTT
!! ɢ
ɝɪ ɧ ɤ
d
T
dt
ɧ
T
ɝɪ
T
;
ɤ
ɧ
TT
, ɤɨɧɞɟɧɫɚɰɢɢ ɩɚɪɚ ɢ ɩɨɫɥɟɞɭɸɳɟ-
ɞɨ ɬɟɦɩɟɪɚɬɭɪɵ
ɠ
ɩ
TTT
:
ɠɧ ɩ
(164)
ɨɬ ɢɫɯɨɞɧɨɣ ɬɟɦɩɟɪɚɬɭ-
ɝɪ
ɧ
T
, ɢɫɩɚɪɟɧɢɟ
ɩ
ɠɢɞɤɨɫɬɢ ɢ ɨɬɜɨɞɢɬɫɹ ɫ ɨɛɪɚɡɭɸɳɟɣɫɹ ɩɚɪɨɜɨɣ ɮɚɡɨɣ.
ȼ ɫɜɟɪɧɭɬɨɦ ɧɚɢɛɨɥɟɟ ɨɛɳɟɦ ɜɢɞɟ ɜɵɪɚɠɟɧɢɟ (164) ɩɪɟɨɛɪɚɡɭɟɬɫɹ ɤ ɜɢɞɭ:
d
M c M c G c Gc Gc Gc
()
. (165)
ɠ ɪɠ ɩ ɪɩ ɝɪ ɪɝɪ ɝɪ ɤ ɪɤ ɤ ɠ ɪɠ ɠ ɩ ɪɩ ɩ
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ ɩɪɢ
Gc Gc Gc Gc
T
dt
d
T
TT TT
ɠ ɪɠ ɩ ɪɩ ɩ ɝɪ ɪɝɪ ɝɪ ɤ ɪɤ ɤɠ
. (166)
TTTT
ɜɵɯ
ɠ
0
:
dt
55
ȼɵɜɨɞɵ ɩɨ ɬɟɩɥɨɜɨɦɭ ɛɚɥɚɧɫɭ ɩɪɨɰɟɫɫɚ:
`
ɜ ɰɟɥɨɦ ɬɟɦɩɟɪɚɬɭɪɚ ɜ ɢɫɩɚɪɢɬɟɥɟ ɡɚɜɢɫɢɬ ɨɬ ɫɥɟɞɭɸɳɢɯ ɩɚɪɚɦɟɬɪɨɜ
ɩɪɨɰɟɫɫɚ:
(), (), ( ), ( ),
GhGhGh Gh
½
ɝɪ ɤ ɤ ɠ ɠ ɩ ɠ
ɤ
°°
T
ɬɚɤ ɤɚɤ ɬɟɦɩɟɪɚɬɭɪɚ ɜ ɢɫɩɚɪɢɬɟɥɟ ɭ ɩɨɜɟɪɯɧɨɫɬɢ ɪɚɡɞɟɥɚ ɮɚɡ, ɬ. ɟ. ɜ
ɡɨɧɟ ɢɫɩɚɪɟɧɢɹ, ɞɨɥɠɧɚ ɛɵɬɶ ɪɚɜɧɚ ɬɟɦɩɟɪɚɬɭɪɟ ɤɢɩɟɧɢɹ, ɬɨ ɦɨɠɧɨ ɩɨɥɚɝɚɬɶ:
f
®¾
TTT
,,,( ),(),
°°
ɝɪ ɤ ɠ ɝɪ ɝɪ ɠ ɩ
¯¿
rP rPc
T
=
T
=
T
ɠ
ɩ
=
T
ɤɢɩ;
; (167)
ɪi
ɬɟɦɩɟɪɚɬɭɪɚ ɤɢɩɟɧɢɹ ɡɚɜɢɫɢɬ ɨɬ ɞɚɜɥɟɧɢɹ ɩɚɪɨɜɨɣ ɮɚɡɵ ɜ ɢɫɩɚɪɢɬɟɥɟ,
ɬ. ɟ. ɩɪɢ Ɋ
ɩ
no
T
n (ɩɪɢ ɷɬɨɦ rɠ p).
ɤɢɩ
ɉɨɷɬɨɦɭ ɬɟɦɩɟɪɚɬɭɪɚ ɧɟ ɦɨɠɟɬ ɢɫɩɨɥɶɡɨɜɚɬɶɫɹ ɤɚɤ ɩɨɤɚɡɚɬɟɥɶ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɩɪɨɰɟɫɫɚ ɢɫɩɚɪɟɧɢɹ.
Ɍɟɦɩɟɪɚɬɭɪɚ ɜɚɠɧɚ ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɪɚɫɱɟɬɧɨɣ ɨɛɳɟɣ ɬɟɩɥɨɜɨɣ ɧɚɝɪɭɡɤɢ Q ɜ ɢɫɩɚɪɢɬɟɥɟ, ɬ. ɟ. ɬɟɩɥɨɜɨɝɨ ɛɚɥɚɧɫɚ ɜ ɚɩɩɚɪɚɬɟ.
ɂɡ ɜɵɪɚɠɟɧɢɹ (167) ɫɥɟɞɭɟɬ, ɱɬɨ ɨɫɧɨɜɧɵɦɢ ɩɚɪɚɦɟɬɪɚɦɢ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɦɢ ɞɚɧɧɵɣ ɩɪɨɰɟɫɫ, ɹɜɥɹɸɬɫɹ:
ɭɪɨɜɟɧɶ h
ɭɪɨɜɟɧɶ h
ɢ ɞɚɜɥɟɧɢɟ Ɋɩ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɩɨɬɨɤɚ ɜ ɢɫɩɚɪɢɬɟɥɟ;
ɠ
ɢ ɞɚɜɥɟɧɢɟ Ɋ
ɤ
ɩɨɬɨɤɚ ɝɪɟɸɳɟɝɨ ɩɚɪɚ ɜ ɤɢɩɹɬɢɥɶɧɢɤɟ.
ɝɪ
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɠɢɞɤɨɣ ɮɚɡɟ ɜ ɢɫɩɚɪɢɬɟɥɟ (ɞɥɹ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ
ɩɨɬɨɤɚ)
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
dh
ɠ
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ ɩɪɢ
SGG
U
ɠɚɩɩ ɠ ɩ
dh
ɠ
:
dt
. (168)
dt
0
GG . (169)
ɠɩ
ɇɚ ɨɫɧɨɜɚɧɢɢ (168) ɢ (169) ɦɨɠɧɨ ɫɱɢɬɚɬɶ:
hfGGG . (170)
ɠɠɩɪ
ɉɪɟɞɩɨɱɬɢɬɟɥɶɧɨɟ ɭɩɪɚɜɥɹɸɳɟɟ ɜɨɡɞɟɣɫɬɜɢɟ G
,( )
^
ɝ
.
ɝɪ
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɠɢɞɤɨɣ ɮɚɡɟ ɜ ɤɢɩɹɬɢɥɶɧɢɤɟ (ɞɥɹ ɤɨɧɞɟɧɫɚɬɚ
ɝɪɟɸɳɟɝɨ ɩɚɪɚ)
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
dh
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ ɩɪɢ
U
ɤɦɬɪ ɝɪ ɤ
dh
ɤ
dt
ɤ
SGG
:
. (171)
dt
0
56
GG . (172)
ɝɪ ɤ
ɇɚ ɨɫɧɨɜɚɧɢɢ (171) ɢ (172) ɦɨɠɧɨ ɫɱɢɬɚɬɶ:
(,)hfGG .
ɤɝɪɤ
ɉɪɟɞɩɨɱɬɢɬɟɥɶɧɨɟ ɭɩɪɚɜɥɹɸɳɟɟ ɜɨɡɞɟɣɫɬɜɢɟ ɹɜɥɹɟɬɫɹ ɨɬɛɨɪ ɤɨɧɞɟɧɫɚɬɚ G
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɩɚɪɨɜɨɣ ɮɚɡɟ ɞɥɹ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɩɨɬɨɤɚ ɜ ɢɫɩɚɪɢɬɟɥɟ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
VM dP
ɩɩ ɩ
R
T
ɩ
ɝɞɟ Ɇ
– ɦɨɥɶɧɚɹ ɦɚɫɫɚ ɩɚɪɨɜɨɣ ɮɚɡɵ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɩɨɬɨɤɚ, ɤɝ/ɦɨɥɶ;
ɩ
Ɋ
– ɞɚɜɥɟɧɢɟ ɩɚɪɨɜɨɣ ɮɚɡɵ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɩɨɬɨɤɚ, ɉɚ;
ɩ
T
– ɬɟɦɩɟɪɚɬɭɪɚ ɩɚɪɨɜɨɣ ɮɚɡɵ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɩɨɬɨɤɚ, Ʉ,
ɩ
V
– ɨɛɴɟɦ ɩɚɪɨɜɨɣ ɮɚɡɵ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɩɨɬɨɤɚ, ɦ3.
ɩ
dP
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ ɩɪɢ
ɩ
0
:
dt
GG
, (173)
ɠɩ
dt
.
ɤ
GG
ɇɚ ɨ
ɫɧɨɜɚɧɢɢ (173) ɢ (174) ɦɨɠɧɨ ɫɱɢɬɚɬɶ:
ɩɩɤ
. (174)
ɠɩ
(,)PfGG . (175)
ɉɪɟɞɩɨɱɬɢɬɟɥɶɧɨɟ ɭɩɪɚɜɥɹɸɳɟɟ ɜɨɡɞɟɣɫɬɜɢɟ G
Ɇɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ ɩɨ ɩɚɪɨɜɨɣ ɮɚɡɟ ɞɥɹ ɤɢɩɹɬɢɥɶɧɢɤɚ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
VM dP
ɝɪ ɝɪ ɝɪ
R
T
ɝɪ
ɝɞɟ Ɇ
Ɋ
T
V
– ɦɨɥɶɧɚɹ ɦɚɫɫɚ ɩɚɪɨɜɨɣ ɮɚɡɵ ɝɪɟɸɳɟɝɨ ɩɚɪɚ, ɤɝ/ɦɨɥɶ;
ɝɪ
– ɞɚɜɥɟɧɢɟ ɩɚɪɨɜɨɣ ɮɚɡɵ ɝɪɟɸɳɟɝɨ ɩɚɪɚ, ɉɚ;
ɝɪ
– ɬɟɦɩɟɪɚɬɭɪɚ ɩɚɪɨɜɨɣ ɮɚɡɵ ɝɪɟɸɳɟɝɨ ɩɚɪɚ, Ʉ
ɝɪ
– ɨɛɴɟɦ ɩɚɪɨɜɨɣ ɮɚɡɵ ɝɪɟɸɳɟɝɨ ɩɚɪɚ, ɦ3.
ɝɪ
dP
ɝɪ
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ ɩɪɢ
dt
, (176)
GG
dt
0
:
GG . (177)
ɝɪ ɤ
ɝɪ ɤ
ɇɚ ɨɫɧɨɜɚɧɢɢ (176) ɢ (177) ɦɨɠɧɨ ɫɱɢɬɚɬɶ:
(,)PfGG . (178)
ɝɪ ɝɪ ɤ
ɉɪɟɞɩɨɱɬɢɬɟɥɶɧɨɟ ɭɩɪɚɜɥɹɸɳɟɟ G
ɝɪ
57
.
.
ɩ
ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɢɫɩɚɪɢɬɟɥɹ ɧɚ ɨɫɧɨɜɟ ɦɚɬɟɪɢɚɥɶɧɨɝɨ ɛɚɥɚɧɫɚ
ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 46
Ɋɢɫ. 46. ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɢɫɩɚɪɢɬɟɥɹ ɧɚ ɨɫɧɨɜɟ ɦɚɬɟɪɢɚɥɶɧɨɝɨ ɛɚɥɚɧɫɚ
ȼɨɡɦɨɠɧɵɟ ɭɩɪɚɜɥɹɸɳɢɟ ɜɨɡɞɟɣɫɬɜɢɹ:
,,,GGGG.
ɠɩɤɝɪ
ȼɨɡɦɨɠɧ
ɵɟ ɭɩɪɚɜɥɹɟɦɵɟ ɩɟɪɟɦɟɧɧɵɟ:
,,,hhPP.
ɠɤɩɝɪ
ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɢɫɩɚɪɢɬɟɥɹ ɞɥɹ ɬɢɩɨɜɨɝɨ ɪɟɲɟɧɢɹ ɚɜɬɨɦɚɬɢɡɚɰɢɢ
(ɪɢɫ. 47).
Ɋɢɫ. 47. ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɢɫɩɚɪɢɬɟɥɹ ɞɥɹ ɬɢɩɨɜɨɝɨ ɪɟɲɟɧɢɹ ɚɜɬɨɦɚɬɢɡɚɰɢɢ
ȼ ɬɢɩɨɜɨɦ ɪɟɲɟɧɢɢ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɢɫɩɚɪɢɬɟɥɟɣ ɨɛɴɟɤɬ ɪɚɫɫɦɚɬɪɢɜɚɸɬ ɤɚɤ
ɨɞɧɨɫɜɹɡɧɵɣ ɞɥɹ ɨɫɧɨɜɧɵɯ ɤɚɧɚɥɨɜ ɭɩɪɚɜɥɟɧɢɹ.
Ɉɞɧɚɤɨ ɧɚ ɨɫɧɨɜɚɧɢɢ ɫɯɟɦɵ ɪɢɫ. 47 ɨɛɴɟɤɬ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɦɧɨɝɨɫɜɹɡɧɵɣ.
Ɇɧɨɝɨɫɜɹɡɧɨɫɬɶ ɨɛɴɟɤɬɚ ɫ ɩɨɡɢɰɢɣ ɮɢɡɢɤɢ ɩɪɨɰɟɫɫɚ ɦɨɠɧɨ ɨɛɴɹɫɧɢɬɶ
ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
ɉɪɢ
ɩɩɠ
ɉɪɢ
ɝɪ ɩ ɠ
,,GPhno p n ; ɬ. ɤ. ɩɪɢ
,GPhno n p; ɬ. ɤ. ɩɪɢ
po p n.
ɩɤɢɩɠ
no n p.
ɩɤɢɩɠ
58
,Pr
T
,Pr
T
Ɍɢɩɨɜɚɹ ɫɯɟɦɚ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɢɫɩɚɪɢɬɟɥɟɣ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 48.
Ɋɟɝɭɥɢɪɨɜɚɧɢɟ:
ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɭɪɨɜɧɹ hɠ ɩɨ ɩɨɞɚɱɟ ɝɪɟɸɳɟɝɨ ɩɚɪɚ Gɝɪ – ɤɚɤ ɩɨɤɚɡɚɬɟ-
ɥɹ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɩɪɨɰɟɫɫɚ ɧɚɝɪɟɜɚɧɢɹ ɜ ɢɫɩɚɪɢɬɟɥɟ.
ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɞɚɜɥɟɧɢɹ Ɋ
ɩɨ ɨɬɛɨɪɭ ɩɚɪɨɜɨɣ ɮɚɡɵ ɢɡ ɢɫɩɚɪɢɬɟɥɹ – ɞɥɹ
ɩ
ɨɛɟɫɩɟɱɟɧɢɹ ɦɚɬɟɪɢɚɥɶɧɨɝɨ ɛɚɥɚɧɫɚ ɩɨ ɩɚɪɨɜɨɣ ɮɚɡɟ ɢ ɫɬɚɛɢɥɢɡɚɰɢɢ r
Ʉɨɧɬɪɨɥɶ:
ɪɚɫɯɨɞɵ – G
ɬɟɦɩɟɪɚɬɭɪɵ –
ɞɚɜɥɟɧɢɟ – Ɋ
ɭɪɨɜɟɧɶ – h
, Gɩ, Gɠ;
ɝɪ
,,,
TTTT
ɝɪ ɤ ɠ ɩ
, Ɋɠ Ɋɩ;
ɝɪ
.
ɠ
;
ɋɢɝɧɚɥɢɡɚɰɢɹ:
ɫɭɳɟɫɬɜɟɧɧɵɟ ɨɬɤɥɨɧɟɧɢɹ h
ɪɟɡɤɨɟ ɩɚɞɟɧɢɟ ɪɚɫɯɨɞɚ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɩɨɬɨɤɚ G
ɢ Ɋɩ ɨɬ ɡɚɞɚɧɢɣ;
ɠ
, ɩɪɢ ɷɬɨɦ ɮɨɪ-
ɠ
ɦɢɪɭɟɬɫɹ ɫɢɝɧɚɥ «ȼ ɫɯɟɦɭ ɡɚɳɢɬɵ».
= f (Pɩ).
ɠ
Ɋɢɫ. 48. Ɍɢɩɨɜɚɹ ɫɯɟɦɚ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɢɫɩɚɪɢɬɟɥɟɣ
59
Ɍɢɩɨɜɨɟ ɪɟɲɟɧɢɟ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɢɫɩɚɪɢɬɟɥɟɣ
ɪ
ɪ
ɪ
ɪ
ɪ
ɋɢɫɬɟɦɚ ɡɚɳɢɬɵ.
ɉɨ ɫɢɝɧɚɥɭ «ȼ ɫɯɟɦɭ ɡɚɳɢɬɵ» – ɨɬɤɥɸɱɚɸɬɫɹ ɦɚɝɢɫɬɪɚɥɢ ɩɨɞɚɱɢ ɝɪɟɸɳɟɝɨ ɩɚɪɚ G
ɢ ɨɬɛɨɪɚ ɩɚɪɚ ɞɥɹ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɧɭɠɞ.
ɝɪ
Ⱥɜɬɨɦɚɬɢɡɚɰɢɹ ɩɪɨɰɟɫɫɚ ɜɵɩɚɪɢɜɚɧɢɹ
Ⱦɜɢɠɭɳɚɹ ɫɢɥɚ ɩɪɨɰɟɫɫɚ ɜɵɩɚɪɢɜɚɧɢɹ.
Ⱦɜɢɠɭɳɟɣ ɫɢɥɨɣ ɩɪɨɰɟɫɫɚ ɜɵɩɚɪɢɜɚɧɢɹ ɹɜɥɹɟɬɫɹ ɩɨɥɟɡɧɚɹ ɪɚɡɧɨɫɬɶ ɬɟɦ-
T
ɩɟɪɚɬɭɪ '
'
Ɉɛɳɚɹ ɪɚɡɧɨɫɬɶ ɬɟɦɩɟɪɚɬɭɪ '
'
Ɉɛɳɚɹ ɪɚɡɧɨɫɬɶ ɬɟɦɩɟɪɚɬɭɪ '
T
'
ɧɚ ɜɟɥɢɱɢɧɭ ɩɨɬɟɪɶ 6':
ɩɨɥɟɡɧ
'
ɩɨɥɟɡɧ
:
T
ɩɨɥɟɡɧ
T
T
ɩɨɥɟɡɧ
ɨɛɳ
T
ɨɛɳ
=
T
=
ɨɛɳ
= '
ɤɢɩ
T
–
T
ɬ
. (179)
ɪɚ
ɜ ɩɪɨɰɟɫɫɟ:
ɤɢɩ
T
–
T
ɬ
. (180)
ɥɹ
ɛɨɥɶɲɟ ɩɨɥɟɡɧɨɣ ɪɚɡɧɨɫɬɢ ɬɟɦɩɟɪɚɬɭɪ
T
– 6'. (181)
ɨɛɳ
ȼɟɥɢɱɢɧɚ ɩɨɬɟɪɶ 6' ɜ ɩɪɨɰɟɫɫɟ ɜɵɩɚɪɢɜɚɧɢɹ:
6' = '
– ɩɨɬɟɪɢ ɡɚ ɫɱɟɬ ɝɢɞɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɷɮɮɟɤɬɚ;
ɝɞɟ '
ɝ
– ɬɟɦɩɟɪɚɬɭɪɧɚɹ ɞɟɩɪɟɫɫɢɹ;
'
ɞ
'
– ɩɨɬɟɪɢ ɬɟɦɩɟɪɚɬɭɪɵ ɡɚ ɫɱɟɬ ɝɢɞɪɚɜɥɢɱɟɫɤɢɯ ɩɨɬɟɪɶ ɜ ɬɪɭɛɨɩɪɨɜɨɞɟ.
ɝɩ
ɇɚ ɨɫɧɨɜɚɧɢɢ ɜɵɪɚɠɟɧɢɣ (181) ɢ (182) ɩɨɥɭɱɢɦ ɜɵɪɚɠɟɧɢɟ:
'
T
ɩɨɥɟɡɧ
=
T
+ 'ɞ + 'ɝɩ, (182)
ɝ
ɤɢɩ
–
T
ɬ
– ( 'ɝ + 'ɞ + 'ɝɩ). (183)
ɥɹ
Ɍɟɦɩɟɪɚɬɭɪɧɚɹ ɞɟɩɪɟɫɫɢɹ.
Ɉɩɪɟɞɟɥɟɧɢɟ '
'ɞ =
ɧɚ ɨɫɧɨɜɚɧɢɢ (179) ɢ (180):
ɞ
ɤɢɩ
T
–
T
ɪɚ
ɤɢɩ
. (184)
ɥɹ
Ɉɩɪɟɞɟɥɟɧɢɟ 'ɞ ɩɨ ɞɢɚɝɪɚɦɦɚɦ «Ɋ – T ».
T
Ⱦɢɚɝɪɚɦɦɚ «Ɋ –
» ɞɥɹ ɪɚɫɬɜɨɪɨɜ ɢ ɪɚɫɬɜɨɪɢɬɟɥɟɣ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 49.
Ɋɢɫ. 49. Ⱦɢɚɝɪɚɦɦɚ «Ɋ – T » ɞɥɹ ɪɚɫɬɜɨɪɨɜ ɢ ɪɚɫɬɜɨɪɢɬɟɥɟɣ
60
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