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Файл:Автоматизация процессов химических производств. Учебное пособие
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Ɋɟɤɨɦɟɧɞɭɟɦɵɟ ɫɤɨɪɨɫɬɢ:
ɞɥɹ ɠɢɞɤɨɫɬɟɣ ɜ ɬɪɭɛɚɯ ɞɢɚɦɟɬɪɨɦ 25–57 ɦɦ ɨɬ (1,5–2) ɦ/c ɞɨ (0,06–
0,3) ɦ/ɫ;
ɫɪɟɞɧɹɹ ɪɟɤɨɦɟɧɞɭɟɦɚɹ ɫɤɨɪɨɫɬɶ ɞɥɹ ɦɚɥɨɜɹɡɤɢɯ ɠɢɞɤɨɫɬɟɣ ɫɨɫɬɚɜɥɹ-
ɟɬ 0,2–0,3 ɦ/ɫ;
ɞɥɹ ɝɚɡɨɜ ɩɪɢ ɚɬɦɨɫɮɟɪɧɨɦ ɞɚɜɥɟɧɢɢ ɞɨɩɭɫɤɚɸɬɫɹ ɦɚɫɫɨɜɵɟ ɫɤɨɪɨɫɬɢ
2
ɨɬ 15–20 ɞɨ 2–2,5 ɤɝ/(ɦ
Âɫ), ɚ ɥɢɧɟɣɧɵɟ ɫɤɨɪɨɫɬɢ ɞɨ 25 ɦ/ɫ;
ɞɥɹ ɧɚɫɵɳɟɧɧɵɯ ɩɚɪɨɜ ɩɪɢ ɤɨɧɞɟɧɫɚɰɢɢ ɪɟɤɨɦɟɧɞɭɸɬɫɹ ɞɨ 10 ɦ/ɫ.
Ɍɟɩɥɨɜɚɹ ɧɚɝɪɭɡɤɚ ɚɩɩɚɪɚɬɚ
Ɍɟɩɥɨ, ɨɬɞɚɜɚɟɦɨɟ ɛɨɥɟɟ ɧɚɝɪɟɬɵɦ ɬɟɩɥɨɧɨɫɢɬɟɥɟɦ Q
ɧɚɝɪɟɜ ɛɨɥɟɟ ɯɨɥɨɞɧɨɝɨ ɬɟɩɥɨɧɨɫɢɬɟɥɹ Q
Q
Ɍɚɤ ɤɚɤ Qɩɨɬ = 2–3 %, ɬɨ ɢɦ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ ɢ ɫɱɢɬɚɬɶ:
Q
ɢ ɧɚ ɩɨɬɟɪɢ ɜ ɨɤɪɭɠɚɸɳɭɸ ɫɪɟɞɭ Q
2
= Q2 + Q
1
= Q2 = Q, (95)
1
. (94)
ɩɨɬ
, ɡɚɬɪɚɱɢɜɚɟɬɫɹ ɧɚ
1
ɝɞɟ Q – ɬɟɩɥɨɜɚɹ ɧɚɝɪɭɡɤɚ ɚɩɩɚɪɚɬɚ.
ɍɪɚɜɧɟɧɢɟ ɬɟɩɥɨɜɨɝɨ ɛɚɥɚɧɫɚ ɚɩɩɚɪɚɬɚ
Q = G1(I
– I1Ʉ) = G2(I
1ɇ
– I2ɇ), (96)
2Ʉ
ɝɞɟ G1 ɢ G2 – ɦɚɫɫɨɜɵɟ ɪɚɫɯɨɞɵ ɬɟɩɥɨɧɨɫɢɬɟɥɟɣ, ɤɝ/ɫ;
I
ɢ I
– ɧɚɱɚɥɶɧɵɟ ɷɧɬɚɥɶɩɢɢ ɬɟɩɥɨɧɨɫɢɬɟɥɟɣ, Ⱦɠ/ɤɝ;
1ɇ
2ɇ
I
ɢ I
– ɤɨɧɟɱɧɵɟ ɷɧɬɚɥɶɩɢɢ ɬɟɩɥɨɧɨɫɢɬɟɥɟɣ, Ⱦɠ/ɤɝ.
1Ʉ
2Ʉ
ɗɧɬɚɥɶɩɢɢ ɬɟɩɥɨɧɨɫɢɬɟɥɟɣ:
I
= c
. (97)
i
iTi
Ɍɟɩɥɨɜɨɣ ɛɚɥɚɧɫ ɚɩɩɚɪɚɬɚ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɬɟɩɥɨɧɨɫɢɬɟɥɟɣ, ɧɟ ɢɡɦɟɧɹɸɳɢɯ ɚɝɪɟɝɚɬɧɨɝɨ ɫɨɫɬɨɹɧɢɹ:
Q = G1ɫ1(
T
–
T
1 ɇ
) = G2ɫ2(
1 Ʉ
T
–
T
2 Ʉ
), (98)
2 ɇ
ɝɞɟ ɫ1 ɢ ɫ2 – ɫɪɟɞɧɢɟ ɭɞɟɥɶɧɵɟ ɬɟɩɥɨɟɦɤɨɫɬɢ.
Ɍɟɩɥɨɜɵɟ ɛɚɥɚɧɫɵ ɬɟɩɥɨɧɨɫɢɬɟɥɹ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɟɝɨ ɚɝɪɟɝɚɬɧɨɝɨ ɫɨɫɬɨɹɧɢɹ.
Ɍɟɩɥɨɧɨɫɢɬɟɥɶ – ɧɚɫɵɳɟɧɧɵɣ ɩɚɪ, ɤɨɬɨɪɵɣ ɤɨɧɞɟɧɫɢɪɭɟɬɫɹ, ɢ ɤɨɧɞɟɧɫɚɬ
ɧɟ ɨɯɥɚɠɞɚɟɬɫɹ:
G
T
=
T
=
T
ɧɩ
– i
.
ɤɬ
ɤɬ
= Gɬɫ
)
ɪɬTɬ
– G
ɬ ɫɪɤɬTɤɬ
= Gɬrɬ.
ɬ
ɬ (iɬ
Ɍɟɩɥɨɧɨɫɢɬɟɥɶ – ɩɟɪɟɫɵɳɟɧɧɵɣ ɩɚɪ, ɤɨɬɨɪɵɣ ɤɨɧɞɟɧɫɢɪɭɟɬɫɹ, ɢ ɤɨɧɞɟɧ-
ɫɚɬ ɧɟ ɨɯɥɚɠɞɚɟɬɫɹ:
T
>
T
=
T
ɧɩ
.
ɤɬ
ɬ
ɩɨɬ
.:
41
Q = Qɬ – Q
= G
Ɍɟɩɥɨɧɨɫɢɬɟɥɶ
ɨɯɥɚɠɞɚɟɬɫɹ:
– ɩɟɪɟɫɵɳɟɧɧɵɣ ɩɚɪ, ɤɨɬɨɪɵɣ ɤɨɧɞɟɧɫɢɪɭɟɬɫɹ, ɢ ɤɨɧɞɟɧɫɚɬ
T
>
T
ɬ
ɧɩ
= G
Ɉɫɧɨɜɧɨɟ ɭɪɚɜɧɟɧɢɟ ɬɟɩɥɨɩɟɪɟɞɚɱɢ
Q = K F 'tɫɪ W, (99)
= Gɬ (iɬ – i
ɤɬ
T
– Gɬ ɫ
ɬ ɫɪɬ
ɧɩ
>
T
:
ɤɬ
Q = Qɬ – Qɤɬ = G
(
T
ɬ ɫɪɬ
ɬ
= G
ɬ ɫɪɬ Tɬ
– G
ɬ ɫɪɤɬTɧɩ
ɪɬ Tɧɩ
= G
ɬ ɫɪɬ
–
T
) + Gɬ rɬ + Gɬ ɫ
ɧɩ
– Gɬ ɫ
+ Gɬ ɫ
= G
ɬ ɫɪɬ Tɬ
= Gɬ ɫɪɬ(
ɤɬ)
+ Gɬ ɫ
T
– Gɬ ɫ
ɬ
ɪɬ Tɧɩ
ɪɤɬ
– Gɬ ɫ
ɪɬ Tɧɩ
ɪɤɬTɤɬ
(iɬ – iɤɬ) =
ɬ
+ Gɬ ɫ
T
– Gɬ ɫ
ɧɩ
ɪɤɬTɤɬ
T
ɪɤɬ
ɬ
–
T
– Gɬ ɫ
.
(
T
ɧɩ
ɪɬ Tɧɩ
ɪɤɬTɤɬ
.
) + Gɬ rɬ =
ɧɩ
ɪɤɬ Tɤɬ
–
T
) =
ɤɬ
–
=
=
ɝɞɟ F – ɩɨɜɟɪɯɧɨɫɬɶ ɬɟɩɥɨɨɛɦɟɧɚ;
't
– ɫɪɟɞɧɢɣ ɬɟɦɩɟɪɚɬɭɪɧɵɣ ɧɚɩɨɪ;
ɫɪ
W – ɜɪɟɦɹ ɬɟɩɥɨɨɛɦɟɧɚ;
Ʉ – ɤɨɷɮɮɢɰɢɟɧɬ ɬɟɩɥɨɩɟɪɟɞɚɱɢ:
Q
K
Ft
'
W
ɫɪ
Ⱦɠ ȼɬ
22
ɦɫɝɪɚɞ ɦɝɪɚɞ
. (100)
ȼɵɪɚɠɟɧɢɹ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɚ K ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɫɩɨɫɨɛɚ
ɩɟɪɟɞɚɱɢ ɬɟɩɥɚ.
ɉɪɢ ɩɟɪɟɞɚɱɟ ɬɟɩɥɚ ɬɟɩɥɨɩɪɨɜɨɞɧɨɫɬɶɸ K – ɷɬɨ ɤɨɷɮɮɢɰɢɟɧɬ ɬɟɩɥɨɩɪɨ-
O
ɜɨɞɧɨɫɬɢ
, ɨɩɪɟɞɟɥɹɟɦɵɣ ɧɚ ɨɫɧɨɜɟ ɡɚɤɨɧɚ Ɏɭɪɶɟ:
dQ n
O
K
w
dF t d
W
w
Ⱦɠ ɦ ȼɬ
2
ɦɝɪɚɞɫ
ɦɝɪɚɞ
.
(101)
ɉɪɢ ɤɨɧɜɟɤɬɢɜɧɨɦ ɬɟɩɥɨɨɛɦɟɧɟ K – ɷɬɨ ɤɨɷɮɮɢɰɢɟɧɬ ɬɟɩɥɨɨɬɞɚɱɢ D,
ɨɩɪɟɞɟɥɹɟɦɵɣ ɧɚ ɨɫɧɨɜɟ ɡɚɤɨɧɚ ɇɶɸɬɨɧɚ:
K
D
K
D
()
dF t t d
dF t t d
()
dQ
ɫɬ ɠ
dQ
ɫɬ ɠ
W
W
Ⱦɠ ȼɬ
22
ɦɫɝɪɚɞ ɦɝɪɚɞ
Ⱦɠ ȼɬ
22
ɦɫɝɪɚɞ ɦɝɪɚɞ
,
. (102)
ɉɪɢ ɩɟɪɟɞɚɱɟ ɬɟɩɥɚ ɩɭɬɟɦ ɢɡɥɭɱɟɧɢɹ K – ɤɨɷɮɮɢɰɢɟɧɬ ɜɡɚɢɦɧɨɝɨ ɢɡɥɭɱɟɧɢɹ ɫ
ɢɡɥɭɱɚɸɳɢɯ ɬɟɥ:
1-2
K = ɫ
1-2
=
H
ɩɪ
. K0 . 108
42
2
ɦɝɪɚɞ
ȼɬ
, (103)
ɝɞɟ Ʉ0 – ɤɨɧɫɬɚɧɬɚ ɥɭɱɟɢɫɩɭɫɤɚɧɢɹ;
.
H
=
H
H
ɩɪ
H
1
– ɩɪɢɜɟɞɟɧɧɚɹ ɫɬɟɩɟɧɶ ɱɟɪɧɨɬɵ;
1
2
ɢ
H
– ɫɬɟɩɟɧɢ ɱɟɪɧɨɬɵ ɢɡɥɭɱɚɸɳɢɯ ɬɟɥ.
2
Ⱦɜɢɠɭɳɚɹ ɫɢɥɚ ɩɪɢ ɩɪɹɦɨɬɨɤɟ ɬɟɩɥɨɧɨɫɢɬɟɥɟɣ (ɪɢɫ. 36, ɪɢɫ. 37).
Ɋɢɫ. 36. ɋɯɟɦɚ ɩɪɹɦɨɬɨɱɧɨɝɨ ɞɜɢɠɟɧɢɹ ɬɟɩɥɨɧɨɫɢɬɟɥɟɣ
Ɋɢɫ. 37. Ƚɪɚɮɢɤ ɢɡɦɟɧɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɫɪɟɞɵ ɩɪɢ ɩɪɹɦɨɬɨɤɟ
ɉɪɢ (ǻt
ɉɪɢ
tt'
ɦɚɤɫ
ɦɚɤɫ
ɦɢɧ
/ǻt
2
!':
ɦɢɧ
ɧ 1ɧ 2ɧɤ1ɤ 2ɤ
) < 2:
; ɢ .tt t tt t' ' (104)
tt
''
ɧ
t
' . (105)
ɫɪ
''
tt
ɫɪ
ɦɚɤɫ ɦɢɧ
'
t
2,3lg
ɤ
2
§·
'
¨¸
'
©¹
. (106)
t
ɦɚɤɫ
t
ɦɢɧ
Ⱦɜɢɠɭɳɚɹ ɫɢɥɚ ɩɪɢ ɩɪɨɬɢɜɨɬɨɤɟ ɬɟɩɥɨɧɨɫɢɬɟɥɟɣ
ɋɯɟɦɚ ɩɪɨɬɢɜɨɬɨɱɧɨɝɨ ɞɜɢɠɟɧɢɹ ɬɟɩɥɨɧɨɫɢɬɟɥɟɣ ɩɪɟɞɫɬɚɜɥɟɧ ɧɚ ɪɢɫ. 38.
Ɋɢɫ. 38. ɋɯɟɦɚ ɩɪɨɬɢɜɨɬɨɱɧɨɝɨ ɞɜɢɠɟɧɢɹ ɬɟɩɥɨɧɨɫɢɬɟɥɟɣ
43
Ƚɪɚɮɢɤ ɢɡɦɟɧɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪ ɩɪɢ ɩɪɨɬɢɜɨɬɨɤɟ ɩɪɟɞɫɬɚɜɥɟɧ ɧɚ ɪɢɫ. 39.
Ɋɢɫ. 39. Ƚɪɚɮɢɤ ɢɡɦɟɧɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪ ɩɪɢ ɩɪɨɬɢɜɨɬɨɤɟ
ɧ 1ɧ 2ɤɤ1ɤ 2ɧ
; tt t tt t' ' . (107)
Ɂɚɬɟɦ ɢɫɩɨɥɶɡɭɸɬ ɬɟ ɠɟ ɫɨɨɬɧɨɲɟɧɢɹ, ɱɬɨ ɢ ɞɥɹ ɩɪɹɦɨɬɨɤɚ, ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɫɪɟɞɧɟɣ ɞɜɢɠɭɳɟɣ ɫɢɥɵ ɩɪɨɰɟɫɫɚ.
Ⱥɜɬɨɦɚɬɢɡɚɰɢɹ ɤɨɠɭɯɨɬɪɭɛɧɵɯ ɬɟɩɥɨɨɛɦɟɧɧɢɤɨɜ
ɋɯɟɦɚ ɤɨɠɭɯɨɬɪɭɛɧɨɝɨ ɬɟɩɥɨɨɛɦɟɧɧɢɤɚ ɫ ɧɟɢɡɦɟɧɹɸɳɢɦɫɹ ɚɝɪɟɝɚɬɧɵɦ
ɫɨɫɬɨɹɧɢɟɦ ɜɟɳɟɫɬɜ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 40.
Ɋɢɫ. 40. ɋɯɟɦɚ ɤɨɠɭɯɨɬɪɭɛɧɨɝɨ ɬɟɩɥɨɨɛɦɟɧɧɢɤɚ ɫ ɧɟɢɡɦɟɧɹɸɳɢɦɫɹ ɚɝɪɟɝɚɬɧɵɦ
ɫɨɫɬɨɹɧɢɟɦ ɜɟɳɟɫɬɜ
Ɍɟɯɧɨɥɨɝɢɱɟɫɤɢɣ ɩɪɨɰɟɫɫ: ɧɚɝɪɟɜɚɧɢɟ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɩɨɬɨɤɚ G ɞɨ ɬɟɦ-
ɜɵɯ
ɩɟɪɚɬɭɪɵ ș
ɫ ɩɨɦɨɳɶɸ ɬɟɩɥɨɧɨɫɢɬɟɥɹ Gɬ ɫ ɧɟɢɡɦɟɧɹɸɳɢɦɫɹ ɚɝɪɟɝɚɬɧɵɦ ɫɨ-
ɫɬɨɹɧɢɟɦ.
ɉɨɤɚɡɚɬɟɥɶ ɷɮɮɟɤɬɢɜɧɨɫɬɢ: ș
ɐɟɥɶ ɭɩɪɚɜɥɟɧɢɹ: ɩɨɞɞɟɪɠɚɧɢɟ ș
ɜɵɯ
.
ɜɵɯ
= șɡɞ.
44
Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɩɢɫɚɧɢɟ ɧɚ ɨɫɧɨɜɟ ɮɢɡɢɤɢ ɩɪɨɰɟɫɫɚ
U
U
f
Ⱦɜɢɠɟɧɢɟ ɬɟɩɥɨɧɨɫɢɬɟɥɟɣ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɪɨɬɢɜɨɬɨɤɨɦ ɩɪɢ ɡɚɞɚɧɧɵɯ
ɜɯ ɜɵɯ
ș , ș , ș , ș .
ɬɬ ɜɵɯɜɯ
Ⱦɜɢɠɭɳɚɹ ɫɢɥɚ ɩɪɨɰɟɫɫɚ:
TT
''
ɝɞɟ
' '
ɜɯ ɜɵɯ ɜɵɯ ɜɯ
TT T TT T
ɧɬ ɤɬ
,
'
T
ɫɪ
.
ɧɤ
, (108)
2
Ɍɟɩɥɨɜɚɹ ɧɚɝɪɭɡɤɚ ɚɩɩɚɪɚɬɚ:
Ⱦɠ
Q(Ⱦɠ/ɫ) ɩɨɡɜɨɥɹɟɬ ɨɩɪɟɞɟɥɢɬɶ
QKF
'
G ɢ G
ɬɪɬ ɬ ɬ
ɷɮɮ
G
ɬ
cQ Q
ɪ
ɷɮɮ
.
G
cQ Q
§·
T
ɫɪ
ɷɮɮ
ɬ
ɜɯ ɜɵɯ
()QGc Q Q ; (110)
Q
ɜɯ ɜɵɯ
()
ɪɬ ɬ ɬ
ɜɵɯ ɜɯ
()QGcQ Q ; (112)
Q
ɜɵɯ ɜɯ
()
ɪ
. (109)
¨¸
ɫ
©¹
ɧɚ ɨɫɧɨɜɟ ɬɟɩɥɨɜɵɯ ɛɚɥɚɧɫɨɜ:
ɷɮɮ
; (111)
(113)
ɗɮɮɟɤɬɢɜɧɨɟ ɜɪɟɦɹ ɩɪɟɛɵɜɚɧɢɹ:
ɷɮɮ
W
ɩɪɟɛ
V
. (114)
Ɍ
ɷɮɮ
G
Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɩɢɫɚɧɢɟ ɧɚ ɨɫɧɨɜɟ ɬɟɩɥɨɜɨɝɨ ɛɚɥɚɧɫɚ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
ɜɵɯ
d
T
Vc Gc Gc
ɪɬɪɬɬɬɪ
ɍɪɚɜɧɟɧɢɟ ɫɬɚɬɢɤɢ ɩɪɢ
ɇɚ ɨɫɧɨɜɚɧɢɢ (115) ɢ (116) ɦɨɠɧɨ ɩɪɢɧɹɬɶ:
. (115)
dt
d
T
ɜɯ ɜɵɯ ɜɵɯ ɜɯ
()()Gc Gc
TT T T
ɬɪɬ ɬ ɬ ɪ
ɜɯ ɜɵɯ ɜɵɯ ɜɯ
()()
TT T T
ɜɵɯ
0
:
dt
. (116)
ɜɵɯ
(,)
T
GG
. (117)
ɬ
45
ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɨɛɴɟɤɬɚ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 41.
U
U
U
Ɋɢɫ. 41. ɂɧɮɨɪɦɚɰɢɨɧɧɚɹ ɫɯɟɦɚ ɨɛɴɟɤɬɚ
ȼɨɡɦɨɠɧɵɟ ɭɩɪɚɜɥɹɸɳɢɟ ɜɨɡɞɟɣɫɬɜɢɹ:
ȼɨɡɦɨɠɧɵɟ ɤɨɧɬɪɨɥɢɪɭɟɦɵɟ ɜɨɡɦɭɳɟɧɢɹ:
ȼɨɡɦɨɠɧɵɟ ɧɟɤɨɧɬɪɨɥɢɪɭɟɦɵɟ ɜɨɡɦɭɳɟɧɢɹ: c
ȼɨɡɦɨɠɧɚɹ ɭɩɪɚɜɥɹɟɦɚɹ ɩɟɪɟɦɟɧɧɚɹ:
,GG .
TTT
ɜɵɯ
T
.
ɬ
ɜɯ ɜɯ ɜɯ
,,
ɬɬ
.
p, cpɬ
.
Ⱥɧɚɥɢɡ ɞɢɧɚɦɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɨɛɴɟɤɬɚ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ ɜ ɧɨɪɦɚɥɢɡɨɜɚɧɧɨɦ ɜɢɞɟ.
ɜɵɯ
d
T
Vc Gc Gc Gc
ɪɪɬɪɬɬɬɪ
. (118)
dt
ɇɚ ɨɫɧɨɜɟ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ ɞɢɧɚɦɢɤɢ ɨɛɴɟɤɬ ɩɨ ɤɚɧɚɥɭ
ɜɵɯ ɜɯ ɜɵɯ ɜɯ
TTTT
()
GT ɨɩɢɫɵɜɚ-
ɬ
ɜɵɯ
ɟɬɫɹ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɶɸ ɚɩɟɪɢɨɞɢɱɟɫɤɨɝɨ ɡɜɟɧɚ 1-ɝɨ ɩɨɪɹɞɤɚ:
K
()
Wp
ɨɛ
Tp
ɨɛ
, (119)
1
ɝɞɟ
0 ɜɯ0 ɜɵɯ0
()Gc
TT
Ɍ
;
ɨɛ
0
G
V
K
ɬɪɬ ɬ ɬ
ɨɛ
0 ɜɵɯ0
Gc
ɪ
.
T
Ɉɛɴɟɤɬ ɢɦɟɟɬ ɬɪɚɧɫɩɨɪɬɧɨɟ ɡɚɩɚɡɞɵɜɚɧɢɟ:
V
ɬɪɭɛ
ɬ
WW
, (120)
ɬɪ ɨɛ
ɜɯ
G
ɬ
ɝɞɟ
V
– ɨɛɴɟɦ ɬɪɭɛɨɩɪɨɜɨɞɚ 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:
46
J
Tp
K
ɨɛ
Wp e
()
p
W
ɨɛ
ɨɛ
1
. (121)
Ⱥɧɚɥɢɡ ɫɬɚɬɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɨɛɴɟɤɬɚ
T
ɂɡ ɭɪɚɜɧɟɧɢɹ ɫɬɚɬɢɤɢ ɜɵɪɚɡɢɦ
ɜɵɯ ɜɯ
TT
. (122)
ɋɬɚɬɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɥɢɧɟɣɧɚ ɩɨ ɤɚɧɚɥɚɦ:
ɋɬɚɬɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɧɟɥɢɧɟɣɧɚ ɩɨ ɤɚɧɚɥɭ
ɜ ɹɜɧɨɦ ɜɢɞɟ:
ɜɵɯ
ɜɯ ɜɵɯ
()Gc
TT
Gc
ɪ
ɬɪɬ ɬ ɬ
ɜɯ ɜɯ ɜɵɯ ɜɵɯ
,, ,G
TTT T
ɬɬ ɬ
ɜɵɯ
GT .
.
ɋɬɚɬɢɱɟɫɤɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɦɨɠɧɨ ɥɢɧɟɚɪɢɡɨɜɚɬɶ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ G
GG
ɜɜɟɞɟɧɢɟɦ ɫɬɚɛɢɥɢɡɚɰɢɢ ɫɨɨɬɧɨɲɟɧɢɹ ɪɚɫɯɨɞɨɜ:
ɜɯ ɜɵɯ
()Gc
JTT
ɜɵɯ ɜɯ
TT
ɪɬ ɬ ɬ
Gc
ɪ
, ɬɨɝɞɚ ɩɨɥɭɱɢɦ:
ɬ
. (123)
Ʌɢɧɟɚɪɢɡɨɜɚɧɧɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɫɬɚɬɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɱɟɪɟɡ ɪɚɡɥɨɠɟɧɢɟ ɜ ɪɹɞ Ɍɟɣɥɨɪɚ:
§· §· §·
ɜɵɯ ɜɯ
' ' ' '
TT
¨¸ ¨¸ ¨¸
©¹ ©¹ ©¹
000
ɜɵɯ ɜɵɯ ɜɵɯ
www
TTT
GG
ww
''
GG
ɬ
§· §·
¨¸ ¨¸
©¹ ©¹
ɬ
00
ɜɵɯ ɜɵɯ
ww
TT
ɜɯ ɜɵɯ
TT
ww
ɬɬ
ɜɯ ɜɵɯ
TT
ɬɬ
T
w
ɜɯ
. (124)
Ʌɢɧɟɚɪɢɡɨɜɚɧɧɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɩɪɢɪɚɳɟɧɢɹ ɜɵɯɨɞɧɨɣ ɩɟɪɟɦɟɧɧɨɣ ɱɟɪɟɡ
ɩɪɢɪɚɳɟɧɢɹ ɜɫɟɯ ɜɨɡɦɨɠɧɵɯ ɜɯɨɞɧɵɯ ɩɟɪɟɦɟɧɧɵɯ:
ɜɵɯ ɜɯ ɜɯ ɜɵɯ
KG K G K K K
TTTT
' '''''. (125)
1 ɬ 23 4ɬ 5 ɬ
Ɍɢɩɨɜɚɹ ɫɯɟɦɚ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɤɨɠɭɯɨɬɪɭɛɧɨɝɨ ɬɟɩɥɨɨɛɦɟɧɧɢɤɚ.
Ɍɢɩɨɜɨɟ ɪɟɲɟɧɢɟ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɤɨɠɭɯɨɬɪɭɛɧɵɯ ɬɟɩɥɨɨɛɦɟɧɧɢɤɨɜ (ɪɢɫ. 42)
ɜɤɥɸɱɚɟɬ ɜ ɫɟɛɹ ɩɨɞɫɢɫɬɟɦɵ ɪɟɝɭɥɢɪɨɜɚɧɢɹ, ɤɨɧɬɪɨɥɹ, ɫɢɝɧɚɥɢɡɚɰɢɢ ɢ ɡɚɳɢɬɵ.
47
Ɋɢɫ. 42. Ɍɢɩɨɜɚɹ ɫɯɟɦɚ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɤɨɠɭɯɨɬɪɭɛɧɨɝɨ ɬɟɩɥɨɨɛɦɟɧɧɢɤɚ
Ɍɢɩɨɜɨɟ ɪɟɲɟɧɢɟ ɚɜɬɨɦɚɬɢɡɚɰɢɢ
Ɋɟɝɭɥɢɪɨɜɚɧɢɟ.
ɜɵɯ
T
Ɋɟɝɭɥɢɪɨɜɚɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ
ɩɨ ɩɨɞɚɱɟ ɬɟɩɥɨɧɨɫɢɬɟɥɹ Gɬ ɤɚɤ ɩɨɤɚɡɚ-
ɬɟɥɹ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɩɪɨɰɟɫɫɚ ɧɚɝɪɟɜɚɧɢɹ ɜ ɤɨɠɭɯɨɬɪɭɛɧɨɦ ɬɟɩɥɨɨɛɦɟɧɧɢɤɟ.
Ʉɨɧɬɪɨɥɶ:
ɪɚɫɯɨɞɵ – G
ɬɟɦɩɟɪɚɬɭɪɵ –
ɞɚɜɥɟɧɢɟ – Ɋ
, G;
ɬ
ɜɯɜɵɯɜɯɜɵɯ
,,,
TT TT
ɬɬ
, Ɋ.
ɬ
;
ɋɢɝɧɚɥɢɡɚɰɢɹ:
ɫɭɳɟɫɬɜɟɧɧɵɟ ɨɬɤɥɨɧɟɧɢɹ T
ɪɟɡɤɨɟ ɩɚɞɟɧɢɟ ɪɚɫɯɨɞɚ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɝɨ ɩɨɬɨɤɚ Gp , ɩɪɢ ɷɬɨɦ ɮɨɪ-
ɨɬ ɡɚɞɚɧɢɹ;
ɜɵɯ
ɦɢɪɭɟɬɫɹ ɫɢɝɧɚɥ «ȼ ɫɯɟɦɭ ɡɚɳɢɬɵ».
ɋɢɫɬɟɦɚ ɡɚɳɢɬɵ.
ɉɨ ɫɢɝɧɚɥɭ «ȼ ɫɯɟɦɭ ɡɚɳɢɬɵ» – ɨɬɤɥɸɱɚɟɬɫɹ ɦɚɝɢɫɬɪɚɥɶ ɩɨɞɚɱɢ ɬɟɩɥɨɧɨɫɢɬɟɥɹ G
.
ɬ
ɋɯɟɦɚ ɩɚɪɨɠɢɞɤɨɫɬɧɨɝɨ ɬɟɩɥɨɨɛɦɟɧɧɢɤɚ (ɫ ɢɡɦɟɧɹɸɳɢɦɫɹ ɚɝɪɟɝɚɬɧɵɦ
ɫɨɫɬɨɹɧɢɟɦ ɬɟɩɥɨɧɨɫɢɬɟɥɹ) ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 43.
48
Ɋɢɫ. 43. ɋɯɟɦɚ ɩɚɪɨɠɢɞɤɨɫɬɧɨɝɨ ɬɟɩɥɨɨɛɦɟɧɧɢɤɚ (ɫ ɢɡɦɟɧɹɸɳɢɦɫɹ ɚɝɪɟɝɚɬɧɵɦ
ɫɨɫɬɨɹɧɢɟɦ ɬɟɩɥɨɧɨɫɢɬɟɥɹ)
Ɍɟɯɧɨɥɨɝɢɱɟɫɤɢɣ ɩɨɬɨɤ (ɧɚɝɪɟɜɚɟɦɚɹ ɠɢɞɤɨɫɬɶ) Gɠ ɩɨɞɚɟɬɫɹ ɩɨ ɬɪɭɛɤɚɦ
ɬɟɩɥɨɨɛɦɟɧɧɢɤɚ.
Ɍɟɩɥɨɧɨɫɢɬɟɥɶ ɫ ɢɡɦɟɧɹɸɳɢɦɫɹ ɚɝɪɟɝɚɬɧɵɦ ɫɨɫɬɨɹɧɢɟɦ (ɝɪɟɸɳɢɣ ɩɚɪ) G
ɩɨɞɚɟɬɫɹ ɩɨ ɦɟɠɬɪɭɛɧɨɦɭ ɩɪɨɫɬɪɚɧɫɬɜɭ.
ɜɵɯ
T
ɉɨɤɚɡɚɬɟɥɶ ɷɮɮɟɤɬɢɜɧɨɫɬɢ:
ɐɟɥɶ ɭɩɪɚɜɥɟɧɢɹ: ɩɨɞɞɟɪɠɚɧɢɟ
.
ɠ
ɜɵɯ ɜɵɡ.ɡɞ
TT
.
ɠɠ
Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɩɢɫɚɧɢɟ ɧɚ ɨɫɧɨɜɟ ɮɢɡɢɤɢ ɩɪɨɰɟɫɫɚ
Ɍɟɩɥɨɩɟɪɟɞɚɱɚ ɨɬ ɩɚɪɨɜɨɣ ɮɚɡɵ ɬɟɩɥɨɧɨɫɢɬɟɥɹ:
ɩɠ
QKF
'. (126)
ɩɩɩɫɪ
o
T
Ɍɟɩɥɨɩɟɪɟɞɚɱɚ ɨɬ ɠɢɞɤɨɣ ɮɚɡɵ ɬɟɩɥɨɧɨɫɢɬɟɥɹ:
ɤɠ
o
T
ɝɞɟ
QKF
,QQ – ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɚ, ɩɟɪɟɞɚɜɚɟɦɨɟ ɨɬ ɩɚɪɨɜɨɣ ɮɚɡɵ ɢ ɤɨɧɞɟɧɫɚɬɚ
ɩɤ
', (127)
ɤɤɤɫɪ
ɬɟɩɥɨɧɨɫɢɬɟɥɹ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ, Ⱦɠ/ɫ;
,ɄɄ – ɤɨɷɮɮɢɰɢɟɧɬɵ ɬɟɩɥɨɩɟɪɟɞɚɱɢ ɞɥɹ ɩɚɪɨɜɨɣ ɮɚɡɵ ɢ ɤɨɧɞɟɧɫɚɬɚ ɬɟɩɥɨ-
ɩɤ
ɧɨɫɢɬɟɥɹ, Ⱦɠ/(ɦ
,FF – ɩɨɜɟɪɯɧɨɫɬɶ ɬɟɩɥɨɩɟɪɟɞɚɱɢ ɞɥɹ ɩɚɪɨɜɨɣ ɮɚɡɵ ɢ ɤɨɧɞɟɧɫɚɬɚ ɬɟɩɥɨɧɨ-
ɩɤ
ɫɢɬɟɥɹ, ɦ
2
;
.
2
Ʉ.ɫ);
49
ɩ
ɩɠ ɤɠ
K
f
U
oo
,
TT
'' – ɫɪɟɞɧɹɹ ɞɜɢɠɭɳɚɹ ɫɢɥɚ ɩɪɢ ɬɟɩɥɨɩɟɪɟɞɚɱɟ ɨɬ ɩɚɪɨɜɨɣ ɮɚɡɵ ɤ
ɫɪ ɫɪ
ɠɢɞɤɨɦɭ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɦɭ ɩɨɬɨɤɭ ɢ ɨɬ ɤɨɧɞɟɧɫɚɬɚ ɤ ɠɢɞɤɨɦɭ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɦɭ ɩɨɬɨɤɭ.
Ɉɛɳɚɹ ɬɟɩɥɨɜɚɹ ɧɚɝɪɭɡɤɚ ɩɚɪɨɠɢɞɤɨɫɬɧɨɝɨ ɬɟɩɥɨɨɛɦɟɧɧɢɤɚ:
QQQ
Ɍɚɤ ɤɚɤ
K!! , ɬɨ ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɬɟɩɥɨɩɟɪɟɞɚɱɢ ɨɬ ɩɚɪɨɜɨɣ ɮɚɡɵ ɡɧɚ-
ɩɤ
. (128)
ɤɩ
ɱɢɬɟɥɶɧɨ ɜɵɲɟ, ɱɟɦ ɨɬ ɤɨɧɞɟɧɫɚɬɚ.
/Fɤ, ɤɨɬɨɪɚɹ ɡɚɜɢ-
ɉɨɷɬɨɦɭ ɧɚ ɜɟɥɢɱɢɧɭ Q ɜɥɢɹɟɬ ɜɟɥɢɱɢɧɚ ɫɨɨɬɧɨɲɟɧɢɹ F
ɩ
ɫɢɬ ɨɬ ɭɪɨɜɧɹ ɤɨɧɞɟɧɫɚɬɚ:
F
ɩ
()
h
, (129)
F
ɤ
ɤ
ɝɞɟ
ɤɤ
ɢ
()Ffh
()FfH h . (130)
ɩɬɪɭɛɤ
ɇɚ ɨɫɧɨɜɚɧɢɢ (129) ɨɛɳɚɹ ɬɟɩɥɨɜɚɹ ɧɚɝɪɭɡɤɚ Q ɬɚɤɠɟ ɛɭɞɟɬ ɡɚɜɢɫɟɬɶ ɨɬ
ɭɪɨɜɧɹ ɤɨɧɞɟɧɫɚɬɚ h
Q (Ⱦɠ/ɫ) ɩɨɡɜɨɥɹɟɬ ɨɩɪɟɞɟɥɢɬɶ
ɩɪɢ
h
= h
.
ɤ
ɷɮɮ
:
ɤ
()Qfh , (131)
ɤ
ɷɮɮ
G
ɩ
QGc Gc
G
G
TT
0; (132)
ɩɪɩɩ ɤɪɤɤ
QGc
ɷɮɮ
ɩ
ɷɮɮ
ɠ
c
ɪɠ ɠ ɠ
ɷɮɮ
ɢ
c
ɪɩ ɩ
ɜɵɯ
ɠɪɠɠ
Qh
ɜɵɯ ɜɯ
()
TT
ɧɚ ɨɫɧɨɜɟ ɬɟɩɥɨɜɵɯ ɛɚɥɚɧɫɨɜ:
G
ɠ
T
ɤɪɤɤ
; (133)
T
)
ɜɯ
)ș(
T
cGQ
; (134)
ɠ
()
ɤ
, (135)
ɗɮɮɟɤɬɢɜɧɨɟ ɜɪɟɦɹ ɩɪɟɛɵɜɚɧɢɹ:
ɷɮɮ
W
ɩɪɟɛ ɨɛ
V
ɠɠ
. (136)
G
ɷɮɮ
ɠ
Ɍ
Ɍɟɩɥɨɜɨɣ ɛɚɥɚɧɫ ɩɚɪɨɠɢɞɤɨɫɬɧɨɝɨ ɬɟɩɥɨɨɛɦɟɧɧɢɤɚ
ɍɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɤɢ:
TTT
ɉɨɥɚɝɚɟɦ: ɩɚɪ ɩɟɪɟɝɪɟɬɵɣ ɢ ɤɨɧɞɟɧɫɚɬ ɨɯɥɚɠɞɚɟɬɫɹ
ɜɵɯ
T
d
UTT
Vc Gc Gr
ɠɠɪɠ ɩɪɩ ɩ ɧ ɩɩ
Gc Gc Gc
ɤ ɪɤ ɧ ɤ ɠ ɪɠ ɠ ɠ ɪɠ ɠ
ɠ
dt
TT T T
()
()
ɜɯ ɜɵɯ
50
!!:
ɩɧɤ
. (137)
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