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ɜɚɧɢɟ ɱɚɫɬɢ ɤɨɧɞɟɧɫɚɬɚ, ɢɞɭɳɟɝɨ ɜ ɢɫɩɚɪɢɬɟɥɶ; 89 – ɤɢɩɟɧɢɟ ɜ ɢɫɩɚɪɢɬɟɥɟ; 671 – ɧɚɝɪɟɜ ɜɨɞɵ ɢ ɩɚɪɨɨɛɪɚɡɨɜɚɧɢɟ ɜ ɩɚɪɨɝɟɧɟɪɚɬɨɪɟ.
ȼ ɦɚɲɢɧɟ ɫɨɜɟɪɲɚɟɬɫɹ ɞɜɚ ɰɢɤɥɚ. ȿɫɥɢ ɭɫɥɨɜɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɫɠɚɬɢɟ ɜ
ɷɠɟɤɬɨɪɟ ɨɬɞɟɥɶɧɨ ɪɚɛɨɱɟɝɨ ɩɚɪɚ (ɩɪɨɰɟɫɫ 2S11) ɢ ɯɨɥɨɞɧɨɝɨ ɩɚɪɚ (ɩɪɨɰɟɫɫ 910), ɬɨ ɩɪɹɦɨɣ ɰɢɤɥ ɛɭɞɟɬ ɢɡɨɛɪɚɠɚɬɶɫɹ ɩɪɨɰɟɫɫɚɦɢ 1115671,
ɚ ɨɛɪɚɬɧɵɣ – ɩɪɨɰɟɫɫɚɦɢ 910589.
ȼ ɫɨɩɥɟ ɩɪɨɢɫɯɨɞɢɬ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ ɞɚɜɥɟɧɢɹ
ɜ ɤɢɧɟɬɢɱɟɫɤɭɸ – ɩɪɨɰɟɫɫ 12
ɧɨɦɭ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɜ ɤɚɦɟɪɟ ɫɦɟɲɟɧɢɹ – ɩɪɨɰɟɫɫ 2
ɜ ɨɛɪɚɬɧɨɦ ɰɢɤɥɟ ɩɪɨɢɫɯɨɞɢɬ ɜ ɞɢɮɮɭɡɨɪɟ – ɩɪɨɰɟɫɫ 34
ɲɢɪɟɧɢɹ 112
ɨɬ ɞɚɜɥɟɧɢɹ ɪɄ ɞɨ ɞɚɜɥɟɧɢɹ ɪ0 ɫ ɩɨɫɥɟɞɭɸɳɢɦ ɫɠɚɬɢɟɦ
S
ɫɦɟɲɚɧɧɨɝɨ ɩɚɪɚ (ɩɪɨɰɟɫɫ 34
; ɩɟɪɟɞɚɱɚ ɷɧɟɪɝɢɢ ɩɪɹɦɨɝɨ ɰɢɤɥɚ ɨɛɪɚɬ-
S
39; ɡɚɬɪɚɬɚ ɪɚɛɨɬɵ
S
. ɉɪɨɰɟɫɫɵ ɪɚɫ-
S
) ɨɬ ɞɚɜɥɟɧɢɹ ɪ0 ɞɨ ɪɄ ɩɨ ɫɭɳɟɫɬɜɭ ɜɵɩɨɥ-
S
ɧɹɟɬɫɹ ɞɥɹ ɩɟɪɟɞɚɱɢ ɪɚɛɨɬɵ ɩɪɹɦɨɝɨ ɰɢɤɥɚ ɨɛɪɚɬɧɨɦɭ.
Ɉɬɧɨɲɟɧɢɟ ɦɚɫɫɨɜɵɯ ɪɚɫɯɨɞɨɜ ɪɚɛɨɱɟɝɨ ɩɚɪɚ G
ɤ ɯɨɥɨɞɧɨɦɭ Gɏɉ
Ɋɉ
ɧɚɡɵɜɚɟɬɫɹ ɤɪɚɬɧɨɫɬɶɸ ɰɢɪɤɭɥɹɰɢɢ ɢɥɢ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɭɞɟɥɶɧɨɝɨ ɪɚɫ-
ɯɨɞɚ ɩɚɪɚ:
ɚ = GɊɉ / Gɏɉ.
ȿɫɥɢ ɩɟɪɟɞɚɱɚ ɪɚɛɨɬɵ ɩɪɹɦɨɝɨ ɰɢɤɥɚ ɨɛɪɚɬɧɨɦɭ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɛɟɡ
ɩɨɬɟɪɶ, ɬɨ ɞɥɹ ɬɟɨɪɟɬɢɱɟɫɤɨɝɨ ɰɢɤɥɚ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ, ɱɬɨ ɚɌ l = l0, ɝɞɟ l ɢ l0 –
ɪɚɛɨɬɵ ɩɪɹɦɨɝɨ ɢ ɨɛɪɚɬɧɨɝɨ ɰɢɤɥɨɜ.
Ɍɨɝɞɚ
ɝɞɟ h – ɷɧɬɚɥɶɩɢɹ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɬɨɱɤɚɯ ɰɢɤɥɚ (ɫɦ. ɪɢɫ. 6.1, ɛ).
Ɍɟɩɥɨɜɨɣ ɛɚɥɚɧɫ ɉɗɏɆ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɤɚɤ:
ɝɞɟ (1 + ɚɌ) qɄ = (1 + ɚɌ)(h
q
= h9 – h8 – ɭɞɟɥɶɧɚɹ ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ;
0
a
= ɚɌ (h1 – h6) – ɬɟɩɥɨɬɚ, ɩɨɞɜɟɞɟɧɧɚɹ ɤ ɩɚɪɨɝɟɧɟɪɚɬɨɪɭ;
Ɍ qȽ
aT qɇ = ɚɌ (h6 – h5) – ɪɚɛɨɬɚ ɧɚɫɨɫɚ.
ɚɌ = l0 / l = (h10 – h9) / [(h1 – h11) – (h6 – h5)],
(1 + ɚɌ) qɄ = q0 + aT qȽ + aT qɇ,
– h5) – ɨɬɜɟɞɟɧɧɚɹ ɬɟɩɥɨɬɚ;
S
4
ɗɮɮɟɤɬɢɜɧɨɫɬɶ ɪɚɛɨɬɵ ɩɪɹɦɨɝɨ ɰɢɤɥɚ ɨɰɟɧɢɜɚɟɬɫɹ ɬɟɪɦɢɱɟɫɤɢɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ:
hhhh
l
K
t
q
Ƚ
81
hh
)()(
56111
.
61
ɏɨɥɨɞɢɥɶɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɹɜɥɹɟɬɫɹ ɷɧɟɪɝɟɬɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɨɛɪɚɬɧɨɝɨ ɰɢɤɥɚ:
q
0
H
T
l
0
hh
89
.
hh
910
Ⱦɥɹ ɷɧɟɪɝɟɬɢɱɟɫɤɨɣ ɨɰɟɧɤɢ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɜɫɟɣ ɦɚɲɢɧɵ ɢɫɩɨɥɶɡɭɟɬɫɹ ɬɟɩɥɨɜɨɣ ɤɨɷɮɮɢɰɢɟɧɬ, ɪɚɜɧɵɣ ɨɬɧɨɲɟɧɢɸ ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ
ɰɢɤɥɚ ɤ ɡɚɬɪɚɱɟɧɧɨɣ ɪɚɛɨɬɟ:
q
]
T
qa
hh
890
.
)(
hhɚ
ɌȽT
61
ɉɚɪɨɷɠɟɤɬɨɪɧɵɟ ɦɚɲɢɧɵ ɪɚɛɨɬɚɸɬ ɥɢɲɶ ɩɪɢ ɫɪɚɜɧɢɬɟɥɶɧɨ ɜɵɫɨɤɢɯ
ɬɟɦɩɟɪɚɬɭɪɚɯ ɤɢɩɟɧɢɹ (45 °ɋ). ɂɯ ɩɪɢɦɟɧɹɸɬ ɱɚɳɟ ɜɫɟɝɨ ɜ ɭɫɬɚɧɨɜɤɚɯ
ɤɨɧɞɢɰɢɨɧɢɪɨɜɚɧɢɹ ɜɨɡɞɭɯɚ ɢɥɢ ɧɚ ɩɪɟɞɩɪɢɹɬɢɹɯ, ɝɞɟ ɬɪɟɛɭɟɬɫɹ ɜ ɛɨɥɶɲɢɯ ɤɨɥɢɱɟɫɬɜɚɯ ɯɨɥɨɞɧɚɹ ɜɨɞɚ ɞɥɹ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɧɭɠɞ.
Ɂɚɞɚɱɚ 6.0. ȼɵɩɨɥɧɢɬɶ ɪɚɫɱɟɬ ɨɫɧɨɜɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɩɚɪɨɷɠɟɤɬɨɪɧɨɣ
ɯɨɥɨɞɢɥɶɧɨɣ ɦɚɲɢɧɵ, ɪɚɛɨɬɚɸɳɟɣ ɩɨ ɬɟɨɪɟɬɢɱɟɫɤɨɦɭ ɰɢɤɥɭ (ɪɢɫ. 6.1), ɞɥɹ
ɫɥɟɞɭɸɳɢɯ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ: ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ Q
= 400 ɤȼɬ;
0
ɬɟɦɩɟɪɚɬɭɪɚ ɤɢɩɟɧɢɹ ɜ ɢɫɩɚɪɢɬɟɥɟ Ɍ0 = 283 Ʉ; ɬɟɦɩɟɪɚɬɭɪɭ ɤɢɩɟɧɢɹ ɜ ɩɚɪɨɝɟɧɟɪɚɬɨɪɟ Ɍ
Ɋ
h
ɩɪɢɧɹɬɶ ɪɚɜɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɝɪɟɸɳɟɝɨ ɩɚɪɚ Ɍh,
Ɋ
Ʉ
ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɵ ɩɪɢɧɹɬɶ ɪɚɜɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɨɯɥɚɠɞɚɸɳɟɣ ɜɨɞɵ
Ɍ
= Ɍ
Ɉɋ
= 293 Ʉ; ɫɬɟɩɟɧɶ ɫɭɯɨɫɬɢ ɩɚɪɚ ɧɚ ɜɵɯɨɞɟ ɢɡ ɩɚɪɨɝɟɧɟɪɚɬɨɪɚ
W
1
ɯ = 1, ɧɚ ɜɵɯɨɞɟ ɢɡ ɢɫɩɚɪɢɬɟɥɹ ɯ = 1. Ɋɚɛɨɱɟɟ ɜɟɳɟɫɬɜɨ ɜɨɞɚ.
Ɋɟɲɟɧɢɟ. ɉɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɫɯɟɦɟ ɢ ɰɢɤɥɭ, ɩɪɟɞɫɬɚɜɥɟɧɧɵɦ ɧɚ ɪɢ-
ɫɭɧɤɟ 6.1, ɩɚɪɚɦɟɬɪɵ ɭɡɥɨɜɵɯ ɬɨɱɟɤ ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥɢɰɟ 6.1.
ɉɚɪɚɦɟɬɪɵ ɪɚɛɨɱɟɝɨ ɜɟɳɟɫɬɜɚ ɜ ɬɨɱɤɚɯ 1, 5, 7, 9 ɨɩɪɟɞɟɥɟɧɵ ɩɨ «Ɍɚɛɥɢɰɚɦ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɯ ɫɜɨɣɫɬɜ ɜɨɞɵ ɢ ɜɨɞɹɧɨɝɨ ɩɚɪɚ» [9], ɚ
ɩɚɪɚɦɟɬ-
ɪɵ ɜ ɬɨɱɤɚɯ 2, 4, 10, 11 – ɩɨ hs-ɞɢɚɝɪɚɦɦɟ ɞɥɹ ɜɨɞɵ ɢ ɜɨɞɹɧɨɝɨ ɩɚɪɚ.
ɍɞɟɥɶɧɚɹ ɦɚɫɫɨɜɚɹ ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ ɰɢɤɥɚ:
q0 = h9 – h8 = 2519,4 – 125,66 = 2394 ɤȾɠ/ɤɝ.
Ɍɟɨɪɟɬɢɱɟɫɤɚɹ ɤɪɚɬɧɨɫɬɶ ɰɢɪɤɭɥɹɰɢɢ:
ɚɌ = l0 / l = (h10 – h9) / [(h1 – h11) – (h6 – h5)] =
= (2730 – 2519,4) / [(2754,4 – 2050) – (125,66 – 125,66)] = 0,2990.
82
Ɍɚɛɥɢɰɚ 6.1
ɉɚɪɚɦɟɬɪɵ ɭɡɥɨɜɵɯ ɬɨɱɟɤ
ɉɚɪɚɦɟɬɪɵ
1 2s 3 4s 5
ɪ, Ɇɉɚ 0,5723 0,001 0,001 0,0042 0,0042
Ɍ, Ʉ 430 283 283 303 303
h, ɤȾɠ/ɤɝ 2754,4 1900 ɫɦ. ɪɚɫɱɟɬ 2560 125,66
X
, ɦ3/ɤɝ
0,3300 – – – –
ɍɡɥɨɜɵɟ ɬɨɱɤɢ
ɉɚɪɚɦɟɬɪɵ
6 7 8 9 10 11
ɪ, Ɇɉɚ 0,5723 0,5723 0,001 0,001 0,0042 0,0042
Ɍ, Ʉ – 430 283 283 – 283
h, ɤȾɠ/ɤɝ 125,66 662,4 125,66 2519,4 2730 2050
X
, ɦ3/ɤɝ
– – – 99,90 – –
ɍɡɥɨɜɵɟ ɬɨɱɤɢ
ɉɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢ ɬɟɨɪɟɬɢɱɟɫɤɨɝɨ ɰɢɤɥɚ ɪɚɛɨɬɭ ɧɚɫɨɫɚ ɜɵɱɢɫɥɹɸɬ ɩɨ
ɪɚɡɧɨɫɬɢ ɷɧɬɚɥɶɩɢɢ l
= qɇ = (h6 – h5). Ɍɚɤ ɤɚɤ ɜɨɞɚ ɩɨɱɬɢ ɧɟ ɫɠɢɦɚɟɦɚɹ,
ɇ
ɪɚɡɧɨɫɬɶ ɷɧɬɚɥɶɩɢɢ ɨɱɟɧɶ ɦɚɥɚ, ɢ ɟɸ ɩɪɟɧɟɛɪɟɝɚɸɬ.
Ɇɚɫɫɨɜɵɣ ɪɚɫɯɨɞ ɯɨɥɨɞɧɨɝɨ ɩɚɪɚ, ɰɢɪɤɭɥɢɪɭɸɳɟɝɨ ɜ ɰɢɤɥɟ:
Gɏɉ = Q0 / q0 = 400 / 2394 = 0,167 ɤɝ/ɫ.
Ɇɚɫɫɨɜɵɣ ɪɚɫɯɨɞ ɩɚɪɚ, ɰɢɪɤɭɥɢɪɭɸɳɟɝɨ ɜ ɰɢɤɥɟ:
GɊɉ = aɌ Gɏɉ = 0,2990 ā 0,167 = 0,0499 ɤɝ/ɫ.
ɗɧɬɚɥɶɩɢɹ ɜ ɬɨɱɤɟ 3 ɧɚɯɨɞɢɬɫɹ ɢɡ ɭɪɚɜɧɟɧɢɹ ɫɦɟɲɟɧɢɹ:
GɊɉ h
+ Gɏɉ h9 = (Gɏɉ + G
s
2
Ɋ
) h3,
ɉ
ɝɞɟ
h3 = (GɊɉ h
+ Gɏɉ h9) / (Gɏɉ + GɊɉ) =
s
2
= (0,0499 ā 1900 + 0,167 ā 2519,4) / (0,167 + 0,0499) = 2377 ɤȾɠ/ɤɝ.
Ɍɟɩɥɨɬɚ, ɩɨɞɜɟɞɟɧɧɚɹ ɤ ɪɚɛɨɱɟɦɭ ɜɟɳɟɫɬɜɭ ɜ ɩɚɪɨɝɟɧɟɪɚɬɨɪɟ:
QȽ = GɊɉ (h1 – h6) = 0,0499 ā (2754,4 – 125,66) = 131,2 ɤȼɬ.
Ɍɟɩɥɨɬɚ, ɨɬɜɟɞɟɧɧɚɹ ɨɬ ɪɚɛɨɱɟɝɨ ɜɟɳɟɫɬɜɚ ɜ ɤɨɧɞɟɧɫɚɬɨɪɟ:
QɄ = (GɊɉ + Gɏɉ) (h
– h5) = (0,0499 + 0,167) (2560 – 125,66) = 528,0 ɤȼɬ.
s
4
83
Ɍɟɩɥɨɜɨɣ ɛɚɥɚɧɫ ɦɚɲɢɧɵ:
QɄ = Q0 + QȽ + Qɇ = 400 + 131,2 + 0 = 531,2 ɤȼɬ.
Ɋɚɫɯɨɠɞɟɧɢɟ QɄ = 531,2 ɤȼɬ ɫ ɩɨɥɭɱɟɧɧɵɦ ɡɧɚɱɟɧɢɟɦ ɜɩɨɥɧɟ ɞɨɩɭɫɬɢɦɨ ɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨɝɪɟɲɧɨɫɬɶɸ ɩɪɢ ɧɚɯɨɠɞɟɧɢɢ ɷɧɬɚɥɶɩɢɢ ɩɨ hsɞɢɚɝɪɚɦɦɟ.
Ʉɨɧɬɪɨɥɶɧɚɹ ɡɚɞɚɱɚ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ
Ɂɚɞɚɱɚ 6.1. ȼɵɩɨɥɧɢɬɶ ɪɚɫɱɟɬ ɨɫɧɨɜɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɩɚɪɨɷɠɟɤɬɨɪɧɨɣ
ɯɨɥɨɞɢɥɶɧɨɣ ɦɚɲɢɧɵ, ɪɚɛɨɬɚɸɳɟɣ ɩɨ ɬɟɨɪɟɬɢɱɟɫɤɨɦɭ ɰɢɤɥɭ (ɪɢɫ. 6.1),
ɞɥɹ ɫɥɟɞɭɸɳɢɯ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ: ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ Q
ɪɚɬɭɪɚ ɤɢɩɟɧɢɹ ɜ ɢɫɩɚɪɢɬɟɥɟ Ɍ
; ɬɟɦɩɟɪɚɬɭɪɭ ɤɢɩɟɧɢɹ ɜ ɩɚɪɨɝɟɧɟɪɚɬɨɪɟ ɌɊ
0
; ɬɟɦɩɟ-
0
ɩɪɢɧɹɬɶ ɪɚɜɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɝɪɟɸɳɟɝɨ ɩɚɪɚ Ɍh , ɌɊ = Ɍh; ɬɟɦɩɟɪɚɬɭɪɚ ɤɨɧɞɟɧɫɚɰɢɢ Ɍ
ɪɟ ɨɯɥɚɠɞɚɸɳɟɣ ɜɨɞɵ ɌɈɋ = Ɍ
; ɬɟɦɩɟɪɚɬɭɪɭ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɵ ɩɪɢɧɹɬɶ ɪɚɜɧɨɣ ɬɟɦɩɟɪɚɬɭ-
Ʉ
; ɫɬɟɩɟɧɶ ɫɭɯɨɫɬɢ ɩɚɪɚ ɧɚ ɜɵɯɨɞɟ ɢɡ ɩɚɪɨ-
W
1
ɝɟɧɟɪɚɬɨɪɚ ɯ = 1, ɧɚ ɜɵɯɨɞɟ ɢɡ ɢɫɩɚɪɢɬɟɥɹ ɯ = 1. Ɋɚɛɨɱɟɟ ɜɟɳɟɫɬɜɨ ɜɨɞɚ.
ȼɚɪɢɚɧɬɵ ɤɨɧɬɪɨɥɶɧɵɯ ɡɚɞɚɧɢɣ ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥɢɰɟ 6.2.
Ɍɚɛɥɢɰɚ 6.2
ɉɚɪɚɦɟɬɪɵ
Q0, ɤȼɬ 400 500 600 700 800 900 300 400 500 600 700 800
Ɍ0, Ʉ 280 281 282 283 284 285 280 281 282 283 284 285
ɌɄ, Ʉ 290 291 292 293 294 295 295 294 293 291 294 295
ɌɊ, Ʉ 410 420 430 440 450 460 430 420 410 440 450 420
ɌɈɋ, Ʉ 288 287 286 285 288 289 288 299 287 285 299 285
1 2 3 4 5 6 7 8 9 10 11 12
ȼɚɪɢɚɧɬɵ ɤɨɧɬɪɨɥɶɧɵɯ ɡɚɞɚɧɢɣ
84
7. ȺȻɋɈɊȻɐɂɈɇɇɕȿ ɏɈɅɈȾɂɅɖɇɕȿ ɆȺɒɂɇɕ
Ⱥɛɫɨɪɛɰɢɨɧɧɵɟ ɯɨɥɨɞɢɥɶɧɵɟ ɦɚɲɢɧɵ (ȺɏɆ) ɧɚɯɨɞɹɬ ɲɢɪɨɤɨɟ ɩɪɢɦɟɧɟɧɢɟ ɜ ɪɚɡɥɢɱɧɵɯ ɨɬɪɚɫɥɹɯ ɩɪɨɦɵɲɥɟɧɧɨɫɬɢ, ɧɭɠɞɚɸɳɢɯɫɹ ɜ ɢɫɤɭɫɫɬɜɟɧɧɨɦ ɯɨɥɨɞɟ. ɗɮɮɟɤɬɢɜɧɨɫɬɶ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɷɬɢɯ ɦɚɲɢɧ ɜ ɛɨɥɶɲɨɣ
ɫɬɟɩɟɧɢ ɡɚɜɢɫɢɬ ɨɬ ɫɬɨɢɦɨɫɬɢ ɬɟɩɥɨɬɵ, ɪɚɫɯɨɞɭɟɦɨɣ ɞɥɹ ɢɯ ɪɚɛɨɬɵ. ɉɨɷɬɨɦɭ ȺɏɆ ɛɨɥɟɟ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɩɪɢɦɟɧɹɬɶ, ɝɞɟ ɢɦɟɸɬɫɹ ɞɟɲɟɜɵɟ ɢɫɬɨɱɧɢɤɢ ɬɟɩɥɨɬɵ ɜ ɜɢɞɟ ɨɬɪɚɛɨɬɚɜɲɟɝɨ ɜɨɞɹɧɨɝɨ ɩɚɪɚ, ɝɨɪɹɱɟɣ ɜɨɞɵ
, ɞɵɦɨɜɵɯ ɝɚɡɨɜ ɨɬ ɫɠɢɝɚɧɢɹ ɪɚɡɥɢɱɧɵɯ ɜɢɞɨɜ ɬɨɩɥɢɜ, ɬɟɩɥɨɬɵ ɯɢɦɢɱɟɫɤɢɯ ɪɟɚɤɰɢɣ ɢ ɬ. ɞ. ɗɮɮɟɤɬɢɜɧɨɫɬɶ ɩɪɢɦɟɧɟɧɢɹ ɷɬɢɯ ɦɚɲɢɧ ɡɧɚɱɢɬɟɥɶɧɨ ɜɨɡɪɚɫɬɚɟɬ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɢɯ ɞɥɹ ɨɞɧɨɜɪɟɦɟɧɧɨɝɨ ɩɨɥɭɱɟɧɢɹ ɯɨɥɨɞɚ ɢ ɬɟɩɥɨɬɵ ɡɚ ɫɱɟɬ ɫɛɪɨɫɧɨɣ ɬɟɩɥɨɬɵ ɩɪɟɞɩɪɢɹɬɢɹ.
ɉɪɨɰɟɫɫɵ ɢ ɰɢɤɥɵ ȺɏɆ ɨɫɭɳɟɫɬɜɥɹɸɬɫɹ ɫ ɩɨɦɨɳɶɸ ɪɚɫɬɜɨɪɚ, ɫɨ-
ɫɬɨɹɳɟɝɨ ɢɡ ɞɜɭɯ (ɢɧɨɝɞɚ
ɬɪɟɯ) ɤɨɦɩɨɧɟɧɬɨɜ. ɇɚɢɛɨɥɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɵɦɢ ɹɜɥɹɸɬɫɹ ɦɚɲɢɧɵ, ɪɚɛɨɬɚɸɳɢɟ ɧɚ ɛɢɧɚɪɧɨɦ ɪɚɫɬɜɨɪɟ, ɫɨɫɬɨɹɳɟɦ
ɢɡ ɩɨɝɥɨɬɢɬɟɥɹ (ɚɛɫɨɪɛɟɧɬɚ) ɢ ɯɥɚɞɚɝɟɧɬɚ. ȼ ɤɚɱɟɫɬɜɟ ɪɚɫɬɜɨɪɨɜ ɞɥɹ ȺɏɆ
ɜ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɲɢɪɨɤɨɟ ɩɪɢɦɟɧɟɧɢɟ ɩɨɥɭɱɢɥɢ ɪɚɫɬɜɨɪɵ ɚɦɦɢɚɤɚ ɢ
ɛɪɨɦɢɫɬɨɝɨ ɥɢɬɢɹ. ȼ ɜɨɞɨɚɦɦɢɱɧɨɣ ɦɚɲɢɧɟ ɚɦɦɢɚɤ ɹɜɥɹɟɬɫɹ ɯɥɚɞɚɝɟɧɬɨɦ, ɚ ɜ ɛɪɨɦɢɫɬɨɥɢɬɢɟɜɨɣ – ɜɨɞɚ. ȼɨɞɨɚɦɦɢɚɱɧɵɣ ɪɚɫɬɜɨɪ ɫ ɛɨɥɶɲɢɦ
ɫɨɞɟɪɠɚɧɢɟɦ ɯɥɚɞɚɝɟɧɬɚ ɧɚɡɵɜɚɸɬ
ɤɪɟɩɤɢɦ, ɚ ɫ ɦɟɧɶɲɢɦ – ɫɥɚɛɵɦ.
Ɉɫɧɨɜɧɵɟ ɬɪɟɛɨɜɚɧɢɹ, ɩɪɟɞɴɹɜɥɹɟɦɵɟ ɤ ɚɛɫɨɪɛɟɧɬɭ: ɛɨɥɟɟ ɩɨɥɧɚɹ ɢ
ɛɵɫɬɪɚɹ ɪɚɫɬɜɨɪɢɦɨɫɬɶ ɜ ɧɟɦ ɯɥɚɞɚɝɟɧɬɚ; ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɟɟ ɜɵɫɨɤɚɹ ɧɨɪɦɚɥɶɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɤɢɩɟɧɢɹ ɚɛɫɨɪɛɟɧɬɚ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɯɥɚɞɚɝɟɧɬɨɦ.
ɉɪɨɫɬɟɣɲɚɹ ɫɯɟɦɚ ȺɏɆ ɧɟɩɪɟɪɵɜɧɨɝɨ ɞɟɣɫɬɜɢɹ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫɭɧɤɟ 7.1. ȼ ɝɟɧɟɪɚɬɨɪɟ (ɤɢɩɹɬɢɥɶɧɢɤɟ) Ƚ ɩɪɨɢɫɯɨɞɢɬ ɤɢɩɟɧɢɟ ɤɪɟɩɤɨɝɨ
(ɩɨ ɯɥɚɞɚɝɟɧɬɭ) ɪɚɫɬɜɨɪɚ ɡɚ
ɫɱɟɬ ɩɨɞɜɨɞɚ ɬɟɩɥɨɬɵ QȽ ɨɬ ɜɧɟɲɧɟɝɨ ɢɫɬɨɱ-
ɧɢɤɚ. ɉɪɨɰɟɫɫ ɤɢɩɟɧɢɹ ɩɪɨɬɟɤɚɟɬ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɞɚɜɥɟɧɢɢ ɪɄ ɢ ɧɟɩɪɟɪɵɜɧɨɦ ɭɦɟɧɶɲɟɧɢɢ ɤɨɧɰɟɧɬɪɚɰɢɢ ɪɚɫɬɜɨɪɚ ɢ ɩɨɜɵɲɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ
ɟɝɨ ɤɢɩɟɧɢɹ.
Ɉɛɪɚɡɨɜɚɜɲɢɣɫɹ ɩɚɪ ɯɨɥɨɞɢɥɶɧɨɝɨ ɚɝɟɧɬɚ ɩɨɫɬɭɩɚɟɬ ɜ ɤɨɧɞɟɧɫɚɬɨɪ Ʉɞ,
ɝɞɟ ɤɨɧɞɟɧɫɢɪɭɟɬɫɹ ɜɫɥɟɞɫɬɜɢɟ ɨɬɜɨɞɚ ɨɬ ɧɟɝɨ ɬɟɩɥɨɬɵ Q
ɢɫɬɨɱɧɢɤɨɦ ɫ ɬɟɦ-
Ʉ
ɩɟɪɚɬɭɪɨɣ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɵ. Ʉɨɧɞɟɧɫɚɰɢɹ ɩɚɪɚ ɜ ɤɨɧɞɟɧɫɚɬɨɪɟ ɩɪɨɢɫɯɨɞɢɬ ɩɪɢ ɞɚɜɥɟɧɢɢ ɪ
, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɦ ɬɟɦɩɟɪɚɬɭɪɟ ɤɨɧɞɟɧɫɚɰɢɢ ɫɦɟɫɢ. ȿɫ-
Ʉ
ɥɢ ɧɨɪɦɚɥɶɧɵɟ ɬɟɦɩɟɪɚɬɭɪɵ ɤɢɩɟɧɢɹ ɯɥɚɞɚɝɟɧɬɚ ɢ ɚɛɫɨɪɛɟɧɬɚ ɨɬɥɢɱɚɸɬɫɹ
ɫɭɳɟɫɬɜɟɧɧɨ (ɧɚ 200300 °ɋ), ɬɨ ɩɚɪ ɩɪɚɤɬɢɱɟɫɤɢ ɫɨɫɬɨɢɬ ɢɡ ɯɥɚɞɚɝɟɧɬɚ, ɢ
ɟɝɨ ɤɨɧɞɟɧɫɚɰɢɹ ɩɪɨɢɫɯɨɞɢɬ ɩɪɢ ɩɨɫɬɨɹɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɢ ɞɚɜɥɟɧɢɢ.
85
Ⱦɚɥɟɟ ɠɢɞɤɨɫɬɶ ɞɪɨɫɫɟɥɢɪɭɟɬɫɹ ɜ ɞɪɨɫɫɟɥɶɧɨɦ ɜɟɧɬɢɥɟ Ⱦȼ1 ɨɬ ɞɚɜɥɟɧɢɹ ɪ
ɞɨ ɞɚɜɥɟɧɢɹ ɪ0 ɜ ɢɫɩɚɪɢɬɟɥɟ ɂ ɢ ɩɨɫɬɭɩɚɟɬ ɜ ɩɨɫɥɟɞɧɢɣ. Ⱦɚɜɥɟɧɢɟ ɜ
Ʉ
ɢɫɩɚɪɢɬɟɥɟ ɡɚɜɢɫɢɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɤɢɩɟɧɢɹ ɯɥɚɞɚɝɟɧɬɚ, ɤɨɬɨɪɚɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɟɦɩɟɪɚɬɭɪɨɣ ɨɯɥɚɠɞɚɟɦɨɝɨ ɨɛɴɟɤɬɚ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɨɞɜɨɞɚ ɬɟɩɥɨɬɵ Q
ɨɬ ɨɯɥɚɠɞɚɟɦɨɝɨ ɨɛɴɟɤɬɚ ɜ ɢɫɩɚɪɢɬɟɥɟ ɩɪɨɢɫɯɨɞɢɬ ɤɢɩɟɧɢɟ ɠɢɞɤɨ-
0
ɫɬɢ. Ɉɛɪɚɡɨɜɚɜɲɢɣɫɹ ɩɚɪ ɩɨɫɬɭɩɚɟɬ ɚɛɫɨɪɛɟɪ.
Ʉɞ
Q
Ʉ
Q
ɇ
Ƚ
ɪ
Ʉ
ɪ
0
Q
Ⱥ
Ⱦȼ
Ƚ
2
Ⱥ
ɉɆ
Ʉɦ
Ⱦȼ
ɪ
ɂ
ɪ
Ʉ
1
0
Q
0
Ɋɢɫ. 7.1. ɉɪɨɫɬɟɣɲɚɹ ɫɯɟɦɚ ɚɛɫɨɪɛɰɢɨɧɧɨɣ ɯɨɥɨɞɢɥɶɧɨɣ ɦɚɲɢɧɵ:
Ƚ – ɝɟɧɟɪɚɬɨɪ; Ʉɞ – ɤɨɧɞɟɧɫɚɬɨɪ; ɂ – ɢɫɩɚɪɢɬɟɥɶ; Ⱥ – ɚɛɫɨɪɛɟɪ;
Ⱦȼ
– ɞɪɨɫɫɟɥɶɧɵɣ ɜɟɧɬɢɥɶ ɯɥɚɞɚɝɟɧɬɚ; Ⱦȼ2 – ɞɪɨɫɫɟɥɶɧɵɣ ɜɟɧɬɢɥɶ
1
ɪɚɫɬɜɨɪɚ; ɉɆ – ɩɚɪɨɜɚɹ ɦɚɲɢɧɚ; Ʉɦ – ɤɨɦɩɪɟɫɫɨɪ; ɇ – ɧɚɫɨɫ ɪɚɫɬɜɨɪɚ
ɋɥɚɛɵɣ (ɩɨ ɯɥɚɞɚɝɟɧɬɭ) ɪɚɫɬɜɨɪ ɢɡ ɝɟɧɟɪɚɬɨɪɚ ɱɟɪɟɡ ɞɪɨɫɫɟɥɶɧɵɣ
ɜɟɧɬɢɥɶ Ⱦȼ
ɞɚɜɥɟɧɢɟ ɪ
ɩɨɞɚɟɬɫɹ ɜ ɚɛɫɨɪɛɟɪ. ȼ ɝɟɧɟɪɚɬɨɪɟ ɦɚɲɢɧɵ ɩɨɞɞɟɪɠɢɜɚɟɬɫɹ
2
, ɚ ɜ ɚɛɫɨɪɛɟɪɟ – ɞɚɜɥɟɧɢɟ ɪ0, ɬɚɤ ɤɚɤ ɷɬɢ ɚɩɩɚɪɚɬɵ ɩɨ ɩɚɪɨɜɨ-
Ʉ
ɦɭ ɩɪɨɫɬɪɚɧɫɬɜɭ ɫɨɟɞɢɧɟɧɵ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɫ ɤɨɧɞɟɧɫɚɬɨɪɨɦ ɢ ɢɫɩɚɪɢɬɟɥɟɦ. ȼ ɚɛɫɨɪɛɟɪɟ ɩɪɨɢɫɯɨɞɢɬ ɩɨɝɥɨɳɟɧɢɟ ɩɚɪɚ ɫɥɚɛɵɦ ɪɚɫɬɜɨɪɨɦ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɱɟɝɨ ɟɝɨ ɤɨɧɰɟɧɬɪɚɰɢɹ ɩɨɜɵɲɚɟɬɫɹ ɢ ɞɨɯɨɞɢɬ ɞɨ ɤɨɧɰɟɧɬɪɚɰɢɢ,
ɪɚɜɧɨɣ ɧɚɱɚɥɶɧɨɣ ɜ ɩɪɨɰɟɫɫɟ ɤɢɩɟɧɢɹ ɜ ɝɟɧɟɪɚɬɨɪɟ. ɉɪɨɰɟɫɫ ɚɛɫɨɪɛɰɢɢ
ɫɨɩɪɨɜɨɠɞɚɟɬɫɹ, ɤɚɤ ɩɪɚɜɢɥɨ, ɜɵɞɟɥɟɧɢɟɦ ɬɟɩɥɨɬɵ ɚɛɫɨɪɛɰɢɢ Q
, ɤɨɬɨɪɚɹ
Ⱥ
ɨɬɜɨɞɢɬɫɹ ɢɫɬɨɱɧɢɤɨɦ, ɢɦɟɸɳɢɦ ɬɟɦɩɟɪɚɬɭɪɭ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɵ. Ʉɪɟɩɤɢɣ ɪɚɫɬɜɨɪ ɢɡ ɚɛɫɨɪɛɟɪɚ ɧɚɫɨɫɨɦ ɇ ɩɟɪɟɤɚɱɢɜɚɟɬɫɹ ɜ ɝɟɧɟɪɚɬɨɪ.
ȼ ɚɛɫɨɪɛɰɢɨɧɧɨɣ ɯɨɥɨɞɢɥɶɧɨɣ ɦɚɲɢɧɟ ɫ ɩɨɦɨɳɶɸ ɝɟɧɟɪɚɬɨɪɚ, ɞɪɨɫɫɟɥɶɧɨɝɨ ɜɟɧɬɢɥɹ Ⱦȼ
, ɚɛɫɨɪɛɟɪɚ ɢ ɧɚɫɨɫɚ ɫɨɜɟɪɲɚɟɬɫɹ ɩɪɹɦɨɣ ɬɟɪɦɨɞɢ-
2
86
ɧɚɦɢɱɟɫɤɢɣ ɰɢɤɥ, ɚ ɫ ɩɨɦɨɳɶɸ ɤɨɧɞɟɧɫɚɬɨɪɚ, ɞɪɨɫɫɟɥɶɧɨɝɨ ɜɟɧɬɢɥɹ Ⱦȼ1 ɢ
ɢɫɩɚɪɢɬɟɥɹ – ɨɛɪɚɬɧɵɣ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɣ ɰɢɤɥ. Ɉɫɬɚɧɨɜɢɦɫɹ ɧɚ ɷɬɨɦ
ɩɨɞɪɨɛɧɟɟ.
ɉɚɪ ɢɡ ɝɟɧɟɪɚɬɨɪɚ ɦɨɠɧɨ ɧɚɩɪɚɜɢɬɶ ɜ ɩɚɪɨɜɭɸ ɦɚɲɢɧɭ ɉɦ, ɝɞɟ ɩɨɫɥɟ
ɪɚɫɲɢɪɟɧɢɹ ɨɬ ɞɚɜɥɟɧɢɹ ɪ
ɞɨ ɪ0 ɩɨɥɭɱɚɥɚɫɶ ɛɵ ɜɧɟɲɧɹɹ ɪɚɛɨɬɚ L, ɩɨɫɥɟ
Ʉ
ɱɟɝɨ ɨɧ ɧɚɩɪɚɜɥɹɥɫɹ ɛɵ ɜ ɚɛɫɨɪɛɟɪ ɧɚ ɩɨɝɥɨɳɟɧɢɟ ɫɥɚɛɵɦ ɪɚɫɬɜɨɪɨɦ. ȼ ɬɨ
ɠɟ ɜɪɟɦɹ ɩɚɪ ɢɡ ɢɫɩɚɪɢɬɟɥɹ ɦɨɝ ɛɵ ɩɨɫɬɭɩɚɬɶ ɜ ɤɨɦɩɪɟɫɫɨɪ Ʉɦ, ɝɞɟ ɡɚ
ɫɱɟɬ ɡɚɬɪɚɬɵ ɪɚɛɨɬɵ L
ɫɠɢɦɚɥɫɹ ɛɵ ɨɬ ɞɚɜɥɟɧɢɹ ɪ0 ɞɨ ɪɄ ɢ ɩɨɞɚɜɚɥɫɹ
0
ɜ ɤɨɧɞɟɧɫɚɬɨɪ. Ɍɚɤ ɤɚɤ ɜɫɹ ɪɚɛɨɬɚ, ɩɨɥɭɱɟɧɧɚɹ ɜ ɩɚɪɨɜɨɣ ɦɚɲɢɧɟ ɩɪɹɦɨɝɨ
ɰɢɤɥɚ, ɩɨɥɧɨɫɬɶɸ ɪɚɫɯɨɞɭɟɬɫɹ ɧɚ ɩɪɢɜɨɞ ɤɨɦɩɪɟɫɫɨɪɚ ɨɛɪɚɬɧɨɝɨ ɰɢɤɥɚ,
ɬ. ɟ. L = L
, ɬɨ, ɩɨɞɚɜɚɹ ɩɚɪ ɢɡ ɝɟɧɟɪɚɬɨɪɚ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɜ ɤɨɧɞɟɧɫɚɬɨɪ,
0
ɦɨɠɟɦ ɢɫɤɥɸɱɢɬɶ ɢɡ ɫɯɟɦɵ ɩɚɪɨɜɭɸ ɦɚɲɢɧɭ ɢ ɤɨɦɩɪɟɫɫɨɪ ɢ ɬɟɦ ɫɚɦɵɦ
ɫɨɜɦɟɫɬɢɬɶ ɩɪɹɦɨɣ ɢ ɨɛɪɚɬɧɵɣ ɰɢɤɥɵ.
Ɍɟɩɥɨɜɨɣ ɛɚɥɚɧɫ ɩɪɨɫɬɟɣɲɟɣ ɚɛɫɨɪɛɰɢɨɧɧɨɣ ɯɨɥɨɞɢɥɶɧɨɣ ɦɚɲɢɧɵ
ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɬɚɤ:
QȽ + Q0 + QH = QK +QA,
ɝɞɟ QȽ – ɬɟɩɥɨɬɚ, ɩɨɞɜɟɞɟɧɧɚɹ ɜ ɝɟɧɟɪɚɬɨɪɟ ɨɬ ɝɪɟɸɳɟɝɨ ɢɫɬɨɱɧɢɤɚ;
Q
– ɬɟɩɥɨɬɚ, ɩɨɞɜɟɞɟɧɧɚɹ ɜ ɢɫɩɚɪɢɬɟɥɟ ɨɬ ɨɯɥɚɠɞɚɟɦɨɝɨ ɢɫɬɨɱɧɢɤɚ
0
(ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ ɦɚɲɢɧɵ);
Q
– ɪɚɛɨɬɚ ɧɚɫɨɫɚ ɞɥɹ ɩɨɞɚɱɢ ɤɪɟɩɤɨɝɨ ɪɚɫɬɜɨɪɚ ɢɡ ɚɛɫɨɪɛɟɪɚ ɜ ɝɟɧɟ-
ɇ
ɪɚɬɨɪ;
Q
– ɬɟɩɥɨɬɚ, ɨɬɜɟɞɟɧɧɚɹ ɜ ɤɨɧɞɟɧɫɚɬɨɪɟ ɨɯɥɚɠɞɚɸɳɟɣ ɜɨɞɨɣ (ɨɤɪɭ-
Ʉ
ɠɚɸɳɟɣ ɫɪɟɞɨɣ);
Q
– ɬɟɩɥɨɬɚ, ɨɬɜɟɞɟɧɧɚɹ ɜ ɚɛɫɨɪɛɟɪɟ ɨɯɥɚɠɞɚɸɳɟɣ ɜɨɞɨɣ (ɨɤɪɭɠɚ-
Ⱥ
ɸɳɟɣ ɫɪɟɞɨɣ).
ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɷɮɮɟɤɬɢɜɧɨɫɬɶ ȺɏɆ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɟɩɥɨɜɵɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ:
]
= Q0 / (QȽ + Qɇ).
Ɍɚɤ ɤɚɤ QH << QȽ, ɬɨ ɬɟɩɥɨɜɨɣ ɤɨɷɮɮɢɰɢɟɧɬ
]
= Q0 / QȽ.
87
8. ȽȺɁɈȼɕȿ ɏɈɅɈȾɂɅɖɇɕȿ ɆȺɒɂɇɕ
ɏɨɥɨɞɢɥɶɧɵɟ ɦɚɲɢɧɵ, ɜɟɫɶ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɣ ɰɢɤɥ ɤɨɬɨɪɵɯ ɫɨɜɟɪɲɚɟɬɫɹ ɜ ɨɛɥɚɫɬɢ ɫɢɥɶɧɨ ɩɟɪɟɝɪɟɬɨɝɨ ɩɚɪɚ – ɝɚɡɚ, ɧɚɡɵɜɚɸɬɫɹ ɝɚɡɨɜɵɦɢ
ɯɨɥɨɞɢɥɶɧɵɦɢ ɦɚɲɢɧɚɦɢ (ȽɏɆ).
ɉɨ ɩɪɢɧɰɢɩɭ ɩɨɥɭɱɟɧɢɹ ɧɢɡɤɢɯ ɬɟɦɩɟɪɚɬɭɪ ȽɏɆ ɞɟɥɹɬɫɹ ɧɚ ɞɜɚ ɬɢɩɚ:
1) ȽɏɆ, ɜ ɤɨɬɨɪɵɯ ɷɮɮɟɤɬ ɨɯɥɚɠɞɟɧɢɹ ɩɨɥɭɱɚɟɬɫɹ ɜɫɥɟɞɫɬɜɢɟ ɪɚɫɲɢɪɟɧɢɹ ɝɚɡɚ ɜ ɫɩɟɰɢɚɥɶɧɵɯ ɦɚɲɢɧɚɯ – ɞɟɬɚɧɞɟɪɚɯ ɫ ɨɬɞɚɱɟɣ ɜɧɟɲɧɟɣ ɩɨɥɟɡɧɨɣ ɪɚɛɨɬɵ;
2) ȽɏɆ
, ɜ ɤɨɬɨɪɵɯ ɷɮɮɟɤɬ ɨɯɥɚɠɞɟɧɢɹ ɩɨɥɭɱɚɟɬɫɹ ɜ ɜɢɯɪɟɜɵɯ ɬɪɭɛɚɯ
ɛɟɡ ɨɬɞɚɱɢ ɩɨɥɟɡɧɨɣ ɪɚɛɨɬɵ.
ȽɏɆ ɦɨɝɭɬ ɪɚɛɨɬɚɬɶ ɩɨ ɧɟɪɟɝɟɧɟɪɚɬɢɜɧɨɦɭ ɢɥɢ ɪɟɝɟɧɟɪɚɬɢɜɧɨɦɭ
ɰɢɤɥɭ. ȽɏɆ, ɪɚɛɨɱɢɦ ɜɟɳɟɫɬɜɨɦ ɤɨɬɨɪɵɯ ɹɜɥɹɟɬɫɹ ɜɨɡɞɭɯ, ɧɚɡɵɜɚɸɬɫɹ
ɜɨɡɞɭɲɧɵɦɢ ɯɨɥɨɞɢɥɶɧɵɦɢ ɦɚɲɢɧɚɦɢ. ȼɨɡɞɭɯ ɧɟɜɡɪɵɜɨɨɩɚɫɟɧ, ɝɢɝɢɟɧɢɱɟɧ, ɦɨɠɟɬ ɩɨɞɚɜɚɬɶɫɹ ɩɪɹɦɨ ɜ ɨɯɥɚɠɞɚɟɦɨɟ ɩɨɦɟɳɟɧɢɟ, ɬɨɥɶɤɨ ɧɚ ɜɨɡɞɭɯɟ ɦɨɠɧɨ ɩɪɚɤɬɢɱɟɫɤɢ ɨɫɭɳɟɫɬɜɥɹɬɶ ɰɢɤɥɵ ɫ ɬɟɩɥɨɦɚɫɫɨɨɛɦɟɧɨɦ,
ɱɬɨ
ɩɨɡɜɨɥɹɟɬ ɨɛɨɣɬɢɫɶ ɛɟɡ ɜɨɞɹɧɨɝɨ ɬɟɩɥɨɨɛɦɟɧɧɢɤɚ, ɫɧɢɡɢɬɶ ɦɟɬɚɥɥɨɟɦɤɨɫɬɶ ɦɚɲɢɧɵ ɢ ɫɞɟɥɚɬɶ ɟɟ ɩɪɨɫɬɨɣ ɜ ɷɤɫɩɥɭɚɬɚɰɢɢ, ɚ ɩɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ
ɢ ɬɪɚɧɫɩɨɪɬɚɛɟɥɶɧɨɣ.
8.1. Ɍɭɪɛɨɯɨɥɨɞɢɥɶɧɵɟ ɦɚɲɢɧɵ
Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɰɢɤɥ ɧɟɪɟɝɟɧɟɪɚɬɢɜɧɨɣ ȽɏɆ ɫ ɞɟɬɚɧɞɟɪɨɦ. ȽɏɆ
ɜɤɥɸɱɚɟɬ ɫɥɟɞɭɸɳɢɟ ɷɥɟɦɟɧɬɵ (ɪɢɫ. 8.1, ɚ): ɤɨɦɩɪɟɫɫɨɪ Ʉ, ɩɪɨɦɟɠɭɬɨɱɧɵɣ ɯɨɥɨɞɢɥɶɧɢɤ ɉɏ, ɞɟɬɚɧɞɟɪ Ⱦ, ɬɟɩɥɨɨɛɦɟɧɧɵɣ ɚɩɩɚɪɚɬ ɌɈ ɢ ɞɜɢɝɚɬɟɥɶ Ⱦɜ.
Ƚɚɡ ɩɨɫɬɭɩɚɟɬ ɜ ɤɨɦɩɪɟɫɫɨɪ ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ Ɍ
ɟɬɫɹ ɜ ɩɪɨɰɟɫɫɟ 12 ɞɨ ɞɚɜɥɟɧɢɹ ɪ
. ɉɪɢ ɷɬɨɦ ɟɝɨ ɬɟɦɩɟɪɚɬɭɪɚ ɩɨɜɵɲɚɟɬɫɹ
2
, ɞɚɜɥɟɧɢɟɦ ɪ1 ɢ ɫɠɢɦɚ-
1
ɞɨ Ɍ2. Ⱦɚɥɟɟ ɝɚɡ ɩɨɫɬɭɩɚɟɬ ɜ ɩɪɨɦɟɠɭɬɨɱɧɵɣ ɯɨɥɨɞɢɥɶɧɢɤ, ɝɞɟ ɨɬ ɧɟɝɨ ɨɬɜɨɞɢɬɫɹ ɬɟɩɥɨɬɚ Q, ɢ ɨɧ ɨɯɥɚɠɞɚɟɬɫɹ ɞɨ ɬɟɦɩɟɪɚɬɭɪɵ Ɍ
(ɩɪɨɰɟɫɫ 23). Ɂɚ-
3
ɬɟɦ ɝɚɡ ɧɚɩɪɚɜɥɹɟɬɫɹ ɜ ɞɟɬɚɧɞɟɪ, ɝɞɟ ɜ ɩɪɨɰɟɫɫɟ ɪɚɫɲɢɪɟɧɢɹ 34 ɟɝɨ ɬɟɦɩɟɪɚɬɭɪɚ ɫɧɢɠɚɟɬɫɹ ɞɨ Ɍ
ɢ ɪ
= ɪ1). ɉɨɫɥɟ ɷɬɨɝɨ ɯɨɥɨɞɧɵɣ ɝɚɡ ɩɨɫɬɭɩɚɟɬ ɜ ɬɟɩɥɨɨɛɦɟɧɧɵɣ ɚɩɩɚɪɚɬ,
4
, ɚ ɞɚɜɥɟɧɢɟ – ɞɨ ɪ4 (ɜ ɬɟɨɪɟɬɢɱɟɫɤɨɦ ɰɢɤɥɟ ɪ3 = ɪ2
4
ɝɞɟ ɤ ɧɟɦɭ ɩɨɞɜɨɞɢɬɫɹ ɬɟɩɥɨɬɚ Q0 ɨɬ ɢɫɬɨɱɧɢɤɚ ɧɢɡɤɨɣ ɬɟɦɩɟɪɚɬɭɪɵ ɜ
ɩɪɨɰɟɫɫɟ 41. Ɍɟɦɩɟɪɚɬɭɪɚ ɝɚɡɚ ɩɨɜɵɲɚɟɬɫɹ ɞɨ Ɍ
, ɢ ɨɧ ɫɧɨɜɚ ɧɚɩɪɚɜɥɹɟɬ-
1
ɫɹ ɧɚ ɜɫɚɫɵɜɚɧɢɟ ɤɨɦɩɪɟɫɫɨɪɚ.
88
ɉɥɨɳɚɞɶ ɩɨɞ ɩɪɨɰɟɫɫɨɦ 41 ɞɨ ɨɫɢ s (ɪɢɫ. 8.1, ɛ) ɷɤɜɢɜɚɥɟɧɬɧɚ ɭɞɟɥɶ-
ɧɨɣ ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ ɰɢɤɥɚ:
q0 = h1 – h4 = cɊ (Ɍ1 – Ɍ4),
ɚ ɩɥɨɳɚɞɶ ɩɨɞ ɩɪɨɰɟɫɫɨɦ 23 ɞɨ ɨɫɢ s ɷɤɜɢɜɚɥɟɧɬɧɚ ɤɨɥɢɱɟɫɬɜɭ ɬɟɩɥɨɬɵ,
ɨɬɜɨɞɢɦɨɣ ɨɬ ɝɚɡɚ ɜ ɩɪɨɦɟɠɭɬɨɱɧɨɦ ɯɨɥɨɞɢɥɶɧɢɤɟ:
q = h2 – h3 = cP (T2 – T3).
Ⱦ
ɉɏ
4
Q
0
ɌɈ
Q
2 3
Ɍ
Ɍ
Ɍ
Ɉɋ
ɂɇɌ
Ⱦɜ
Ʉ
1
ɚ ɛ
2
ɪ
2
3
4
ɪ
1
1
s
Ɋɢɫ. 8.1. ɉɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ (ɚ)
ɢ ɰɢɤɥ (ɛ) ɝɚɡɨɜɨɣ ɯɨɥɨɞɢɥɶɧɨɣ ɦɚɲɢɧɵ
Ɋɚɛɨɬɚ, ɡɚɬɪɚɱɢɜɚɟɦɚɹ ɜ ɰɢɤɥɟ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɬɟɩɥɨɜɨɝɨ ɛɚɥɚɧɫɚ ɢ
ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɪɚɡɧɨɫɬɶ ɪɚɛɨɬ ɤɨɦɩɪɟɫɫɨɪɚ ɢ ɞɟɬɚɧɞɟɪɚ:
l = q – q0 = (h2 – h1) – (h3 – h4) = lK – lȾ,
ɝɞɟ lK = h2 – h1 – ɪɚɛɨɬɚ ɤɨɦɩɪɟɫɫɨɪɚ ɢ lȾ = h3 – h4 – ɪɚɛɨɬɚ ɞɟɬɚɧɞɟɪɚ.
Ɋɚɛɨɬɚ ɤɨɦɩɪɟɫɫɨɪɚ ɜɫɟɝɞɚ ɛɨɥɶɲɟ ɪɚɛɨɬɵ ɞɟɬɚɧɞɟɪɚ, ɩɨɷɬɨɦɭ ɧɟɞɨ-
ɫɬɚɸɳɚɹ ɪɚɛɨɬɚ ɩɨɞɜɨɞɢɬɫɹ ɤ ȽɏɆ ɢɡɜɧɟ ɨɬ ɩɪɢɜɨɞɧɨɝɨ ɞɜɢɝɚɬɟɥɹ.
Ɇɚɫɫɨɜɵɣ ɪɚɫɯɨɞ ɝɚɡɚ, ɰɢɪɤɭɥɢɪɭɸɳɟɝɨ ɜ ȽɏɆ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɡɚ-
ɞɚɧɧɨɣ ɯɨɥɨɞɨɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ Q
:
0
G = Q0 / q0.
ɏɨɥɨɞɢɥɶɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɰɢɤɥɚ:
H
= q0 / l = q0 / (q – q0).
89
ȿɫɥɢ ɬɟɩɥɨɟɦɤɨɫɬɶ ɝɚɡɚ ɫɱɢɬɚɬɶ ɩɨɫɬɨɹɧɧɨɣ (ɫɊ = const), ɬɨ:
ɌɌ
H
T
41
.
1)/()(1)()(
ɌɌɌɌɌɌɌɌ
41324132
Ⱦɥɹ ɢɡɨɷɧɬɪɨɩɧɵɯ ɩɪɨɰɟɫɫɨɜ 12 ɢ 34, ɩɪɨɯɨɞɹɳɢɯ ɦɟɠɞɭ ɨɞɧɢɦɢ ɢ
ɬɟɦɢ ɠɟ ɞɚɜɥɟɧɢɹɦɢ ɪ
Ɍ
Ɍ
3
2
;
Ɍ
Ɍ
4
1
ɢ ɪ2, ɫɩɪɚɜɟɞɥɢɜɵ ɫɨɨɬɧɨɲɟɧɢɹ:
1
Ɍ
Ɍ
1
2
;
Ɍ
Ɍ
4
3
Ɍ
Ɍ
Ɍ
2
3
1
;11
Ɍ
4
ɌɌ
Ɍ
3
32
ɌɌ
41
,
Ɍ
4
ɫ ɭɱɟɬɨɦ ɤɨɬɨɪɵɯ ɯɨɥɨɞɢɥɶɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɰɢɤɥɚ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ:
H
1
1/
1
.
1/
ɌɌɌɌ
1243
Ɍɟɨɪɟɬɢɱɟɫɤɢɟ ɰɢɤɥɵ ɪɟɝɟɧɟɪɚɬɢɜɧɵɯ ȽɏɆ ɫ ɞɟɬɚɧɞɟɪɨɦ. Ɂɚɦɤ-
ɧɭɬɵɣ ɰɢɤɥ. Ɋɟɝɟɧɟɪɚɬɢɜɧɚɹ ȽɏɆ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɧɟɪɟɝɟɧɟɪɚɬɢɜɧɨɣ ɧɚɥɢ-
ɱɢɟɦ ɪɟɝɟɧɟɪɚɬɨɪɚ Ɋ (ɪɢɫ. 8.2, ɚ), ɜ ɤɨɬɨɪɨɣ «ɩɪɹɦɨɣ» ɩɨɬɨɤ ɝɚɡɚ, ɜɵɯɨɞɹɳɢɣ ɢɡ ɩɪɨɦɟɠɭɬɨɱɧɨɝɨ ɯɨɥɨɞɢɥɶɧɢɤɚ ɉɏ, ɞɨɩɨɥɧɢɬɟɥɶɧɨ ɨɯɥɚɠɞɚɟɬɫɹ
ɩɟɪɟɞ ɜɯɨɞɨɦ ɜ ɞɟɬɚɧɞɟɪ ɜ ɩɪɨɰɟɫɫɟ 34.
ɉɏ
Ɋ
6
Q
0
ɌɈ
Q
2 3
Ⱦ Ⱦɜ
1
Ɍ
Ɍ
Ɉɋ
Ʉ
Ɍ
ɂɇɌ
4
5
ɚ ɛ
ɪ
2
2
3
4
6
5
q
ɊȿȽ
ɪ
1
1
s
Ɋɢɫ. 8.2. ɉɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ (ɚ) ɢ ɰɢɤɥ (ɛ) ɝɚɡɨɜɨɣ
ɯɨɥɨɞɢɥɶɧɨɣ ɦɚɲɢɧɵ
90
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