0
00:00:01,190 --> 00:00:02,840
下面的內容

1
00:00:04,850 --> 00:00:06,520
接下來呢就是

2
00:00:08,180 --> 00:00:09,830
16.6.1

3
00:00:11,070 --> 00:00:13,440
項流熱平衡分析

4
00:00:15,350 --> 00:00:16,730
這一節

5
00:00:18,860 --> 00:00:20,380
那這里面呢

6
00:00:20,660 --> 00:00:22,620
給出了一個參數圖

7
00:00:23,760 --> 00:00:23,984

8
00:00:23,984 --> 00:00:26,450
參數圖就是par這個

9
00:00:27,120 --> 00:00:28,240
參數

10
00:00:29,490 --> 00:00:32,120
你看參數圖的內容

11
00:00:32,440 --> 00:00:33,990
首先這個block

12
00:00:37,170 --> 00:00:41,670
說明它是針對這個block來畫的一個參數圖

13
00:00:45,790 --> 00:00:49,480
當然，你也可以在包下面畫參數圖

14
00:00:50,280 --> 00:00:54,180
那這里是block，顯然是要在block下面來畫

15
00:00:55,030 --> 00:00:58,602
然后你看這個就是block的名字了

16
00:00:58,602 --> 00:01:00,270
初始蒸餾器分析

17
00:01:00,880 --> 00:01:03,435
那這個block是沒有的，對不對

18
00:01:03,435 --> 00:01:05,990
之前我們沒有這個block

19
00:01:06,340 --> 00:01:07,410
那顯然

20
00:01:08,210 --> 00:01:09,560
要加上去

21
00:01:09,990 --> 00:01:11,160
這樣一個block

22
00:01:12,730 --> 00:01:15,974
所以呢，這個圖它給出來比較突兀

23
00:01:15,974 --> 00:01:16,670
就是說

24
00:01:16,970 --> 00:01:18,190
很多

25
00:01:18,920 --> 00:01:21,500
中間的東西它就沒有給出來

26
00:01:21,500 --> 00:01:24,510
它直接乓就給出這樣一張圖

27
00:01:24,840 --> 00:01:27,290
但這張圖的話，你要畫出來

28
00:01:28,370 --> 00:01:31,210
需要很多很多的準備的工作

29
00:01:35,310 --> 00:01:36,360
然后呢

30
00:01:36,640 --> 00:01:38,550
框框里就是

31
00:01:39,710 --> 00:01:41,550
這個圖的名字了

32
00:01:41,840 --> 00:01:43,440
恒壓熱平衡

33
00:01:43,440 --> 00:01:45,040
這個地方

34
00:01:49,150 --> 00:01:51,988
然后，我們來看，參數圖是干嘛的

35
00:01:51,988 --> 00:01:53,610
參數圖主要是定義

36
00:01:54,790 --> 00:01:59,220
屬性值之間的數學關系

37
00:02:03,760 --> 00:02:04,780
因為

38
00:02:05,310 --> 00:02:08,500
屬性值之間它會有一些約束嘛

39
00:02:12,050 --> 00:02:13,758
只有滿足這個約束

40
00:02:13,758 --> 00:02:18,030
或者不違反這個約束的屬性值才可以存在

41
00:02:24,610 --> 00:02:26,006
我們隨便舉個例子

42
00:02:26,006 --> 00:02:26,530
比如說

43
00:02:27,410 --> 00:02:28,655
人有身高

44
00:02:28,655 --> 00:02:29,590
有體重

45
00:02:29,870 --> 00:02:31,930
有年齡

46
00:02:32,820 --> 00:02:34,747
那現在我們假設

47
00:02:34,747 --> 00:02:37,156
我們說一個舉例

48
00:02:37,156 --> 00:02:38,842
不一定合理

49
00:02:38,842 --> 00:02:41,010
我們舉個例子

50
00:02:41,010 --> 00:02:43,420
假設有公司招人

51
00:02:43,700 --> 00:02:45,180
但是我要招什么

52
00:02:45,590 --> 00:02:51,970
以厘米為單位的身高，減去以千克為體重的單位

53
00:02:54,330 --> 00:02:57,250
不得少于他的年齡

54
00:02:57,940 --> 00:02:58,640

55
00:02:59,170 --> 00:03:01,803
顯然這里面有個約束

56
00:03:01,803 --> 00:03:03,240
身高、體重、年齡

57
00:03:03,780 --> 00:03:05,550
之間有個什么

58
00:03:05,830 --> 00:03:07,320
有一個不等式，是吧

59
00:03:07,600 --> 00:03:09,280
a-b>c

60
00:03:10,580 --> 00:03:12,350
那這個就是一個約束

61
00:03:14,730 --> 00:03:16,230
那這個約束

62
00:03:17,500 --> 00:03:18,860
可以畫在哪里

63
00:03:19,550 --> 00:03:19,773

64
00:03:19,773 --> 00:03:22,233
當然可以畫在這個block上面

65
00:03:22,233 --> 00:03:22,680
對吧

66
00:03:22,680 --> 00:03:24,470
如果你是一個block的

67
00:03:25,190 --> 00:03:27,640
里面的各個部件

68
00:03:28,140 --> 00:03:30,060
各個屬性的

69
00:03:31,080 --> 00:03:31,763
約束

70
00:03:31,763 --> 00:03:33,130
那可以在

71
00:03:33,650 --> 00:03:36,990
在這個block的約束那個地方

72
00:03:37,500 --> 00:03:39,180
加上這個約束

73
00:03:39,470 --> 00:03:41,866
把那個式子寫a+b<c

74
00:03:41,866 --> 00:03:44,077
a-b>c，類似這樣的

75
00:03:44,077 --> 00:03:45,552
當然也可以是等式

76
00:03:45,552 --> 00:03:47,764
a2+b2=c2

77
00:03:47,764 --> 00:03:48,870
也可以的

78
00:03:51,450 --> 00:03:53,620
直接在約束里面寫可以

79
00:03:55,740 --> 00:03:56,910
但是的話

80
00:03:58,290 --> 00:03:59,330
往往

81
00:03:59,990 --> 00:04:02,340
我們是用什么，用約束塊

82
00:04:04,500 --> 00:04:05,820
這樣一個block

83
00:04:06,240 --> 00:04:07,680
它也是一個block

84
00:04:07,680 --> 00:04:09,840
但是它是一個約束block

85
00:04:11,730 --> 00:04:13,020
也就是說把

86
00:04:13,300 --> 00:04:16,090
block的約束這部分的內容

87
00:04:16,400 --> 00:04:18,390
把它單獨分離出來

88
00:04:19,690 --> 00:04:22,450
放到外面變成了一個約束塊

89
00:04:27,260 --> 00:04:28,023
然后呢

90
00:04:28,023 --> 00:04:29,550
再跟原來的block

91
00:04:29,830 --> 00:04:31,750
用類似組合關系

92
00:04:32,490 --> 00:04:32,716

93
00:04:32,716 --> 00:04:34,530
組合關聯這樣把它

94
00:04:35,190 --> 00:04:36,420
畫過來

95
00:04:38,540 --> 00:04:40,880
那把這個分離出來之后

96
00:04:42,510 --> 00:04:44,010
我們就可以

97
00:04:46,020 --> 00:04:47,080
復用

98
00:04:48,570 --> 00:04:50,000
這個式子了

99
00:04:50,280 --> 00:04:50,984
對不對

100
00:04:50,984 --> 00:04:53,800
如果說這個式子

101
00:04:54,500 --> 00:04:56,920
這個關系或這個約束

102
00:04:57,570 --> 00:04:59,540
可以適用于多個地方

103
00:05:01,060 --> 00:05:03,320
比如說，你看這里

104
00:05:04,150 --> 00:05:06,975
這有個相變熱傳輸方程

105
00:05:06,975 --> 00:05:07,540
對吧

106
00:05:07,540 --> 00:05:10,930
這是同一個方程

107
00:05:15,460 --> 00:05:17,080
是同一個約束

108
00:05:17,500 --> 00:05:21,420
但是呢，這個約束它既適用于冷凝的過程

109
00:05:22,520 --> 00:05:24,459
也適用于煮沸的過程

110
00:05:24,459 --> 00:05:26,613
都是相變嘛

111
00:05:26,613 --> 00:05:27,260
對不對

112
00:05:27,910 --> 00:05:30,950
所以它里面的熱傳輸方程是一樣的

113
00:05:34,150 --> 00:05:36,533
那我們就定義一個約束就行了

114
00:05:36,533 --> 00:05:37,083
然后呢

115
00:05:37,083 --> 00:05:38,916
在參數圖上把它拖上來

116
00:05:38,916 --> 00:05:41,483
變成兩個約束的實例

117
00:05:41,483 --> 00:05:42,950
你看它前面有冒號

118
00:05:42,950 --> 00:05:44,050
冒號前面有

119
00:05:44,050 --> 00:05:45,150
這是煮沸

120
00:05:45,900 --> 00:05:47,080
這是冷凝

121
00:05:48,510 --> 00:05:48,785

122
00:05:48,785 --> 00:05:50,987
一個是可以復用它

123
00:05:50,987 --> 00:05:53,740
第二個就是，分離出來就

124
00:05:54,280 --> 00:05:57,630
我們這里有更大的空間來描述

125
00:05:58,280 --> 00:06:02,980
一些細節來表達更復雜的一些

126
00:06:03,520 --> 00:06:05,440
方程式的細節

127
00:06:06,690 --> 00:06:09,962
所以這里面就有一個這樣的知識點

128
00:06:09,962 --> 00:06:11,190
就是說約束塊

129
00:06:11,720 --> 00:06:14,320
然后，定義好約束塊之后

130
00:06:15,340 --> 00:06:17,040
我們就可以把

131
00:06:17,570 --> 00:06:20,993
各種各樣的block上面的屬性值

132
00:06:20,993 --> 00:06:22,420
把它綁定到

133
00:06:23,170 --> 00:06:25,425
這個約束或者參數這里來

134
00:06:25,425 --> 00:06:25,835
你看

135
00:06:25,835 --> 00:06:28,295
所以這個線是綁定的關系

136
00:06:28,295 --> 00:06:30,140
有一個綁定的關系

137
00:06:30,540 --> 00:06:31,890
綁定到這里來

138
00:06:34,050 --> 00:06:34,290

139
00:06:34,290 --> 00:06:35,730
一個個這樣綁定

140
00:06:40,770 --> 00:06:44,250
所以呢，它們之間是多對一的

141
00:06:47,310 --> 00:06:50,080
同樣的一個

142
00:06:50,460 --> 00:06:51,610
方程式

143
00:06:51,890 --> 00:06:54,160
它可以和很多很多的

144
00:06:54,500 --> 00:06:55,631
block綁定

145
00:06:55,631 --> 00:06:56,310
對不對

146
00:06:56,680 --> 00:07:01,650
因為很可能有很多很多種東西符合，這個方程式本身代表一個什么

147
00:07:02,530 --> 00:07:03,923
本質的規律

148
00:07:03,923 --> 00:07:04,620
對不對

149
00:07:05,150 --> 00:07:07,031
相變熱傳輸方程

150
00:07:07,031 --> 00:07:08,677
這是本質規律

151
00:07:08,677 --> 00:07:10,794
你是煉鋼、煉鐵、煉什么

152
00:07:10,794 --> 00:07:13,381
還是那個蒸餾水

153
00:07:13,381 --> 00:07:16,909
不都是一樣的道理嘛

154
00:07:16,909 --> 00:07:17,380

155
00:07:17,830 --> 00:07:20,030
遵循基本的規律嘛

156
00:07:21,080 --> 00:07:21,950
所以呢

157
00:07:22,990 --> 00:07:25,045
可以有很多很多個

158
00:07:25,045 --> 00:07:27,100
只要你滿足這個

159
00:07:27,380 --> 00:07:28,735
符合這個規律的

160
00:07:28,735 --> 00:07:32,610
你就可以把你的相關屬性值綁定到這里來

161
00:07:32,930 --> 00:07:36,430
你看，它這里綁定的就是我們前面蒸餾水這個

162
00:07:36,720 --> 00:07:38,438
這是初始蒸餾器

163
00:07:38,438 --> 00:07:38,930
這個

164
00:07:40,810 --> 00:07:43,085
這個實例的main1

165
00:07:43,085 --> 00:07:44,451
這是一個流嘛

166
00:07:44,451 --> 00:07:44,906
對吧

167
00:07:44,906 --> 00:07:47,410
然后這里有一個質量流率

168
00:07:47,760 --> 00:07:47,982

169
00:07:47,982 --> 00:07:49,985
單位，單位，這樣

170
00:07:49,985 --> 00:07:52,210
然后綁定到這個地方來

171
00:07:54,980 --> 00:07:55,647
這樣

172
00:07:55,647 --> 00:07:57,650
然后這個綁定到這里

173
00:07:59,370 --> 00:08:00,720
那這里的話

174
00:08:01,610 --> 00:08:04,410
剛才講了有很多準備工作要做了

175
00:08:04,410 --> 00:08:05,410
你看這里

176
00:08:06,380 --> 00:08:08,190
首先你這個單位

177
00:08:09,720 --> 00:08:11,664
你得建立起來吧

178
00:08:11,664 --> 00:08:12,220
對吧

179
00:08:13,410 --> 00:08:15,230
像你看這個是

180
00:08:15,510 --> 00:08:20,240
質量流率，克每秒，水溫是攝氏度

181
00:08:21,570 --> 00:08:23,608
然后這里有一個比熱

182
00:08:23,608 --> 00:08:24,220
比熱

183
00:08:25,650 --> 00:08:27,170
比熱是卡

184
00:08:27,450 --> 00:08:28,620
然后克

185
00:08:30,180 --> 00:08:32,148
每攝氏度

186
00:08:32,148 --> 00:08:33,330
相當于

187
00:08:34,870 --> 00:08:42,270
每克，單位質量，單位溫度變化，需要的熱量，比熱

188
00:08:43,840 --> 00:08:44,620
這個

189
00:08:45,840 --> 00:08:46,684
你看這里

190
00:08:46,684 --> 00:08:49,850
這里是main1

191
00:08:50,130 --> 00:08:52,199
·這個，說明main1是什么

192
00:08:52,199 --> 00:08:53,027
它是水

193
00:08:53,027 --> 00:08:53,441
對吧

194
00:08:53,441 --> 00:08:54,890
所以這個是水的

195
00:08:56,620 --> 00:08:58,289
這個也是水的

196
00:08:58,289 --> 00:08:59,680
你看這個

197
00:09:01,090 --> 00:09:03,363
比熱這個，你看，它是到這里

198
00:09:03,363 --> 00:09:04,311
綁定到這里

199
00:09:04,311 --> 00:09:04,690
你看

200
00:09:05,150 --> 00:09:06,569
水的比熱，對吧

201
00:09:06,569 --> 00:09:07,988
你看它是main4

202
00:09:07,988 --> 00:09:08,934
這里，是吧

203
00:09:08,934 --> 00:09:09,880
水的比熱

204
00:09:10,510 --> 00:09:12,020
這也是水的

205
00:09:15,310 --> 00:09:15,622

206
00:09:15,622 --> 00:09:16,560
這里

207
00:09:16,970 --> 00:09:17,940
水的

208
00:09:18,220 --> 00:09:19,090
水的

209
00:09:20,060 --> 00:09:21,344
還有什么

210
00:09:21,344 --> 00:09:23,270
還有這個

211
00:09:26,000 --> 00:09:28,773
質量流率，還有水溫

212
00:09:28,773 --> 00:09:30,930
水溫和這個溫度

213
00:09:32,840 --> 00:09:34,595
這個綁定，對不對

214
00:09:34,595 --> 00:09:36,100
水溫，溫度，綁定

215
00:09:36,380 --> 00:09:37,374
這也是水的

216
00:09:37,374 --> 00:09:38,965
你看main1這里

217
00:09:38,965 --> 00:09:39,363
對吧

218
00:09:39,363 --> 00:09:39,960

219
00:09:40,780 --> 00:09:42,555
還有一個是什么

220
00:09:42,555 --> 00:09:43,570
這個潛熱

221
00:09:46,020 --> 00:09:47,317
潛熱什么意思

222
00:09:47,317 --> 00:09:47,750
就是

223
00:09:48,450 --> 00:09:49,400

224
00:09:49,890 --> 00:09:51,955
沒有相變的情況下

225
00:09:51,955 --> 00:09:52,730
就是

226
00:09:53,430 --> 00:09:56,471
就純粹是加熱或者是冷卻

227
00:09:56,471 --> 00:09:58,960
沒有相變的情況下

228
00:09:59,580 --> 00:10:00,500
那么

229
00:10:01,820 --> 00:10:03,470
單位質量

230
00:10:06,000 --> 00:10:07,510
的這個

231
00:10:11,820 --> 00:10:12,031

232
00:10:12,031 --> 00:10:14,150
說錯了，說錯了

233
00:10:14,430 --> 00:10:18,630
比熱是沒有相變的情況下

234
00:10:18,630 --> 00:10:23,390
那個單位質量，每變化一度的

235
00:10:24,020 --> 00:10:25,733
需要的熱量

236
00:10:25,733 --> 00:10:27,446
潛熱是什么

237
00:10:27,446 --> 00:10:29,160
相變的情況下

238
00:10:29,950 --> 00:10:31,820
在相變的情況下

239
00:10:32,170 --> 00:10:34,028
每單位質量，就是一克

240
00:10:34,028 --> 00:10:36,584
一克，多少多少卡

241
00:10:36,584 --> 00:10:39,140
單位質量的單位熱量

242
00:10:39,140 --> 00:10:41,232
單位質量所需要的熱量

243
00:10:41,232 --> 00:10:41,464

244
00:10:41,464 --> 00:10:44,950
你看，它是這里是main4，這也是水嘛

245
00:10:45,230 --> 00:10:47,835
所以呢，這個是水的

246
00:10:47,835 --> 00:10:49,920
這是水的，這是水的

247
00:10:50,300 --> 00:10:51,490
這是水的

248
00:10:52,540 --> 00:10:54,200
還有比熱這個

249
00:10:57,280 --> 00:10:58,960
這個地方

250
00:11:00,970 --> 00:11:01,154

251
00:11:01,154 --> 00:11:02,260
你看，放這里

252
00:11:02,260 --> 00:11:03,920
這地方，這個也是水的

253
00:11:05,630 --> 00:11:08,397
水有四個屬性

254
00:11:08,397 --> 00:11:09,320
對吧

255
00:11:10,360 --> 00:11:13,260
那這四個屬性我們怎么表達

256
00:11:13,260 --> 00:11:16,160
我們要給它加上四個值類型

257
00:11:17,180 --> 00:11:19,000
水有四個值

258
00:11:19,300 --> 00:11:21,350
值類型作為它的屬性

259
00:11:21,830 --> 00:11:23,560
那下面這個，你看

260
00:11:26,990 --> 00:11:27,970

261
00:11:28,510 --> 00:11:30,415
dQ/dt

262
00:11:30,415 --> 00:11:32,593
這是一個微分嘛

263
00:11:32,593 --> 00:11:33,410
對不對

264
00:11:34,050 --> 00:11:35,932
微分，下面是時間

265
00:11:35,932 --> 00:11:40,637
然后這個熱量，相當于時間、熱量一個切線

266
00:11:40,637 --> 00:11:41,343
斜率嘛

267
00:11:41,343 --> 00:11:43,931
為什么叫微分

268
00:11:43,931 --> 00:11:46,519
就是那個曲線上的斜率

269
00:11:46,519 --> 00:11:46,990
對吧

270
00:11:49,420 --> 00:11:51,861
你看這個，它就不是水的了

271
00:11:51,861 --> 00:11:53,489
你看，這不是main4

272
00:11:53,489 --> 00:11:54,710
而是整個什么

273
00:11:55,710 --> 00:11:58,400
整個這個蒸餾器的一個

274
00:11:59,960 --> 00:12:01,680
傳熱速率

275
00:12:02,140 --> 00:12:02,574

276
00:12:02,574 --> 00:12:05,612
每秒多少卡

277
00:12:05,612 --> 00:12:06,480
對吧

278
00:12:08,120 --> 00:12:09,146
那這個不是水的

279
00:12:09,146 --> 00:12:10,172
這是哪一個的

280
00:12:10,172 --> 00:12:11,370
這是蒸餾器的

281
00:12:12,940 --> 00:12:14,080
一個屬性

282
00:12:14,360 --> 00:12:14,530

283
00:12:14,530 --> 00:12:16,410
那這個我們都要定義上去

284
00:12:16,410 --> 00:12:18,460
因為我們之前是沒有這個的

285
00:12:18,740 --> 00:12:19,470
對吧

286
00:12:20,820 --> 00:12:21,020

287
00:12:21,020 --> 00:12:22,620
都得一個一個定義

288
00:12:24,930 --> 00:12:28,545
下面還有一些假設什么的，這個就不管它了

289
00:12:28,545 --> 00:12:29,630
就不管它了

290
00:12:32,360 --> 00:12:33,334
這樣來

291
00:12:33,334 --> 00:12:38,450
那這個是非常啰嗦的，那我們一點點來，把這個圖給

292
00:12:38,870 --> 00:12:40,090
弄出來