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͠ΗͱҐཔɼͤͲͶ  ೧Ν‫ܨ‬գͪ͢ɽ͞͹ؔͶླྀΗָ͹‫ڂݜ‬ͺ໪ְΉ͢͏਒ิ൅ఴΝͳͪ͗͝ɼຌॽ͹Ճ஍ͺ͏͖͠͠΍ਲ͓Ζ͞ͳͺ͵͖ͮͪɽ͞͹ͪΌɼָਫ਼ɼ‫ंڂݜ‬ɼͨ͢ͱΦϱζωΠ͖Δ͹‫͏ک‬གྷ๮ͶԢ͓ͱ಼༲Νร͓ͥॽ੸͹ରࡍΝร͓ͱ࠸൤ͤΖ͞ͳͳͪ͢ɽ ಣंͺɼຌॽ͹ߨؔͶඁΌΔΗͱ͏Ζໃ‫ݸ‬͹ླྀΗָ͹ຽΝద֮Ͷᅁ͙෾͜ͱɼ৿ͪ͵‫ڂݜ‬τʖϜΝ‫ͯ͜ݡ‬ड़͢ɼೖʓ͹ླྀΗ໲ୌΝմ݀ͤΖࢵ޳Ν͖ͯΊखͮͱཋ͢͏ɽຌॽ͗ɼ͞ΗΉͲͳಋ༹ɼଡ͚͹ಣं͹ࢩ࣍ΝಚͱɼླྀΗ‫ڂݜ‬͹਒ิͶ߫‫ͤݛ‬Ζ͞ͳ৶ͣͱٛΚ͵͏ɽ                            ೧  ݆  ೖ                                                       പࢃ۱‫ڋ‬Ͷͱ                            ஦ઔ ෤෋

緒言

賢愚を分かたず、国境を厭わず、語学の壁をものともせず、世界の無数の人々から本書「エンジニアのための流れ学」は古典と賞揚されて久しく、すでにその発祥地、ドイツにおいては 12 版を重ねた。本書はヴィリー・ボール教授が週 4 時間の講義のために準備した「工業流れ学」（Technische Strömungslehre）のノートを基に同教授が人智を尽くして丹念に書き上げたものである。ボール教授は 1963 年以来、ハイルブロン工科大学において機械工学専攻の学生のためにこの講義を行ってきた。ただ、第６章の「流れの測定法」はボール教授自身が編集した流体機械と流体技術に関する指導書の一部を改編したものである。
本書は、その内容と構成からも明らかなように、専門の機械工学、河川工学、海岸工学、熱工学、電子工学、燃焼工学、医工学、化学工学、土木工学、航空宇宙工学、生命工学、環境工学、建築学、電気工学、輸送技術およびプロセス技術の学生を対象とする
流れ学の教科書として執筆された。そのために、重要な基礎方程式の導出法、並びに計算精度が明示されている。詳細な計算過程が示された全部で 43 個におよぶ例題は、学生用の試験問題や練習問題として価値のあるものである。これらの例題を有効に用いることによって、教師の諸兄は個々の学習段階における学生一人ひとりの理解度を容易にチェックすることが可能となる。
本書は、しかしながら、見方を変えれば流れ学の一人の天才によって体系的にまとめられた専門書である。この本はすでに実務に就いている技術者または工学者の座右の書としても十分に耐えうる。すなわち、本編者は流体技術分野における重要な文献の購読と並行して、読者がより流れ学の知見を深化せしめようとする際に、本書ほど簡潔にして、明快な副読本はこの世に存在しないと信ずる。
本書には物性や実験係数を含む、エンジニアが日常業務をこなす上で必要な多くの表や図がふんだんに含まれている。これらの情報はエンジニアが現場においてさまざまな問題を解く際に直接役立つはずである。
ところで、本書を理解するための物理学と数学に関する予備知識としては、基本的な力学、並びに微分と積分にすぎない。
本書が多くの大学や大学院における流れ学の教科書としてのみならず、1971 年の初版
発行より今日までの間、極めて広い範囲にわたる教材として用いられてきたことに鑑み、その導出または他の原典より引用された法則と公式は、原則として次元方程式として表されているので、用いられる単位系から独立である。ただし、例題の解法においては、
一貫して国際単位系を用いた。
5

本書の原書「Technische Strömungslehre」を平成元（1989）年 8 月 7 日に、ユーリゲ
ン・ツィーレップ教授の招聘により研究滞在していたカールス・ルーエ大学の正門隣にあった本屋の棚から偶然に発見し、その内容の非凡さを確信した後に歓喜・勇躍して購入以来、すでに 18 年有余の年月が流れ去ってしまった。この間、原書を入手した瞬間に誓った自らの手で和訳出版するという情熱は絶えて冷めることはなかったが、越えようとしても越えられなかった経済的かつ時間的な試練を克服して、ここに、ボール教授の流れ学の不朽の名著を日本の学徒に紹介できる機会を得た幸せを天の神に率直に謝して、本書の緒言に替える。
平成 19 年 元 旦
白山市寓居にて
白山連峰学術院
総長 中 川 武 夫（流水）6総緒言 ·························································

目

5

重要公式記号と単位 ······························ 10

第１巻

次

2.2.3

静水圧の発生 ·········································· 46

2.2.3.1

ピストン圧力 ·········································· 46

2.2.3.2

圧力仕事 ·················································· 48

2.2.3.3

静水圧 ····················································· 48

１

流体と気体の物性 ······························· 13

2.2.3.4

連結容器 ·················································· 49

1.1

序論 ························································· 13

2.3

圧力 ························································· 501.2密度、比体積 ·········································· 13

2.3.1

ピストン圧の作用による圧力 ·············· 50

1.2.1

定義 ························································· 13

2.3.1.1

平面壁に加えられる圧力 ······················ 50

1.2.2

流体の密度 ·············································· 14

2.3.1.2

曲面壁に加えられる圧力 ······················ 51

1.2.3

気体と蒸気の密度 ·································· 15

2.3.2

静水圧の作用による圧力 ······················ 53

1.2.4

空気の密度 ·············································· 15

2.3.2.1

平板壁に加えられる圧力 ······················ 53

1.3

音速 ························································· 16

2.3.2.2

曲面壁に加えられる圧力 ······················ 57

1.4

粘性 ························································· 18

2.3.2.3

上方へ向かう垂直圧力（上方圧） ········· 62

1.4.1

序論 ························································· 18

2.4

浮力と浮動 ·············································· 63

1.4.2

ニュートン流体の粘性 ·························· 18

2.4.1

静浮力 ····················································· 63

1.4.2.1

力学的粘性係数 ······································ 18

2.4.2

熱浮力 ····················································· 64

1.4.2.2

動粘性係数 ·············································· 19

2.4.3

浮動と浮遊 ·············································· 65

1.4.2.3

粘性の温度依存性 ·································· 20

2.4.4

安定性 ····················································· 65

1.4.2.4

粘性の圧力依存性 ·································· 21

2.4.4.1

序論 ························································· 65

1.4.2.5

仕事の基礎と実用公式 ·························· 23

2.4.4.2

完全に没した物体の安定性 ·················· 66

1.4.3

非ニュートン流体の粘性 ······················ 26

2.4.4.3

部分的に没した物体の安定性 ·············· 671.5熱物性値 ·················································· 27

1.5.1

序論 ························································· 27

３空気静力学 ············································ 71

1.5.2

比熱容量 ·················································· 27

3.1

序論 ························································· 71

1.5.3

気体定数 ·················································· 30

3.2

大気の組成 ·············································· 71

1.5.4

エンタルピー ·········································· 31

3.3

大気の成層 ·············································· 72

1.5.5

蒸気圧 ····················································· 31

3.4等温成層 ·················································· 74

1.6表面張力と毛管現象 ······························ 31

3.5

等エントロピー成層 ······························ 75

1.6.1

序論 ························································· 31

3.6

標準大気 ·················································· 77

1.6.2

表面張力 ·················································· 32

1.6.3

付着応力 ·················································· 33

1.6.4

境界面圧力（毛管圧力） ························· 35４非圧縮性流れ ······································· 79

1.6.5

毛管現象 ·················································· 37

4.1

基礎概念 ·················································· 79

4.2

基礎方程式 ·············································· 81

第２巻

２

静水力学 ················································ 41

4.2.1

連続方程式（貫流方程式） ····················· 81

2.1

自由表面の形成 ······································ 41

4.2.2

エネルギー方程式2.2

静水圧 ····················································· 44

2.2.1

基礎概念 ·················································· 44

4.2.2.1

エネルギー方程式の導出 ······················ 82

2.2.2

単位 ························································· 45

4.2.2.2

エネルギー方程式の応用 ······················ 85（ベルヌーイ方程式） ························· 82

74.2.3流向に対して垂直方向への圧力変化 ··· 904.6.2

流速分布 ················································ 157

4.2.4

運動量定理 ·············································· 92

4.6.3

流れ公式 ················································ 158

4.2.4.1

運動量定理の一般的導出法と表示法 ··· 92

4.6.4

水力有効断面 ········································ 160

4.2.4.2

応用と例題 ············································

4.7

容器からの流出 ···································· 162

94

4.2.5

角運動量定理 ········································ 1084.7.1

定水面からの流出 ································ 162

4.2.5.1

定義と導出法 ········································ 108

4.7.1.1

重力影響下における小開口部からの4.2.5.2

応用 ······················································· 109

4.3

相似法則 ················································ 112

4.3.1

相似条件 ················································ 112

4.3.2

レイノルズ数 ········································ 113

4.3.3

フルード数 ············································ 114

4.3.4

模型実験 ················································ 114

4.7.1.4

背圧下の流出 ········································ 167

4.4

流れ形態 ················································ 115

4.7.2

水面高が可変な場合の流出 ················ 168

4.4.1

円管内の層流と乱流（内部流） ··········· 115

4.7.2.1

重力影響下における小開口部からの4.4.2

球周辺の層流と乱流（外部流） ··········· 117

4.4.3

自由表面を有する流れ中の遅い

流出 ···················································· 162
4.7.1.2

小開口部を介する圧力容器からの流出 ···················································· 165

4.7.1.3

重力影響下における大開口部からの流出 ···················································· 166

流出 ···················································· 168
4.7.2.2

背圧下の流出 ········································ 169

運動（常流）と早い運動（射流） ······

118

4.8

物体周辺流 ············································ 172

4.5

閉導管内の物質流（円管水理学） ·····

119

4.8.1

流況 ······················································· 172

4.5.1

粘性流に関するエネルギー

4.8.2

力の効果 ················································ 174

4.8.2.1

摩擦抵抗（表面抵抗） ··························· 174

4.8.2.2

回転円板摩擦·········································· 175

4.8.2.3

圧力抵抗（形状抵抗） ··························· 178

4.8.2.4

総抵抗 ··················································· 178

導管中の圧力降下 ···························· 123

4.8.3

乗物に働く空気力 ································ 180

4.5.3.1

流速分布 ················································ 123

4.8.3.1

空気抵抗 ················································ 180

4.5.3.2

圧力降下 ················································ 126

4.8.3.2

揚力 ······················································· 181

4.5.4

非ニュートン流体流の圧力降下 ········ 128

4.8.3.3

横風力 ··················································· 181

4.5.5

波状管中の圧力降下 ···························· 129

4.8.4

球の浮動速度 ········································ 182

4.5.6

非円形断面を有する管 ························ 131

4.9

翼 ··························································· 183

4.5.7

導管要素内の流れ損失 ························ 133

4.9.1

序論 ······················································· 183

4.5.7.1

一般論 ··················································· 133

4.9.2

翼理論 ··················································· 183

4.5.7.2

管入口 ··················································· 135

4.9.3

翼の表示法と概念 ································ 185

4.5.7.3

断面変化 ················································ 135

4.9.4

無限幅翼に働く力 ································ 185

4.5.7.4

方向変化 ················································ 139

4.9.5

翼面上の圧力分布 ································ 187

4.5.7.5管の分岐 ················································ 140

4.9.6

極曲線 ··················································· 188

4.5.7.6

ベローズ ················································ 143

4.9.7

誘導抵抗 ················································ 190

方程式 ················································ 1194.5.2

層流の場合の円形断面を有する
導管中の圧力降下 ···························· 120

4.5.3

乱流の場合の円形断面を有する

4.5.7.7

仕切弁と制御弁 ···································· 143

4.5.7.8

絞り装置 ················································ 145

4.5.7.9フィルターとふるい ···························· 145

５圧縮性流れ ·········································· 193

4.5.7.10

合成抵抗 ················································ 147

5.1

序論 ······················································· 193

4.5.7.11

等価管路長 ············································ 148

5.2

音の伝播 ················································ 193

4.5.8

入口区間長 ············································ 150

5.3

基礎方程式 ············································ 195

4.5.9

間隙流 ··················································· 152

5.3.1

連続方程式 ············································ 195

4.6

用水内の流れ ········································ 157

5.3.2

エネルギー方程式 ································ 196

4.6.1

一般論 ··················································· 157

5.3.3

運動量定理 ············································ 197

8

第３巻

5.4

衝撃波と膨張波 ···································· 197

6.1.3

ピストン圧力測定装置 ························ 234

5.4.1

序論 ······················································· 197

6.1.4

バネ弾性マノメータ ···························· 234

5.4.2

衝撃波 ··················································· 197

6.1.5

電気圧力測定装置 ································ 238

5.4.3

膨張波 ··················································· 1996.2

速度測定 ················································ 239

5.5円管流 ··················································· 199

6.2.1

機械的方法 ············································ 239

5.5.1

序論 ······················································· 199

6.2.1.1

ロビンソン風速計 ································ 239

5.5.2

任意熱交換を伴う

6.2.1.2

風車風速計 ············································ 240

圧力降下方程式 ································ 200

6.2.1.3

水車流速計 ············································ 240

5.5.3

等温流れ中の圧力降下 ························ 202

6.2.1.4

風向計 ··················································· 241

5.5.4

断熱流れ中の圧力降下 ························ 202

6.2.2

ピトー管と測定気球 ···························· 241

5.5.5

絞りによる圧力降下 ···························· 204

6.2.2.1

プラントル管 ········································ 241

5.6

流出過程 ················································ 206

6.2.2.2

よどみ板風力計 ···································· 242

5.6.1

圧力容器からの流出 ···························· 206

6.2.2.3

総圧管 ··················································· 243

5.6.1.1

流出速度 ················································ 206

6.2.2.4

方向測定器 ············································ 243

5.6.1.2

流出質量流率 ········································ 208

6.2.3

熱線風速計 ············································ 245

5.6.1.3

臨界圧力比 ············································ 2096.3

流体面測定（水準面測定） ··················· 246

5.6.1.4臨界速度 ················································ 2116.4

容積測定 ················································ 246

5.6.1.5

初期速度を有する場合の流出 ············ 212

6.4.1

ドラム計量器 ········································ 246

5.6.2

ラバール・ノズル ································ 214

6.4.2

環状ピストン計量器 ···························· 247

5.6.2.1

序論 ······················································· 214

6.4.3

卵形回転計量器 ···································· 248

5.6.2.2

拡がり点における流れ関係 ················ 215

6.4.4

羽根車計量器 ········································ 249

5.6.2.3

不適切な背圧の場合の流れ関係 ········ 216

6.4.5

ボルトマン計量器 ································ 249

5.6.2.4

ラバール・ノズルの構造形態 ············ 218

6.5

流量測定 ················································ 250

5.7

圧縮性流れ ············································ 2196.5.1

流速分布と導管（開水路横）断面積

5.7.1

亜音速ディフューザー ························ 219

5.7.2

超音速ディフューザー ························ 220

6.5.2

絞り装置 ················································ 251

5.8

物体周辺流 ············································ 223

6.5.3

越流堰 ··················································· 254

5.8.1

流れ構造 ················································ 223

6.5.4

ベンチュリー水路 ································ 255

から体積流量を求める方法 ············ 250

5.8.2

よどみ点における圧力・温度上昇 ······ 223

6.5.5

浮遊物体装置による流量測定 ············ 256

5.8.3

物体周辺流の抗力 ································ 2256.5.6

電磁流量測定装置 ································ 257

5.8.3.1

平板抗力 ················································ 225

6.5.7

超音速流量計 ········································ 258

5.8.3.2

空間に伸展された物体抗力 ················ 225

6.6

粘度測定法 ············································ 259

5.8.4

翼形 ······················································· 226

6.6.1

細管法 ··················································· 259

5.8.4.1

亜音速流中の翼形 ································ 226

6.6.2

回転法 ··················································· 259

5.8.4.2

局所的圧縮衝撃波を伴う翼形 ············ 227

6.6.3

落下物体法 ············································ 260

5.8.4.3

超音速流中の翼形 ································ 227

第４巻
６

流れの計測 ·········································· 229

6.1

圧力測定 ················································ 229

6.1.1

序論 ······················································· 229

6.1.2

流体圧力計 ············································ 230

第５巻
７

参考文献 ·············································· 263

８付

表 ·················································· 269

９索

引 ·················································· 313

9重要公式記号と単位
S I

公式記号
A

10

m

単

位

2

意

味

面積、横断面2am/s

加速度、減速度

a

m, mm

直径

a

m/s

音速

B

m

幅

b

m

幅

C

N

遠心力

C

1

速度係数

CS

1

推力係数

c

m/s

絶対速度

cA

1

揚力係数

ca

1

揚力係数

cD

1

形状抵抗係数

cF

1

抵抗係数

cM

1

回転モーメント係数cm1モーメント係数cp

J/(kg u K)

等圧比熱容量

cS

1

側風力係数

cv

J/(kg u K)

等容比熱容量

cw

1

抵抗係数

cwi

1

誘導抵抗係数

D

m

直径

<1

D

s

d

m

直径

E

N/m2

弾性係数

e

m

距離、クリアランス

F

N

力

Fr

1

フルード数

f

雑多

係数

f

s <1

周波数

G

N

速度勾配

重力
2

g

m/s

重力加速度

H

m

高さ、落下高さ、全水頭

H

N

水平力

h

m

高さ、越流高hJN u m m2――；―――；――kg
kg
s2

比エンタルピーHe

1

ヘドストローム数4Im

慣性モーメント、遠心モーメントI

kg u m/s

力積

I

A；mA

電流強度

S I

公式記号

単

位

意

味

i

1

位数

J

1；％；‰

水路勾配

K

雑多

積分定数

K

1

係数

K

雑多

KCh

0.5

m /s

バジンの速度係数KMS

1/3

マニング-ストリックラーの速度係数

m /s

装置定数

2

kK

m
―
―
N

圧縮性係数

k

m；mm

粗度高さ

k

雑多

係数

L

m

長さ

l

m

長さ、区間

l

mm

寸法偏差

M

Num

モーメント、回転モーメント

Ma

1

マッハ数

Md

Num

モーメント、回転モーメントMi

kg/kmol

モル質量

m

kg

質量

ṁ

kg/s

質量流率

m

1

絞り装置の開口比n1

混合部分の空隙部分n1

速度分布の指数n1

容器の開口比n1

ある数、ある不定数
2

O

m

P

W

仕事率

p

Pa；bar

圧力

R

m

半径

R

N

合力

Re

1

レイノルズ数Ri

J/(kg u K)

特殊気体定数または比気体定数Rm

J/(kmol u K)

モル気体定数または一般気体定数

r

m

半径

s

m

路程、区間、長さ、距離、板厚Sr

1

ストローハル数

T

K

絶対温度

t

m

翼弦、喫水深、距離、分離距離

t

s

時間

t

℃

摂氏温度

U

m

円周

面積

11