kocin n e kibelj i a roze n v teoreticeskaja gidromehanika cast 1 pdf
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Н.Е.Кочин, И.А.Кибель, Н.В.Розе ТЕОРЕТИЧЕСКАЯ ГИДРОМЕХАНИКА, ЧАСТЬ 1
М.: Физматгиз, 1963, 584 стр. Содержание
Предисловие к шестому изданию 8 Глава первая. Кинематика жидкой среды (Н.В.Розе) 9
А. Деформация жидкой частицы 9 § 1. Формулы Коши—Гельмгольца 9 § 2. Чистая деформация 12 § 3. Эллипсоид деформации 13 § 4. Кубическое расширение 15 § 5. Упражнения 16
Б. Уравнение неразрывности 16 § 6. Переменные Лагранжа 16 § 7. Переменные Эйлера 18 § 8. Переход от переменных Лагранжа к переменным Эйлера и обратно 18 § 9. Поле скоростей 19 § 10. Уравнение неразрывности в переменных Лагранжа 22 § 11. Уравнение неразрывности в переменных Эйлера 24 § 12. Другой метод вывода уравнения неразрывности 25 § 13. Уравнение неразрывности в цилиндрических, сферических и
криволинейных координатах 26
§ 14. Упражнения 29 В. Кинематическая характеристика безвихревого и вихревого движений
31
§ 15. Введение 31 § 16. Потенциал скорости 31 § 17. Свойства безвихревого движения в односвязном объеме 33 § 18. Безвихревое движение в многосвязном объеме 36 § 19. Вихревое поле и его свойства 38 § 20. Упражнения 40 Глава вторая. Основные уравнения динамики идеальной жидкости
(Н.В.Розе) 44
§ 1. Силы массовые и поверхностные 44 § 2. Общее уравнение движения 45 § 3. Гидродинамическое давление в идеальной жидкости 46 § 4. Общие уравнения движения идеальной жидкости 47 § 5. Уравнения движения в форме Эйлера 48 § 6. Векторные формы уравнений движения 53 § 7. Уравнения движения в форме Ламба 54 § 8. Уравнения движения в форме Лагранжа 57 § 9. Общая постановка задач гидродинамики 58 § 10. Случай несжимаемой жидкости 59 § 11. Случаи сжимаемой жидкости. Баротропность и бароклинность. 60
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Уравнение притока энергии § 12. Начальные и граничные условия 64 § 13. Применение закона количеств движения и закона моментов количеств
движения 65
§ 14. Уравнение энергии 72 § 15. Упражнения 75 Глава третья. Гидростатика (Н.В.Розе) 83
А. Гидростатическое давление 83 § 1. Уравнения равновесия 83 § 2. Условие для сил 84 § 3. Барометрическая формула 85 § 4. Условия на поверхности раздела 87 § 5. Общие формулы для определения давления на твердую поверхность 88 § 6. Давление тяжелой несжимаемой жидкости 88 § 7. Давление на плоскую стенку 90 § 8. Закон Архимеда 91 § 9. Давление на криволинейную стенку 92 § 10. Упражнения 94
Б. Равновесие плавающих тел 96 § II. Условия равновесия плавающего тела 96 § 12. Поверхность сечений 97 § 13. Поверхность центров 98 § 14. Радиусы кривизны главных нормальных сечении поверхности
центров 99
§ 15. Устойчивость равновесия 102§ 16. Упражнения 104Глава четвертая. Простейшие случаи движения идеальной жидкости
(Н.В.Розе) 110
А. Интегралы Бернулли Коши 110§ 1. Установившееся движение 110§ 2. Безвихревое движение 113§ 3. Установившееся безвихревое движение 116§ 4. Ограничения, налагаемые на скорость 117§ 5. Формула Торичелли 118§ 6. Истечение газов 118§ 7. Действие мгновенных сил 119§ 8. Кинетическая энергия безвихревого движения 121§ 9. Теорема В. Томсона 122§ 10. Упражнения 124
Б. Плоское безвихревое движение 129§ 11. Введение 129§ 12. функция тока 130§ 13. Связь функции тока с потенциалом скорости 131§ 14. Комплексная скорость и комплексный потенциал 133
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§ 15. Связь плоской гидродинамической задачи с теорией функций комплексного переменного
134
§ 16. Примеры комплексного потенциала 134§ 17. Источники и стоки 136§ 18. Дублеты 138§ 19. Вихревые точки 139§ 20. Вихреисточники 140§ 21. Вычеты комплексной скорости, циркуляция и поток скорости 141§ 22. Упражнения 142Глава пятая. Вихревые движения идеальной жидкости (Н.Е.Кочин) 144
А. Основные уравнения теории вихрей и теоремы Гельмгольца о сохранении вихрей
144
§ 1. Введение 144§ 2. Теорема Томсона 147§ 3. Теорема Лагранжа 151§ 4. Теоремы Гельмгольца 152§ 5. Сохраняемость векторных линий 154§ 6. Уравнения Фридмана. Уравнения Гельмгольца 160§ 7. Теоремы Гельмгольца 161§ 8. Образование вихрей. Теорема В. Бьеркнеса 162§ 9. Примеры образования вихрей 166§ 10. Упражнения 174
Б. Определение поля скоростей по заданному полю вихрей и полю расхождения скорости
176
§ 11. Вычисление вектора скорости по вихрю и расхождению скорости для бесконечного пространства
176
§ 12. Случай одной вихревой нити 187§ 13. Прямолинейная вихревая нить 192§ 14. Две прямолинейные вихревые нити. Движение системы вихрей 193§ 15. Круговая вихревая нить 197§ 16. Вихревой слой 202§ 17. Упражнения 205
В. Вихревые цепочки Кармана 207§ 18. Введение 207§ 19. Одна вихревая цепочка 208§ 20. Две вихревые цепочки 209§ 21. Об устойчивости вихревых цепочек Кармана 211§ 22. Схема Кармана движения тела в жидкости с образованием вихрей 225§ 23. Вычисление лобового сопротивления по Карману 229§ 24. Упражнения 236Глава шестая. Плоская задача о движении тела в идеальной жидкости
(Н.В.Розе) 237
§ 1. Предварительные замечания 237§ 2. Граничные условия. Задачи Дирихле и Неймана 238
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§ 3. Движение кругового цилиндра 243§ 4. Нестационарное течение, вызываемое движущимся круговым
цилиндром 251
§ 5. Общие выражения для гидродинамических реакций при установившемся течении. Формула Блазиуса — Чаплыгина
252
§ 6. Эффективное вычисление гидродинамических реакций при установившемся течении Формула Кутта — Жуковского
254
§ 7. Применение метода конформного отображения 257§ 8. Реакции на контур 262§ 9. Парабола устойчивости 265§ 10. Обтекание эллиптического цилиндра 267§ 11. Обтекание плоской пластинки 272§ 12. Обтекание некоторых форм профилей цилиндров 274§ 13. Обтекание профилей Жуковского 280§ 14. Обтекание решетки 291§ 15. Тонкое крыло 297§ 16. Неустановившееся движение плоского контура 309§ 17. Обтекание с отрывом струй. Метод Кирхгоффа 321§ 18. Метод Жуковского—Митчеля. Истечение из отверстия. Удар струи в
пластинку. Глиссирующая пластинка 329
§ 19. Метод Леви-Чивита 343§ 20. Давление при обтекании со срывом струй и при обтекании с
циркуляцией 352
§ 21. Обтекание с кавитацией 354Глава седьмая. Пространственная задача о движении тела в идеальной
жидкости (Н.В.Розе) 359
§ 1. Безвихревое движение. Движение шара 359§ 2. Обтекание эллипсоида 362§ 3. Функция тока для осесимметрнчного течения 366§ 4. Метод источников и стоков 370§ 5. Поперечное обтекание осесимметричных тел 374§ 6. Движение твердого тела в безграничной жидкости 375§ 7. Расчет гидродинамических реакций при движении тела 380§ 8. Примеры 387§ 9. Движение тела по инерции 396Глава восьмая. Волновые движения идеальной жидкости (Н.Е.Кочин) 401
А. Основные уравнения теории волн 401§ 1. Различные типы волн 401§ 2. Основные уравнения 402§ 3. Начальные условия 407
Б. Плоские волны 409§ 4. Введение 409§ 5. Стоячие волны 409§ 6. Прогрессивные волны 414
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§ 7. Сведение прогрессивных волн к установившемуся движению 418§ 8. Групповая скорость 420§ 9. Общий случай плоской задачи 424§ 10. Профиль волны 431§ 11. Волны при конечной глубине жидкости 436§ 12. Волны на поверхности раздела двух жидкостей 439§ 13. Капиллярные волны 444§ 14. Волны конечной амплитуды 447§ 15. Трохоидальные волны Герстнера 448§ 16. Свойства трохоидальных волн 451§ 17. Энергия волн 455§ 18. Перенос энергии 459§ 19. Волновое сопротивление. Движение тела под свободной
поверхностью 460
§ 20. Волны в сжимаемой жидкости. Обтекание воздухом горного хребта 477§ 21. Упражнения 188
В. Трехмерные волны 489§ 22. Общие формулы 489§ 23. Корабельные волны 499§ 24. Стоячие колебания тяжелой жидкости в сосуде 504§ 25. Колебания жидкости в прямоугольном сосуде и в круговом цилиндре 507§ 26. Упражнения 511
Г. Длинные волны 512§ 27. Основные уравнения 512§ 28. Длинные волны в каналах постоянной глубины 515§ 29. Стоячие колебания в каналах переменной глубины 518§ 30. Стоячие колебания в цилиндрическом сосуде малой глубины 521§ 31. Вынужденные колебания в каналах постоянной глубины 522§ 32. Статическая теория приливов 526§ 33. Выводы статической теории приливов 530§ 34. Каналовая теория приливов 534§ 35. Волны во вращающейся атмосферной оболочке 539§ 36. Центры действия атмосферы 546§ 37. Длинные волны конечной амплитуды. Волны на мелкой воде.
Разрушение плотины 553
§ 38. Обтекание препятствия тяжелой сжимаемой жидкостью. Длинные волны Бора
561
§ 39. Упражнения 570Литература 571Именной указатель 576Предметный указатель 578
Предметный указатель Амплитуда волны 411 Анализ приливов гармонический 533
Антипассат 167, 171 Антициклон 145
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Архимеда закон 91 Атмосфера вихрей 166, 206 Бабине формула 87 Бароклинность 60 Баротропность 60 Бернулли интеграл 70, 111 Бернулли—Эйлера интеграл 117 Био — Савара закон 189 Блазиуса — Чаплыгина формулы
253, 254 Бойля — Мариотта закон 80 Бьеркнеса теорема 165 Взрыв бомбы внутри несжимаемой
жидкости 127 - мины под водой 77 - подводный 120 Вихреисточник 140 Вихрь абсолютный 172 - в криволинейных ортогональных
координатах 42 - скорости 22, 154, 176 - точечный 192 Возникновение вихрей в жидкости
162, 205 Волны 36 - в сжимаемой жидкости 477 - во вращающейся атмосферной
оболочке 539 - вынужденные 471 - Герстнера трохоидальные 448 - гравитационные 401 - длинные 512, 515, 565 - - в каналах постоянной глубины 515 - капиллярные 444, 446 - конечной амплитуды 447 - - - длинные 553 Волны корабельные 401, 499 - мелкие 401, 446 - морские 401 - на поверхности раздела двух
жидкостей 439 - плоские 409 - при конечной глубине жидкости
436
- приливные 401 - прогрессивные 414, 418, 437 - с подветренной стороны 488 - стоячие 409 - трехмерные 489 - трохоидальные Герстнера 448 - упругие 401 Вынос решетки 291 Высота геометрическая 111 - прилива 529 - пьезометрическая 112 - скоростная 112 Вычет комплексной скорости 141 Вязкость 63 Гаусса теорема 22, 177 Гей-Люссака закон 166 Гельмгольца теоремы 152, 153, 161 - уравнение 161 Гельмгольциан вектора полный 159 Гидростатика 83 Гипотеза Жуковского 260 Градиент сверхадиабатический 488 Граница раздела 87 Гребень волны 411 Группа волн 423 Давление взрывное 77 - гидродинамическое 252 - - в идеальной жидкости 46 - гидростатическое 83 - мгновенное 119 - на замкнутую поверхность
погруженную в жидкость твердого тела 91
Давление на криволинейную стенку 92
- - плоскую стенку 90 - - твердое тело 89 - нормальное 45, 46 - при обтекании со срывом струй 352 - - - с циркуляцией 352 - тяжелой несжимаемой жидкости 88 Движение в жидкости плоского
контура неустановившееся 309 - - - по инерции 398
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- - - тела 237, 359—375 - - - цилиндра 225, 243, 251 - - - шара 388 - - - эллипсоида 389 - вихревой нити между двумя
параллельными стенками 236 - вихревых цепочек неустойчивое 211 - - - устойчивое 212 - внутри прямого угла 135 - газа по прямолинейной трубке
постоянного сечения 79 - жидкости адиабатическое 63, 112 - - безвихревое 31, 114, 144, 406 - - в многосвязном объеме 37 - - - односвязном объеме 33, 35 - - - элементарной трубке тока 66 - - - элиптическом цилиндре 242 - - вихревое 31, 38, 145 - - волновое 401 - - идеальной 110, 144 - - изотермическое 60, 112 - - изэнтропическое 112 - - плоское 129, 409 - - под действием сил тяжести 504 - - по прямолинейной трубке
постоянного сечения 80 - - с потенциалом скорости 144 - - стационарное установившееся 21,
110 - - установившееся 116 - системы вихрей 193 - тела под свободной поверхностью
460 - - по инерции 396 - цилиндра в бесконечном потоке 475 - шара поступательное 360 Действие мгновенных сил 119 Деформация жидкой частицы 9 - однородная 16 - чистая 12 Диафрагма 37 Дирихле задача 240 Дисперсия волн 423 Диссипативность объема 73
Длина волны 411 - глиссирующей пластинки 338 Дублет 138 Жидкость бароклинная 61 - баротропная 60, 111, 114, 150 - идеальная 151 - неразрывная 24 - несжимаемая 59 - сжимаемая 60 Жуковского гипотеза 260 - парадокс 96 - профиль 286 - руль 290 Жуковского — Митчеля метод 329 Задача Дирихле 240 - Неймана 241 Закон Архимеда 91 - Био —Савара 189 - Бойля — Мариотта 80, 166 - Гей-Люссака 166 - живой силы 72, 110 - количества движения 65, 226 - моментов количества движения 65 - Паскаля 83 Излучение 63 Импульс давления 402 Индекс циркуляции 543 Интеграл Бернулли 70 - Бернулли—Эйлера 117 - Коши 110, 114 - - Пуассона 347 Интегралы движения центра инерции
194 Интенсивность векторной трубки
154, 157 - вихревой нити 187 - - точки 139 - - трубки 39, 147, 153 - вихря 39, 193, 204, 226 Истечение газа из сосуда через
отверстие 118 - - - тонкой конической трубки 124 - жидкости из сосуда 330 Источник 136
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Каверна 354 Кавитация 354 Капиллярность 444 Кинематика жидкой среды 9 Кирхгоффа метод 322 Клапейрона уравнение 62, 85 Клепсидра 125 Колебания жидкости в круговом
цилиндре 507 - - в прямоугольном сосуде 507 - - вынужденные 522 - - свободные гармонические 408 - - состояние 504, 518, 521 Координаты общие криволинейные
28, 51 - сферические 28, 50 - цилиндрические 27, 48 Коши — Гельмгольца формула 9 Коши интеграл 110, 114 Коши — Римана условие 133 Коэффициент приведенных масс 316 - температурного расширения
воздуха 85 Кривизна линий тока 129 Крыло тонкое 297 Кутта—Жуковского формула 251,
256, 263 Лагранжа переменные 17 - теорема 151 Лапласа уравнение 33 Леви-Чивита метод 343 Линия вихревая 39, 146, 152 - наибольшего ската 506 - равной вертикальной амплитуды
506 - тока 20, 35, 70, 129, 202 Масса жидкости 25 - тела присоединенная 385 Метацентр большой 104 - малый 104 Метод Жуковского — Митчеля 329 - источников и стоков 370 - Кирхгоффа 322 - конформного отображения 257
- Леви-Чивита 343, 350 - Симонова — Серебрийского 298 Момент дублета 138 Мощность источника 136 Муссон 167 Напряжение вихревой точки 139 - косое 45 Натяжение жидкости поверхностное
444 Нить вихревая 187 - - круговая 197 - - прямолинейная 192 Обильность источника 136 Образование вихрей 162, 171, 225 Обтекание воздухом горного хребта
477 - жидкостью неподвижного твердого
тела 67 - круга поступательным потоком
бесциркуляционное 246, 326 - неподвижного кругового цилиндра
246 - осесимметричных тел поперечное
374 - пластины косое 350 - - прямое 355 - плоской пластины 272 - препятствия тяжелой сжимаемой
жидкостью 561 - произвольного тонкого профиля 298 - профилей Жуковского 280 - решетки 291 - - бесциркуляционное 293 - с кавитацией 354 - с образованием поверхностей
разрыва 321 - с отрывом струй 321 - тел вращения 374 - тела безграничным потоком 324 - цилиндров различной формы 274 - эллипсоида 362 - эллиптического цилиндра 267 Объем жидкий 16 - жидкости многосвязный 37
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- - односвязный 35, 57 - - связный 36 - удельный 163 Оператор Лапласа в криволинейных
координатах 43 Ось деформации главная 13 - дублета 138 - контура критическая 264 - нулевой подъемной силы 264 - профиля критическая 289 Отлив морской 401 Отображение конформное 257 Пара вихрей 193, 205 - импульсивная 383, 397 Парабола метацентров (парабола
устойчивости) 266 Парадокс Жуковского 96 - Эйлера — Даламбера 362 Параметры Ламэ 29, 41, 359 Паскаля закон 83 Пассат 167, 171 Переваливание воздушной массы
через хребет 565 Переменные Лагранжа 17, 18, 19 - Эйлера 18 Перенос энергии 459 Период волны 412 - решетки 291 Пластинка глиссирующая 338 Плоскость плавания 97 Плотность жидкости 151 - слоя вихревая 203 - тепловой мощности притока тепла
61 Площадь плавания 97 Поверхность изобарическая 163 - изотермическая 163 - контрольная 68 - равного удельного объема 163 - раздела 87 - разрыва 171, 202 - свободная 83 - сечений 97, 107 - уровня 83
- центров 98 - - для однородного эллипсоида 107 - - для прямого однородного
цилиндра 109 Подошва волны 411 Показатель политропы 60 Поле вихревое 38 - скоростей 19 - - соленоидальное (трубчатое) 22 Порядок вихрей симметричный 211 - - шахматный 211 Постоянная газовая 62, 85 Постоянные циклические 38 Потенциал векторный 183 - комплексный 133 - Ньютона 179, 362 - скорости 32, 34, 131, 144, 152, 359 Поток однородный поступательный
134 - скорости 21, 26, 141, 142 - установившийся циркуляционный
247 Прилив морской 401 - —обращенный» 537 - —прямой» 537 Принцип симметрии Римана —
Шварца 347 - - Шварца 464 Производная по нормали к
поверхности 33 - полная (индивидуальная) 19 Профиль волны 431, 437 - Жуковского 286 - крыла аэроплана 286 - тонкий 298 Процесс изэнтропический 63 - политропический 60, 63 Пуассона уравнение 177 Пучность 411 Равновесие жидкости
изотермическое 88 - плавающих тел 96 - тяжелой несжимаемой жидкости 88
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Радиус кривизны главных нормальных сечений поверхности центров 99
Разрушение вихрей 162 - волны 553 - плотины 554, 557 Расположение вихрей симметричное
211 - - шахматное 211 Растяжение нормальное 45 Расхождение вектора в
криволинейных ортогональных координатах 41
- скорости 22, 176 Расширение жидкости кубическое 15,
74 Реакция при движении тела
гидравлическая 380 Резонанс 524 Руль Жуковского 290 Рябь 401, 446 Свойство сохраняемости вихревых
линий 153 Седло (особая точка) 21 Сейши 401, 504 Сила живая несжимаемой жидкости
122 - Жуковского 315 - импульсивная 383, 397 - капиллярная 444 - массовая 44 - мгновенная 119 - объемная 45 - поверхностная 45, 69 - подсасывающая 274, 304 - подъемная Архимеда 473 - трения 45 Симонова — Серебрийского метод
298 Система вихрей 193, 203 Скорость волн групповая 422 - комплексная 133 Скорость критическая 560
- кубического расширения жидкости 22
- чистой деформации 12 Слой вихревой 203 - - цилиндрический 203 Смерч 145 Сопротивление вихревое 145 - волновое 460, 461 - лобовое 226, 232 - - по Карману 229 Сохраняемость векторных линий 154 Среда бароклинная 61 - баротропная 60 Сток 136 Стокса теорема 22, 40 - формула 147 Стрела прогиба 286 Тело плавающее 96 Тензор упругих напряжений 47 Теорема Бьеркнеса 165 - Гаусса 22, 177 - Гельмгольца 161 - - о постоянстве интенсивности
вихревой трубки 147 - - - сохранении вихревых линий 152 - - - - интенсивности вихревых
трубок 153 - Лагранжа 151 - о постоянстве циркуляции 147 - Стокса 22, 40 - Томсона 122, 147 - - основная 151 - Фридмана 155 - Чаплыгина 265, 286 - Эйлера 67 Теория вихревых дорожек Кармана
322 - приливов каналовая 535 - статическая 526 Течение жидкости пространственное
359 - морское 167 - осесимметричное 366 Точка вихревая 139
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- критическая 20, 248 - особая 20 Трохоида 452 Трубка вихревая 39, 153, 187 - изобаро-изостерическая единичная
163 - тока 26, 112 - - единичная 26 Угол атаки 264, 286 Удар струи в пластинку 70, 334 Удлинение главное 15 Узел (особая точка) 21, 411 Уравнение абсолютного движения
жидкости в подвижной системе координат 57
- Гельмгольца 161 - движения идеальной жидкости
общее 45 - Клапейрона 62, 85 - Лапласа 33, 120 - неразрывности 16, 23, 25 - - в криволинейных координатах 359 - - - общих криволинейных
ортогональных координатах 28 - - - переменных Лагранжа 24 - - - - Эйлера 24 - - - сферических координатах 28 - - - цилиндрических координатах 27 - притока энергии (притока тепла) 62 - Пуассона 177 - состояния 80, 85 - статической теории приливов 527 - Фридмана 160 - энергии 72, 74 Уравнения гидродинамики
идеальной жидкости 44 - движения в векторной форме 53 - - форме Лагранжа 51, 58 - - - - Ламба 54 - - - - Эйлера 48 - - длинных волн 515 - - идеальной жидкости 47 - Ламба гидродинамические 54 - равновесия 83
- Эйлера гидродинамические 48 Уровень поверхности 83 - приведенный 89 Ускорение Кориолиса 56 Условие Коши — Римана 133 - равновесия плавающего тела 96 - устойчивости движения вихревых
цепочек Кармана 218 Условия граничные 64, 239 - начальные 64, 407 Устойчивость вихревых цепочек
Кармана 211 - равновесия 102 Фокус (особая точка) 21 - контура 265 Формула Бабине 87 - барометрическая 85 - Блазиуса — Чаплыгина вторая 254 - Блазиуса — Чаплыгина первая 253 - давления на твердую поверхность
88 - Коши — Гельмгольца 9 - Кутта — Жуковского 251, 256, 263,
285 - Лагранжа — Коши 359 - Леви-Чивита 350 - Стокса 147 - Торричелли 118 - Шварца — Кристоффеля 329, 332 - Эртеля 173 Фридмана теорема 155 - уравнение 160 Функции сопряженные 131 Функция тока 130, 199, 367 - - для осесимметричного течения
366 Характеристика вихревого движения
кинематическая 31 Центр (особая точка) 21 - давления 71, 91, 266 - действия атмосферы 546 Центр инерции вихрей 194 - кривизны главных сечений
поверхности центров 104
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Цепочка вихревая 208 - - Кармана 207, 211 Циклон 145, 171 Циркуляция скорости 22, 32, 37, 40,
142, 151, 193 Чаплыгина теорема 265, 286 Частота колебаний 412 Число кавитации 358 Шаг решетки 291 Шварца — Кристоффеля формула
331 Эйлера — Даламбера парадокс 362
- переменные 18, 24, 25, 64 - теорема 67 Эллипсоид вращения 13 Энергия волн 455 - кинетическая 73 - - безвихревого течения 121 - потенциальная 72, 73 Энтропия 63, 173 Эпициклоида удлиненная 424 - укороченная 424 Эртеля формула 173
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