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Консультация № 182335
28.02.2011, 13:23
51.70 руб.
0
2
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Закрытый цилиндр радиуса R , заполненный на три четверти своего объема жидкостью плотности [$961$], вращается в невесомости вместе с жидкостью с угловой скоростью [$969$] вокруг своей оси. Как меняется давление в жидкости в зависимости от расстояния до стенок цилиндра?
Закрытый цилиндр радиуса R , заполненный на три четверти своего объема жидкостью плотности [$961$], вращается в невесомости вместе с жидкостью с угловой скоростью [$969$] вокруг своей оси. Как меняется давление в жидкости в зависимости от расстояния до стенок цилиндра?
Обсуждение
28.02.2011, 20:22
общий
это ответ
Здравствуйте, Дмитрий Олегович!
В общем случае полный дифференциал давления имеет вид
где X = F[sub]x[/sub]/m, Y = F[sub]y[/sub]/m, Z = F[sub]z[/sub]/m - проекции ускорения массовых сил на координатные оси. Если ось z совпадает с осью вращения цилиндра, то на расстоянии r от стенки цилиндра F[sub]x[/sub] = m[$969$][sup]2[/sup](R-r)cos [$966$] = m[$969$][sup]2[/sup]x, F[sub]y[/sub] = m[$969$][sup]2[/sup](R-r)sin [$966$] = m[$969$][sup]2[/sup]y - составляющие центробежной силы F = m[$969$][sup]2[/sup](R-r), F[sub]z[/sub] = 0 - сила тяжести отсутствует. Тогда X = [$969$][sup]2[/sup]x, Y = [$969$][sup]2[/sup]y, Z = 0 и
Постоянную C выбираем исходя из того, что при r = R/2 (на границе между жидкостью и свободным объемом вдоль оси цилиндра) P = 0. Тогда
В общем случае полный дифференциал давления имеет вид
где X = F[sub]x[/sub]/m, Y = F[sub]y[/sub]/m, Z = F[sub]z[/sub]/m - проекции ускорения массовых сил на координатные оси. Если ось z совпадает с осью вращения цилиндра, то на расстоянии r от стенки цилиндра F[sub]x[/sub] = m[$969$][sup]2[/sup](R-r)cos [$966$] = m[$969$][sup]2[/sup]x, F[sub]y[/sub] = m[$969$][sup]2[/sup](R-r)sin [$966$] = m[$969$][sup]2[/sup]y - составляющие центробежной силы F = m[$969$][sup]2[/sup](R-r), F[sub]z[/sub] = 0 - сила тяжести отсутствует. Тогда X = [$969$][sup]2[/sup]x, Y = [$969$][sup]2[/sup]y, Z = 0 и
Постоянную C выбираем исходя из того, что при r = R/2 (на границе между жидкостью и свободным объемом вдоль оси цилиндра) P = 0. Тогда
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