Name: terminal velocity in a viscous fluid
Uploaded: 2025-05-22T09:06:09.000Z
Duration: 1 min 20 s
Channel: JoVE

Stellen Sie sich ein Objekt vor, das sich durch eine Flüssigkeit bewegt. Die Fluidschichten in der Nähe des Objekts werden mitgerissen und erfahren eine Relativgeschwindigkeit, was zu einer viskosen Kraft auf das Objekt führt. Die viskose Kraft hängt von der Form, Größe, Geschwindigkeit und den Flüssigkeitseigenschaften des Objekts ab. 
Bei einem kugelförmigen Körper, der sich in einer Flüssigkeit bewegt, ist die viskose Kraft proportional zum Radius, der Geschwindigkeit und der Viskosität der Flüssigkeit.
Wenn man die Gleichung dimensional löst, ergibt sich die Abhängigkeit der viskosen Kraft von diesen Parametern. Der erhaltene Ausdruck ist das Stokessche Gesetz, das darauf hinweist, dass die viskose Kraft direkt proportional zur Geschwindigkeit des Objekts ist.
Wird eine Kugel durch eine Flüssigkeit fallen gelassen, zieht das Gewicht des Objekts sie nach unten, während die zähflüssigen und auftriebsstarken Kräfte nach oben wirken.
Mit zunehmender Geschwindigkeit durch Beschleunigung nimmt die viskose Kraft zu. Wenn die viskose Kraft das Gewicht und den Auftrieb ausgleicht, fällt die Kugel mit einer konstanten Geschwindigkeit, die als Endgeschwindigkeit bezeichnet wird.
Bei einer hochviskosen Flüssigkeit kann die Endgeschwindigkeit experimentell gemessen werden. Dann kann mit Hilfe des Stokesschen Gesetzes die Viskosität ermittelt werden.

<ol>
	<li>Verma, H.C. (2008). Konzepte der Physik. Band 1, Bharati Bhawan Pub. & Dis.: Abschnitte 14.17, 14.18; Seiten 291–292.</li>
</ol>

stokes' gesetz

Stokes' Law

Zähigkeitskräfte wie Reibung sind zwischenmolekulare Kräfte, die der relativen Bewegung von Molekülen zueinander entgegenwirken. Wenn sich ein fester Körper durch eine Flüssigkeit bewegt, ziehen zähigkeitsbedingte Kräfte in entgegengesetzter Richtung auf. Die Größee der Kraft hängt von der Form und Größe des festen Körpers ab, sowie von seiner Geschwindigkeit und dem Koeffizienten der Viskosität, Dichte und Temperatur der Flüssigkeit.

Der Ausdruck für die Kraft auf einen festen kugelförmigen Gegenstand in einem Fluid wird Stokes' Gesetz genannt. Stokes Gesetz gilt nur für Fluide mit niedriger Reynolds-Zahl, was bedeutet, dass es nur anwendbar ist, wenn der Fluidfluss laminar und nicht turbulent ist. Die Kraft auf den festen Gegenstand wird experimentell als proportional zum Radius und zur Geschwindigkeit des Objekts gefunden, zusammen mit dem Viskositätskoeffizienten der Flüssigkeit. Die Abhängigkeit jeder Variablen kann durch Dimensionsanalyse ermittelt werden. Die Proportionalitätskonstante wird experimentell bestimmt.

Die Bewegung eines kugelförmigen festen Körpers durch eine Flüssigkeit kann mit dem zweiten Newtonschen Gesetz analysiert werden. Anfangs gibt es keinen zähigkeitsbedingten Widerstand, da der Körper ruht. Die netto ierende Kraft nach unten, gerichth aus dem Unterschied zwischen seinem Gewicht und der Auftriebskraft der Flüssigkeit ergibt, erhöht seine Geschwindigkeit nach unten. Allerdings erhöht eine steigende Geschwindigkeit auch den zähigkeitsbedingten Widerstand. Sobald es einen signifikanten nach oben gerichteten zähigkeitsbedingten Widerstand gibt, gibt es keich die drei Kräfte gegenseitig ausgleicheach unten gerichtete Gewicht, der nach oben gerichtete Auftrieb und der nach oben gerichtete zähigkeitsbedingte Widerstand. Der feste Körper erreicht dann eine konstante Geschwindigkeit, die als Terminalgeschwindigkeit bezeichnet wird.

Stokes' Gesetz

Zähflüssige Kräfte sind, wie Reibung, intermolekulare Kräfte, die der Relativbewegung von Molekülen übereinander widerstehen. Wenn sich ein Festkörper durch eine ...

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KEY TERMS AND CONCEPTS

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terminal velocity in a viscous fluid

Viscous forces act like friction in a liquid. They resist the relative motion of molecules and pull back on a solid body moving through the fluid. The size of this force depends on the body’s shape and size, its speed, and the liquid’s viscosity, density, and temperature.

For a spherical solid object, the force in a fluid is described by Stokes’ law. This law applies only at low Reynolds number, when the flow is laminar and not turbulent. Experiments show that the force is proportional to the sphere’s radius, its speed, and the liquid’s viscosity coefficient. Dimensional analysis helps determine how these variables depend on one another, while the proportionality constant is found experimentally.

A sphere moving through a liquid can also be studied with Newton’s second law. At first, the sphere has no viscous drag because it is at rest. The downward net force, which comes from the difference between its weight and the liquid’s buoyant force, makes it speed up.

As the speed increases, the viscous drag also increases. Eventually, the upward viscous drag becomes large enough to balance the downward weight and the upward buoyant force. When these three forces balance, there is no net force, and the sphere continues at a steady speed called terminal velocity.

Terminal Velocity in a Viscous Fluid

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key terms and concepts

Learn how viscous drag, buoyancy, and weight act on a sphere in a liquid, and how Stokes’ law leads to terminal velocity in low Reynolds number flow.

Terminal Velocity in a Viscous Fluid | JoVE K12

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Terminal Velocity in a Viscous Fluid

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