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

Considere un objeto que se mueve a través de un fluido. Las capas de fluido cerca del objeto son arrastradas con él y experimentan una velocidad relativa, lo que resulta en una fuerza viscosa sobre el objeto. La fuerza viscosa depende de la forma, el tamaño, la velocidad y las propiedades del fluido del objeto. 
Para un cuerpo esférico que se mueve dentro de un fluido, la fuerza viscosa es proporcional al radio, la velocidad y la viscosidad del fluido de la esfera.
Resolviendo la ecuación dimensionalmente, da la dependencia de la fuerza viscosa en estos parámetros. La expresión obtenida es la ley de Stokes, que indica que la fuerza viscosa es directamente proporcional a la velocidad del objeto.
Si una esfera cae a través de un fluido, el peso del objeto la empuja hacia abajo, mientras que las fuerzas viscosas y flotantes actúan hacia arriba.
A medida que la velocidad aumenta debido a la aceleración, la fuerza viscosa aumenta. Cuando la fuerza viscosa equilibra el peso y la flotabilidad, la esfera cae con una velocidad constante, llamada velocidad terminal.
Para un líquido altamente viscoso, la velocidad terminal se puede medir experimentalmente. Luego, usando la ley de Stokes, se puede obtener la viscosidad.

<ol>
	<li>Verma, H.C. (2008). Conceptos de Física. Volumen 1, Bharati Bhawan Pub. & Dis.: secciones 14.17, 14.18; páginas 291 y 292.</li>
</ol>

ley de stokes

Stokes' Law

Las fuerzas viscosas, como la fricción, son fuerzas intermoleculares que resisten el movimiento relativo de las moléculas entre sí. Cuando un cuerpo sólido se mueve a través de un líquido, las fuerzas viscosas lo arrastran en dirección opuesta. La magnitud de la fuerza depende de la forma y el tamaño del sólido, así como de su velocidad y los coeficientes de viscosidad, densidad y temperatura del líquido. La expresión de la fuerza sobre un objeto sólido esférico en un fluido se llama ley de Stokes. La ley de Stokes es válida solo para fluidos con números de Reynolds bajos, lo que significa que solo es aplicable cuando el flujo del fluido es laminar y no turbulento. Experimentalmente, se ha encontrado que la fuerza sobre el objeto sólido es proporcional al radio y la velocidad del objeto, junto con el coeficiente de viscosidad del líquido. El orden de dependencia de cada variable se puede obtener mediante análisis dimensional. La constante de proporcionalidad se obtiene experimentalmente. El movimiento de un sólido esférico a través de un líquido se puede analizar utilizando la segunda ley del movimiento de Newton. Inicialmente, no hay resistencia viscosa, ya que el sólido está en reposo. La fuerza neta hacia abajo, que se determina por la diferencia entre su peso y la fuerza de flotación del líquido, aumenta su velocidad hacia abajo. Sin embargo, a mayor velocidad, la resistencia viscosa aumenta. Una vez que hay una resistencia viscosa significativa hacia arriba, no hay fuerza neta debido a que las tres fuerzas se equilibran entre sí: el peso hacia abajo, la flotabilidad hacia arriba y la resistencia viscosa hacia arriba. Entonces, el sólido alcanza una velocidad constante, que se llama velocidad terminal.

Ley de Stokes

Las fuerzas viscosas, al igual que la fricción, son fuerzas intermoleculares que resisten el movimiento relativo de las moléculas entre sí. Cuando un cuerpo sólido se mueve a través de un ...

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Education

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JoVE Core

Physics

Física

Unit 1

Unidad 1

Fluid Mechanics

Mecánica de fluidos

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

characteristics of fluids

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pascal's law

Pascal’s Principle in Static Fluids

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archimedes' principle

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buoyancy

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bernoulli's equation

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bernoulli's principle

Fluid Pressure and Speed Changes

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energy conservation and bernoulli's equation

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Bernoulli’s Equation in Streamlined Flow

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viscosity

Viscosity and How Fluids Flow

Viscosity describes how easily a fluid flows. Water moves quickly, while honey and maple syrup flow slowly and stick to a surface. That difference comes from fluid friction between liquid layers and between a fluid and the material around it. In this example, water has a lower viscosity than honey and maple syrup. Viscosity is measured in newton-second per meter squared (N·s/m2) or pascal-second (Pa·s). It also changes with temperature and can differ from one fluid to another by several orders...

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stokes' law

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...

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

physics

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Terminal Velocity in a Viscous Fluid

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