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

Considere um objeto se movendo através de um fluido. As camadas de fluido próximas ao objeto são arrastadas junto com ele e experimentam velocidade relativa, resultando em uma força viscosa no objeto. A força viscosa depende da forma, tamanho, velocidade e propriedades do fluido do objeto. 
Para um corpo esférico que se move dentro de um fluido, a força viscosa é proporcional ao raio, velocidade e viscosidade do fluido da esfera.
Resolver a equação dimensionalmente dá a dependência da força viscosa desses parâmetros. A expressão obtida é a lei de Stokes, indicando que a força viscosa é diretamente proporcional à velocidade do objeto.
Se uma esfera é lançada através de um fluido, o peso do objeto a puxa para baixo, enquanto as forças viscosas e flutuantes agem para cima.
À medida que a velocidade aumenta devido à aceleração, a força viscosa aumenta. Quando a força viscosa equilibra o peso e a flutuabilidade, a esfera cai com uma velocidade constante, chamada velocidade terminal.
Para um líquido altamente viscoso, a velocidade terminal pode ser medida experimentalmente. Então, usando a lei de Stokes, a viscosidade pode ser obtida.

<ol>
	<li>Verma, H.C. (2008). Conceitos de Física. Volume 1, Bharati Bhawan Pub. & Dis.: seções 14.17, 14.18; páginas 291–292.</li>
</ol>

lei de stokes

Stokes' Law

Forças viscosas, como a fricção, são forças intermoleculares que resistem ao movimento relativo das moléculas entre si. Quando um corpo sólido se move através de um líquido, as forças viscosas o arrastam na direção oposta. A magnitude da força depende da forma e do tamanho do sólido, bem como de sua velocidade e dos coeficientes de viscosidade, densidade e temperatura do líquido.

A expressão para a força sobre um objeto esférico sólido em um fluido é chamada de lei de Stokes. A lei de Stokes é válida apenas para fluidos com número de Reynolds baixo, ou seja, aplicável apenas quando o fluxo do fluido é laminar, e não turbulento. A força sobre o objeto sólido é experimentalmente encontrada como sendo proporcional ao raio do objeto e à sua velocidade, além do coeficiente de viscosidade do líquido. A ordem de dependência de cada variável pode ser obtida por meio de análise dimensional. A constante de proporcionalidade é obtida experimentalmente.

O movimento de um sólido esférico através de um líquido pode ser analisado usando a segunda lei do movimento de Newton. Inicialmente, não há arraste viscoso, pois o sólido está em repouso. A força resultante para baixo, que é dada pela diferença entre seu peso e a força de empuxo do líquido, aumenta sua velocidade para baixo. No entanto, o aumento da velocidade aumenta o arrasto viscoso. Uma vez que haja arraste viscoso significativo para cima, a força resultante será zero, por conta das três forças presentes estarem se equilibrando: o peso para baixo, a flutuabilidade para cima e o arraste viscoso para cima. O sólido então atinge uma velocidade constante, chamada de velocidade terminal.

Lei de Stokes

Forças viscosas, como o atrito, são forças intermoleculares que resistem ao movimento relativo das moléculas umas sobre as outras. Quando um corpo sólido se move através de um ...

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Education

JoVE Core

Physics

Física

Unit 1

Unidade 1

Fluid Mechanics

Mecânica dos Fluidos

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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

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bernoulli's equation

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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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Fluid resistance, viscosity, and flow regime shape how liquid moves through a horizontal tube. Fluid flows from high pressure to low pressure. The flow rate, Q, is the ratio of the pressure difference to the resistance in the tube. A larger pressure difference gives a higher flow rate. Poiseuille's law describes laminar flow of an incompressible fluid in a tube. In this relation, the factors that affect flow rate except pressure are grouped into resistance. Resistance depends on the tube size...

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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