Name: fluid resistance, viscosity, and flow regime
Uploaded: 2025-05-22T09:05:41.000Z
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Em um fluxo laminar, através de um tubo horizontal, a vazão é definida como a razão entre a diferença de pressão em dois pontos e a resistência ao fluxo.
Aqui, a resistência é diretamente proporcional ao coeficiente de viscosidade e comprimento do tubo, e inversamente proporcional à quarta potência do raio do tubo. Quando combinada com a equação da taxa de fluxo, essa relação fornece a lei de Poiseuille para o fluxo laminar.
Considerando a viscosidade constante, uma ligeira diminuição no raio do tubo causa uma redução significativa na vazão. Para manter a mesma vazão, a diferença de pressão deve aumentar de acordo.
Da mesma forma, é difícil para um fluido mais viscoso fluir através do tubo do que um fluido menos viscoso a temperatura constante.
O número de Reynolds é um valor que indica se o fluxo de um fluido é laminar ou turbulento.
Se o número de Reynolds for inferior a dois mil, o fluxo é laminar e turbulento se for maior que três mil. Entre dois e três mil, o fluxo é instável e pode apresentar comportamento caótico.

lei de poiseuille e número de reynolds

Poiseuille's Law and Reynolds Number

Qualquer fluido em um tubo horizontal pode fluir devido a diferenças de pressão - o fluido flui de uma pressão mais alta para uma pressão mais baixa. A taxa de fluxo (Q) é a relação entre a diferença de pressão e a resistência através de um tubo horizontal. Quanto maior a diferença de pressão, maior a taxa de fluxo. A resistência ao fluxo é expressa como:

<img alt="Equation1" src="/files/ftp_upload/12743/12743_Equation_1.png" style="text-align: center; height: 32px;" />

Quando combinada com a taxa de fluxo (Q), essa relação fornece a lei de Poiseuille para o fluxo laminar de um fluido incompressível em um tubo.

<img alt="Equation2" src="/files/ftp_upload/12743/12743_Equation_2.png" style="text-align: center; height: 32px;" />

Todos os fatores que afetam a taxa de fluxo, exceto a pressão, estão incluídos na resistência. A resistência depende das dimensões do tubo e da viscosidade do fluido. A resistência é diretamente proporcional ao comprimento do tubo e inversamente proporcional à quarta potência do raio do tubo.

No caso de um fluido não viscoso, o fluxo do fluido é livre de atrito e a resistência ao fluxo é zero. Isso resulta no movimento de todas as camadas com a mesma velocidade. Em contraste, a resistência ao fluxo de fluidos viscosos é diferente de zero. Nesses casos, a velocidade é maior no meio do tubo e diminui em direção às bordas do tubo. Podemos ver o efeito em uma chama de bico de Bunsen.

O fluxo pode ser considerado laminar ou turbulento, conforme classificado pelo número de Reynolds. Se o número de Reynolds for inferior a 2.000, o fluxo é laminar; se for maior que 3.000, o fluxo é turbulento. O fluxo é considerado instável e pode apresentar comportamento caótico se o número de Reynolds estiver entre 2.000 e 3.000. O fluxo instável indica que inicialmente ele é laminar, mas que, devido a obstruções ou a rugosidade da superfície, o fluxo pode se tornar turbulento e pode oscilar aleatoriamente entre ser laminar e turbulento. Neste caso, uma pequena variação em um fator pode ter um efeito exagerado (ou não linear) em um sistema, apresentando assim comportamento caótico.

Este texto foi adaptado de <a href="https://openstax.org/books/university-physics-volume-1/pages/14-7-viscosity-and-turbulence">Openstax, University Physics Volume 1, Section 14.7: Viscosity and Turbulence.</a>

Lei de Poiseuille e Número de Reynolds

Qualquer fluido em um tubo horizontal pode fluir devido a diferenças de pressão - o fluido flui de alta para baixa pressão. A vazão (Q) é a razão de ...

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Fluid Mechanics

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KEY TERMS AND CONCEPTS

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fluid resistance, viscosity, and flow regime

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 and the fluid's viscosity. It is directly proportional to tube length and inversely proportional to the fourth power of the tube radius.

A non-viscous fluid has frictionless flow, so its resistance is zero. In that case, all layers move at the same speed. Viscous fluids behave differently. Their flow resistance is not zero, and the speed is highest in the middle of the tube and lower near the edges. A Bunsen burner flame can show this effect.

Flow can also be classified by the Reynolds number. When the Reynolds number is below 2,000, the flow is laminar. When it is above 3,000, the flow is turbulent. If the Reynolds number is between 2,000 and 3,000, the flow is unstable and may switch between laminar and turbulent behavior. Small obstructions or surface roughness can trigger this change and lead to chaotic motion.

Fluid Resistance, Viscosity, and Flow Regime

fluid-resistance-viscosity-and-flow-regime

characteristics of fluids

Fluid Behavior Under Force

Fluid behavior under force differs from the behavior of solids. When a force acts parallel to the top surface of a solid, the solid resists it because of internal friction between its layers. This is called shearing resistance. If the force is removed, the shearing forces help the solid return to its original shape. Other deformation forces can also change the shape of a solid for a short time, as long as the force stays below a threshold magnitude. Solids usually keep their shape, which makes...

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density

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Density helps explain why objects sink or float in a fluid. It is also useful for identifying a substance and for learning about its phase and substructure. The SI unit of density is kg/m3, and the cgs unit is g/cm3. Liquids and solids usually have densities that are roughly comparable. That matches the fact that their atoms are in close contact. Gases have much lower densities than liquids and solids because their atoms are separated by large amounts of empty space. Density does not always...

pressure of fluids

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Fluid pressure appears in many everyday situations, including blood pressure and weather systems. The same force can have a very different effect depending on the area it acts on. A force spread over 1 mm² creates 100 times more pressure than the same force spread over 1 cm². That is why a sharp needle can pierce skin with a small force, while the same force from a finger usually does not. Pressure is especially important when studying fluids. A fluid does not offer much resistance to a force...

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Atmospheric pressure and altitude are closely linked. As height increases, atmospheric pressure decreases. This happens because the gravitational force per unit area becomes smaller as we move away from Earth’s surface. To describe this change, the atmosphere is treated with a constant air temperature at a given altitude. The ideal gas law of thermodynamics is also used as a good approximation for the air. Let p(y) be the atmospheric pressure at height y. The density ρ at y, the temperature T...

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pascal's law

Pascal’s Principle in Static Fluids

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application of pascal's law

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archimedes' principle

Buoyant Force from Fluid Pressure

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excess pressure inside a drop and a bubble

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Surface Tension in Drops and Bubbles

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buoyancy

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contact angle

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rise of liquid in a capillary tube

Capillary Action in Thin Tubes

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Fluid flow in a pipe is described by flow rate and average speed. Flow rate, or volume flow rate, is the amount of fluid that passes a point through an area in a given time. It depends on both how fast the fluid moves and the size and shape of the conduit. For a river or pipe, a greater speed usually means a greater flow rate. A larger cross-sectional area also increases flow rate. That is why the same fluid can move differently through conduits of different sizes. The relationship becomes...

bernoulli's equation

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bernoulli's principle

Fluid Pressure and Speed Changes

Bernoulli's equation links fluid pressure and fluid speed in a static, incompressible fluid. For horizontal flow, where gravitational energy density stays constant, the equation is especially useful. In that setting, the result is known as Bernoulli's principle. Bernoulli's principle says that fluid pressure drops when speed increases, and pressure rises when speed decreases. This pressure-speed relationship helps explain how moving fluids behave in simple flow situations. It also provides a...

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energy conservation and bernoulli's equation

energy-conservation-and-bernoulli-s-equation

Bernoulli’s Equation in Streamlined Flow

Bernoulli’s equation describes energy in a moving fluid. It comes from the conservation of energy principle, or the work-energy theorem, applied to an incompressible, inviscid fluid in laminar, steady, irrotational flow. The equation says that pressure energy, potential energy, and kinetic energy per unit volume stay constant along a streamline. Each term has the units of energy per unit volume. The kinetic energy per unit volume is called kinetic energy density, and the potential energy per...

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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...

poiseuille's law and reynolds number

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

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...

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key terms and concepts

Explore how pressure, viscosity, and tube size affect fluid flow. Learn Poiseuille's law, laminar flow, and Reynolds number thresholds in tubes.

Fluid Resistance, Viscosity, and Flow Regime | JoVE K12

physics

JoVE Core - Fisica apresenta a teoria e a aplicação de tópicos fundamentais da física, incluindo cinemática, dinâmica, mecânica dos fluidos, estática, ondas e acústica, com vídeos animados concisos e de fácil compreensão. Além disso, os vídeos de cientistas em ação demonstram a aplicação de conceitos relacionados em experimentos de pesquisa clássica e original realizados nos laboratórios de todo o mundo hoje em dia.

Fluid Resistance, Viscosity, and Flow Regime

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