Name: pascal’s principle in static fluids
Uploaded: 2023-04-30T11:04:20.000Z
Duration: 1 min 4 s
Channel: JoVE

K12 Standards

Alabama Course of Study Science

9-12

Physics

motion-and-stability-forces-and-interactions

Motion and Stability: Forces and Interactions

9-12.P.1.4.b

Pascal's Law

O princípio de Pascal afirma que, se a pressão em um fluido confinado for alterada, a mudança é transmitida para todo o fluido e para as paredes do recipiente sem ser diminuída em magnitude.
Para entender esse princípio, considere uma pistola de água de bico múltiplo da área da seção transversal A cheia de água.
Quando o pistão é pressionado com uma força F, a mudança de pressão correspondente F/A é transmitida através de todo o volume de água e atinge cada bico.
A água é liberada com a mesma pressão por cada bico, seguindo o princípio de Pascal.
Tomando outro exemplo, deixe um barril ser conectado a um tubo longo e fino através do qual a água é derramada.
Quando o barril está cheio e uma quantidade adicional de água é despejada nele, a pressão exercida pela água que entra aumenta rapidamente em todo o seu volume no barril, fazendo com que ele vaze por todos os lados.

lei de pascal

Em 1653, o filósofo e cientista francês Blaise Pascal publicou o "Tratado sobre o Equilíbrio dos Líquidos", que discutia os princípios dos fluidos estáticos. Um fluido estático é um fluido que não está em movimento. Quando um fluido não está fluindo, dizemos que o fluido está em equilíbrio estático. Se o fluido for água, dizemos que está em equilíbrio hidrostático. Para um fluido em equilíbrio estático, a força resultante em qualquer parte do fluido deve ser zero; caso contrário, o fluido começará a fluir. Pascal observou que uma mudança na pressão aplicada a um fluido fechado é transmitida sem diminuição por todo o fluido e pelas paredes do seu recipiente. Além disso, o princípio de Pascal implica que a pressão total em um fluido é a soma das pressões de diferentes fontes. Por exemplo, a pressão em uma determinada profundidade em um fluido depende da profundidade do fluido e da pressão da atmosfera.

Em um fluido fechado, uma vez que os átomos do fluido são livres para se movimentar, eles transmitem pressão para todas as partes do fluido e para as paredes do recipiente. Qualquer mudança na pressão é transmitida sem diminuição. Observa-se que esse princípio não afirma que a pressão é a mesma em todos os pontos de um fluido - o que não é verdade, pois a pressão em um fluido próximo à Terra varia com a altura. Em vez disso, esse princípio se aplica à mudança na pressão. Suponha que água seja adicionada a um recipiente cilíndrico de altura (H) e área de seção transversal (A) que possui um pistão móvel de massa m. Adicionar peso (mg) no topo do pistão aumenta a pressão no topo em mg/A, uma vez que o peso adicional também atua sobre a área (A) da tampa.

De acordo com o princípio de Pascal, a pressão em todos os pontos da água muda na mesma quantidade, mg/A. Portanto, a pressão na parte inferior também aumenta em mg/A. Assim, a pressão na parte inferior do recipiente é igual à soma da pressão atmosférica, da pressão devida ao fluido e da pressão fornecida pela massa.

Este texto foi adaptado de <a href="https://openstax.org/books/university-physics-volume-1/pages/14-3-pascals-principle-and-hydraulics"> Openstax, University Physics Volume 1, Section 14.3: Pascal's Principle and Hydraulics</a>.

Lei de Pascal

Em 1653, o filósofo e cientista francês Blaise Pascal publicou "Tratado sobre o Equilíbrio de Líquidos", que discutia o ...

Education

JoVE Core

Física

Unit 1

Unidade 1

Fluid Mechanics

Mecânica dos Fluidos

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

pascal’s principle in static fluids

Pascal’s principle explains how pressure changes move through a fluid that is not flowing. A fluid at rest is in static equilibrium. If the fluid is water, it is in hydrostatic equilibrium. In this state, the net force on any part of the fluid must be zero, or the fluid will begin to flow.

Blaise Pascal described this idea in 1653 in Treatise on the Equilibrium of Liquids. He showed that when pressure changes in an enclosed fluid, that change is transmitted without loss through the fluid and to the walls of the container. The principle applies to pressure changes, not to the total pressure being the same everywhere. In fluid near Earth, pressure still varies with height.

The total pressure in a fluid can come from more than one source. At a certain depth, pressure depends on the fluid depth and the pressure of the atmosphere. Inside an enclosed fluid, the moving atoms pass pressure along to all parts of the fluid and to the container walls. That is why any added pressure spreads undiminished.

A simple piston example shows this clearly. Imagine water in a cylindrical container with height H and cross-sectional area A, and a movable piston of mass m. If an extra weight of mg is placed on the piston, the pressure at the top increases by mg/A because the weight acts over area A. Pascal’s principle says the pressure throughout the water changes by the same amount, so the bottom pressure also rises by mg/A. The pressure at the bottom is then the sum of atmospheric pressure, fluid pressure, and the pressure from the added mass.

Pascal’s Principle in Static Fluids

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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pressure of fluids

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variation of atmospheric pressure

Atmospheric Pressure and Altitude

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 explains how pressure changes move through a fluid that is not flowing. A fluid at rest is in static equilibrium. If the fluid is water, it is in hydrostatic equilibrium. In this state, the net force on any part of the fluid must be zero, or the fluid will begin to flow. Blaise Pascal described this idea in 1653 in Treatise on the Equilibrium of Liquids. He showed that when pressure changes in an enclosed fluid, that change is transmitted without loss through the fluid and...

application of pascal's law

Hydraulic Force Transfer with Pascal's Law

Hydraulic force transfer uses Pascal's law to move pressure through an enclosed fluid. Pascal showed experimentally that a change in pressure applied to a confined fluid is transmitted undiminished throughout the fluid and to the walls of its container. That idea is the basis of hydraulics, a major part of modern mechanical technology. Hydraulic systems appear in automotive brakes, hydraulic jacks, and many other machines. A simple hydraulic system uses two pistons at the same height. Because...

pressure gauges

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archimedes' principle

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density and archimedes' principle

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accelerating fluids

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excess pressure inside a drop and a bubble

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buoyancy

Buoyant Force in Sinking and Floating

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contact angle

Wetting and Surface Curvature

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rise of liquid in a capillary tube

Capillary Action in Thin Tubes

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Fluid Motion Patterns in Air and Water

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Fluid Flow in Narrowing Pipes

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

Fluid Pressure and Speed in Motion

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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...

bernoulli's principle: applications

Bernoulli's Principle in Fluid Devices

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energy conservation and bernoulli's equation

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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

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

Learn how pressure changes move through static fluids, why pressure is added in enclosed liquids, and how a piston changes pressure in water.

Pascal’s Principle in Static Fluids | JoVE K12

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Pascal’s Principle in Static Fluids

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