Name: hydraulic force transfer with pascal's law
Uploaded: 2023-04-30T11:04:28.000Z
Duration: 1 min 3 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

Application of Pascal's Law

Sistemas hidráulicos como o macaco hidráulico são baseados na lei de Pascal.
Consiste em um tubo em forma de U com colunas de seção transversal desigual. O pistão A é montado na coluna menor, enquanto o pistão B é instalado na coluna maior.
O tubo é preenchido com um fluido de tal forma que atinge a mesma altura em ambas as colunas. Quando uma força é aplicada ao pistão A, ela exerce uma pressão p1 sobre o fluido.
De acordo com a lei de Pascal, essa pressão é transmitida ao pistão B através do fluido, devido ao qual o pistão B é empurrado para fora.
A pressão p2 sentida pelo pistão B é igual a p1. Agora, usando a relação entre pressão e força, uma expressão para as forças em um sistema hidráulico é obtida desde que o atrito no sistema seja insignificante. A força de saída pode ser aumentada no sistema hidráulico aplicando uma força em uma área menor.

aplicação da lei de pascal

As observações experimentalmente comprovadas de Pascal - que uma mudança na pressão aplicada a um fluido fechado é transmitida sem diminuir por todo o fluido e pelas paredes de seu recipiente - fornecem as bases para a hidráulica, um dos desenvolvimentos mais importantes na tecnologia mecânica moderna.

Sistemas hidráulicos são utilizados para operar freios automotivos, macacos hidráulicos e inúmeros outros sistemas mecânicos. Podemos derivar uma relação entre as forças em um sistema hidráulico simples aplicando o princípio de Pascal. No sistema, existem dois pistões na mesma altura, portanto não há diferença de pressão devido a uma diferença de profundidade. A pressão devida à força atuando na área menor é transmitida sem diminuição por todo o fluido e por todas as paredes do recipiente. Assim, a pressão sentida no pistão maior é igual à pressão transmitida pela área menor. Isso gera uma equação que relaciona as razões de força em relação a área em qualquer sistema hidráulico, desde que os pistões estejam na mesma altura vertical e que o atrito no sistema seja negligenciável. Sistemas hidráulicos podem aumentar ou diminuir a força aplicada a eles. Para aumentar a força, a pressão é aplicada a uma área maior. Por exemplo, se uma força de 100 N é aplicada no cilindro menor, e o outro cilindro tem uma área cinco vezes maior, então a força de saída é de 500 N.

O macaco hidráulico é um exemplo desse sistema hidráulico. Ele é usado para levantar cargas pesadas, como aquelas usadas por mecânicos automotivos para levantar um automóvel. Uma pequena força aplicada sobre uma área pequena pode equilibrar uma força muito maior do outro lado sobre uma área maior. A partir do princípio de Pascal, pode-se demonstrar que a força necessária para levantar um carro é menor do que o peso do carro.

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</a>'<a href="https://openstax.org/books/university-physics-volume-1/pages/14-3-pascals-principle-and-hydraulics">s Principle and Hydraulics</a>.

Aplicação da Lei de Pascal

As observações experimentalmente comprovadas de Pascal - que uma mudança na pressão aplicada a um fluido fechado é transmitida sem diminuição ao longo do ...

Education

JoVE Core

Física

Unit 1

Unidade 1

Fluid Mechanics

Mecânica dos Fluidos

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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 the pistons are at the same vertical level, there is no pressure change from depth. The pressure created by the force on the smaller area travels through the fluid and reaches the larger piston with the same value.

This pressure balance gives a relationship between force and area in a hydraulic system. It works when the pistons are at the same height and friction in the system is negligible. Hydraulic systems can increase or decrease the force applied to them. To increase the output force, the pressure is applied over a larger area.

For example, if a 100 N force is applied to the smaller cylinder and the other cylinder has five times the area, the output force is 500 N. A hydraulic jack uses this principle to lift heavy loads. Auto mechanics use hydraulic jacks to raise cars. A small force over a small area can balance a much larger force on the other side over a larger area. From Pascal's principle, the force needed to lift a car is less than the car's weight.

Hydraulic Force Transfer with Pascal's Law

hydraulic-force-transfer-with-pascals-law

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

Density, Floating, and Specific Gravity

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

Fluid Pressure in Everyday Life

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...

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 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...

application of 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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Why Liquids Form Drops and Float

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excess pressure inside a drop and a bubble

excess-pressure-inside-a-drop-and-a-bubble

Surface Tension in Drops and Bubbles

Surface tension sets the pressure difference in small drops and bubbles. For a tiny liquid drop, gravity can be neglected, so the drop is treated as spherical. It can also be viewed as two equal hemispherical drops joined together by surface tension. The forces on the drop come from three sources. The liquid inside pushes outward, the air outside pushes inward, and surface tension acts along the diameter between the two hemispheres. Since surface tension is force per unit length, it creates a...

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buoyancy

Buoyant Force in Sinking and Floating

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contact angle

Wetting and Surface Curvature

Wetting and surface curvature describe how a liquid behaves where it meets a solid. When a solid is dipped into a liquid, the liquid surface can bend near the contact line. In some cases, the liquid rises along the solid. In others, the surface becomes convex or depressed near the solid. This behavior comes from cohesive and adhesive forces. Adhesive force is the attraction between molecules of different materials, such as a solid and a liquid. Cohesive force is the attraction between...

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rise of liquid in a capillary tube

Capillary Action in Thin Tubes

Capillary action explains why liquid can rise or fall in a very thin tube compared with the liquid around it. A capillary is a narrow cylindrical tube, and the effect becomes noticeable when it is dipped into a liquid. The movement happens because two forces act in opposite directions. Cohesive forces make liquid molecules stick to each other, so the liquid tends to hold together and form a rounded shape. Adhesive forces pull the liquid toward the walls of the container. In a narrow glass...

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laminar and turbulent flow

Fluid Motion Patterns in Air and Water

Fluid dynamics studies fluids in motion. Scientists often use velocity vectors to show fluid motion in places like meteorology. For example, wind in the atmosphere can be mapped with vectors that show the speed and direction of the wind at each point. Another way to show fluid motion is with a streamline. A streamline shows the path of a small volume of fluid as it flows. When the flow changes with time, the streamlines do not match the flow lines. The fluid velocity is always tangential to...

equation of continuity

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

Bernoulli's equation connects fluid pressure with fluid speed. It helps explain why moving fluids can create pressure changes in everyday situations. One example is when two trains pass each other quickly and seem to pull inward. The same effect can happen when two cars pass each other at high speed. As the air between the trains or cars speeds up, its pressure drops. The air on the outside stays at atmospheric pressure. That pressure difference creates a net inward force on the vehicles.

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

Bernoulli's principle helps explain how many fluid devices work when the fluid moves at a constant height. It is useful for devices that use fast flow to create low pressure and for devices that measure fluid speed. Some devices use this pressure change to pull one fluid into another. These are called entrainment devices. A Bunsen burner uses an adjustable gas nozzle to entrain air for proper combustion. An atomizer uses a squeeze bulb to make a jet of air that pulls perfume drops into the...

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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

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

See how Pascal's law explains hydraulic force transfer in brakes and jacks, with pressure passing through a fluid and changing force through area.

Hydraulic Force Transfer with Pascal's Law | JoVE K12

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Hydraulic Force Transfer with Pascal's Law

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