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

パスカルの原理では、閉じ込められた流体の圧力が変化すると、その変化は大きさを減少させることなく、流体全体と容器の壁に伝達されると述べています。
この原理を理解するために、断面積Aが水で満たされたマルチノズルウォーターガンを考えてみましょう。
ピストンがFの力で押されると、対応する圧力変化F / Aが全水量を介して伝達され、各ノズルに到達します。
水は、パスカルの原理に従って、各ノズルから同じ圧力で放出されます。
別の例を挙げると、水が注がれる細長いパイプにバレルを接続します。
樽がいっぱいになり、さらに水が注がれると、入ってくる水によって加えられる圧力は、樽内の水の体積全体で急速に増加し、すべての側面から漏れます。

パスカルの法則

1653 年、フランスの哲学者で科学者であるブレーズ パスカルは、静止流体の原理を論じた「液体の平衡に関する論文」を出版しました。 静的流体とは、動いていない流体です。 流体が流れていないとき、流体は静的平衡にあると言います。 流体が水の場合、静水圧平衡状態にあると言います。 静的平衡にある流体の場合、流体のどの部分にかかる正味の力もゼロでなければなりません。 そうしないと、流体が流れ始めます。 パスカルは、密閉された流体に加えられる圧力の変化が、減衰することなく流体全体とその容器の壁に伝わることを観察しました。 さらに、パスカルの原理は、流体内の全圧力はさまざまな源からの圧力の合計であることを暗示しています。 たとえば、流体内の特定の深さの圧力は、流体の深さと大気の圧力に依存します。

密閉された流体では、流体の原子が自由に動き回ることができるため、流体のすべての部分と容器の壁に圧力が伝わります。 圧力の変化はそのまま伝わります。 この原理は、流体のすべての点で圧力が同じであると言っているわけではないことに注意してください。地球近くの流体内の圧力は高さによって変化するため、これは真実ではありません。 むしろ、この原理は圧力の変化に当てはまります。 質量 m の可動ピストンを備えた高さ (H)、断面積 (A) の円筒形の容器に水を加えたとします。 ピストンの上部に重量 (mg) を追加すると、追加の重量は蓋の面積 (A) にも作用するため、上部の圧力が mg/A ずつ増加します。

パスカルの原理によれば、水中のすべての点の圧力は同じ量 (mg/A) だけ変化します。 したがって、底部の圧力も mg/A ずつ増加します。 したがって、コンテナの底部の圧力は、大気圧、流体による圧力、質量によって供給される圧力の合計に等しくなります。

このテキストは<a href="https://openstax.org/books/university-physics-volume-1/pages/14-3-pascals-principle-and-hydraulics">から編集されたものです。 Openstax, University Physics Volume 1, Section 14.3: Pascal's Principle and Hydraulics</a>.

1653年、フランスの哲学者で科学者のブレーズ・パスカルは「液体の平衡に関する論文」を出版しました。

Education

JoVE Core

物理学

Unit 1

ユニット1

Fluid Mechanics

流体力学

KEY TERMS AND CONCEPTS

主要用語と概念

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

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 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

Gauge vs Absolute Pressure

Pressure gauges often show pressure relative to atmospheric pressure. Many gauges, including those on scuba tanks, are set to read zero at atmospheric pressure. That reading is called gauge pressure. When the pressure inside the tank is higher than atmospheric pressure, the gauge shows a positive value. Some gauges can also measure negative pressure. This is useful in a vacuum chamber, which is a rigid chamber where some air has been pumped out. Because the pressure inside the chamber is below...

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archimedes' principle

Buoyant Force from Fluid Pressure

Archimedes' principle explains buoyant force in a fluid. An upward buoyant force acts on an object that is partially or fully immersed in a fluid. This force is equal to the weight of the fluid displaced by the object. To see why an object floats, imagine removing a submerged object from the fluid. The space it occupied would be filled by fluid with weight w_fl. That weight is supported by the surrounding fluid, so the buoyant force must match the weight of the displaced fluid. The principle...

density and archimedes' principle

How Buoyancy Depends on Density

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accelerating fluids

Fluid Pressure in an Accelerating Elevator

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surface tension and surface energy

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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

Buoyant force explains why objects float, sink, or stay suspended in a fluid. A fluid can be a liquid or a gas, and every object placed in it experiences this upward force. A metal ball sinks, while a rubber ball floats. A submarine also changes its buoyancy to move up or down. The force comes from pressure changes in the fluid. Fluid pressure increases with depth because the weight of the fluid above also increases. That means the bottom of an object feels more pressure than the top. This...

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

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

physics

JoVE Core 物理学は、運動学、力学、流体力学、静力学、波動、音響などの基礎的な物理学の理論と応用を、簡潔でわかりやすいアニメーション ビデオで紹介します。さらに、科学者の実際のビデオでは、世界中の今日の研究所で行われている古典的および独自の研究実験における関連概念の適用を示しています。

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Pascal’s Principle in Static Fluids

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