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

Принцип Паскаля гласит, что если давление в замкнутой жидкости изменяется, то это изменение передается на всю жидкость и на стенки контейнера без уменьшения его величины.
Чтобы понять этот принцип, рассмотрим водяную пушку с несколькими форсунками с площадью поперечного сечения А, заполненную водой.
Когда поршень прижимается с силой F, соответствующее изменение давления F/A передается по всему объему воды и достигает каждого сопла.
Вода выходит с одинаковым давлением через каждую форсунку, следуя принципу Паскаля.
Возьмем другой пример: пусть бочка будет соединена с длинной тонкой трубой, через которую льется вода.
Когда бочка заполнена и в нее вливается дополнительное количество воды, давление, оказываемое входящей водой, быстро возрастает по всему ее объему в бочке, вызывая ее утечку со всех сторон.

Закон Паскаля

В 1653 году французский философ и ученый Блез Паскаль опубликовал "Трактат об уравновешенности жидкостей", в котором рассуждал о принципах статических жидкостей. Статическая жидкость - это жидкость, которая не движется. Когда жидкость не течёт, мы говорим, что она находится в статическом равновесии. Если это вода, мы говорим, что она находится в гидростатическом равновесии. Для жидкости в статическом равновесии чистая сила, действующая на любую часть жидкости, должна быть равна нулю; в противном случае жидкость начнёт течь. Паскаль заметил, что изменение давления, приложенного к закрытой жидкости, передается без ослабления через всю жидкость и к стенкам её контейнера. Кроме того, принцип Паскаля подразумевает, что общее давление в жидкости является суммой давлений от разных источников. Например, давление на определённой глубине в жидкости зависит от глубины жидкости и давления атмосферы.

В закрытой жидкости, поскольку атомы жидкости свободно перемещаются, они передают давление всем частям жидкости и стенкам контейнера. Любое изменение давления передаётся без ослабления. Следует отметить, что этот принцип не утверждает, что давление во всех точках жидкости одинаковое - что не является верным, поскольку давление в жидкости около Земли меняется с высотой. Скорее, этот принцип применяется к изменению давления. Предположим, в цилиндрический контейнер с высотой (Н) и поперечным сечением (А), имеющий подвижный поршень массой (m), добавлено некоторое количество воды. Добавление веса (mg) сверху поршня увеличивает давление сверху на mg/A, так как дополнительный вес также действует на площадь (А) крышки.

Согласно закону Паскаля, давление во всех точках воды изменяется на одну и ту же величину, mg/A. Таким образом, давление внизу также увеличивается на mg/A. Таким образом, давление внизу контейнера равно сумме атмосферного давления, давления жидкости и давления, создаваемого массой.

Этот текст адаптирован из <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>

В 1653 году французский философ и ученый Блез Паскаль опубликовал «Трактат о равновесии жидкостей», в котором обсуждался ...

Education

JoVE Core

Физика

Unit 1

Раздел 1

Fluid Mechanics

Механика текучих сред

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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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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

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archimedes' principle

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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...

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bernoulli's principle

Fluid Pressure and Speed Changes

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bernoulli's principle: applications

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energy conservation and bernoulli's equation

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Bernoulli’s Equation in Streamlined Flow

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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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stokes' law

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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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