Name: pascal’s principle in static fluids
Uploaded: 2023-04-30T11:04:20.000Z
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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

Das Pascalsche Prinzip besagt, dass, wenn der Druck in einem eingeschlossenen Fluid geändert wird, die Änderung auf das gesamte Fluid und auf die Wände des Behälters übertragen wird, ohne dass sich die Größe verringert.
Um dieses Prinzip zu verstehen, betrachten Sie eine mit Wasser gefüllte Wasserpistole mit mehreren Düsen und der Querschnittsfläche A.
Wenn der Kolben mit einer Kraft F gedrückt wird, wird die entsprechende Druckänderung F/A durch das gesamte Wasservolumen übertragen und erreicht jede Düse.
Das Wasser tritt mit dem gleichen Druck durch jede Düse ab, nach dem Pascalschen Prinzip.
Nehmen wir ein anderes Beispiel: Lassen Sie ein Fass mit einem langen, dünnen Rohr verbinden, durch das das Wasser gegossen wird.
Wenn das Fass voll ist und eine zusätzliche Menge Wasser hineingegossen wird, steigt der Druck, der durch das eindringende Wasser ausgeübt wird, schnell über sein gesamtes Volumen im Fass an, wodurch es von allen Seiten austritt.

pascal'sches gesetz

Im Jahr 1653 veröffentlichte der französische Philosoph und Wissenschaftler Blaise Pascal "Abhandlung über das Gleichgewicht der Flüssigkeiten", in der die Prinzipien der statischen Flüssigkeiten behandelt werden. Eine statische Flüssigkeit ist eine Flüssigkeit, die sich nicht bewegt. Wenn eine Flüssigkeit nicht fließt, sagen wir, dass die Flüssigkeit im statischen Gleichgewicht ist. Wenn es sich um Wasser handelt, sagen wir, dass es im hydrostatischen Gleichgewicht ist. Für eine Flüssigkeit im statischen Gleichgewicht muss die resultierende Kraft auf einen beliebigen Teil der Flüssigkeit null sein. Andernfalls wird die Flüssigkeit zu fließen beginnen. Pascal beobachtete, dass eine Änderung des Drucks, der auf eine eingeschlossene Flüssigkeit ausgeübt wird, unvermindert durch die gesamte Flüssigkeit und an die Wände ihres Behälters übertragen wird. Darüber hinaus impliziert Pascals Prinzip, dass der Gesamtdruck in einer Flüssigkeit die Summe der Drücke aus verschiedenen Quellen ist. Zum Beispiel hängt der Druck in einer bestimmten Tiefe in einer Flüssigkeit von der Tiefe der Flüssigkeit und dem Druck der Atmosphäre ab.

In einer eingeschlossenen Flüssigkeit übertragen die Atome der Flüssigkeit, da sie sich frei bewegen können, den Druck auf alle Teile der Flüssigkeit und auf die Wände des Behälters. Jede Änderung des Drucks wird unvermindert übertragen. Beachten Sie, dass dieses Prinzip nicht besagt, dass der Druck an allen Punkten einer Flüssigkeit gleich ist, was nicht stimmt, da der Druck in einer Flüssigkeit in der Nähe der Erde mit der Höhe variiert. Vielmehr gilt dieses Prinzip für die Änderung des Drucks. Angenommen, es wird etwas Wasser in einen zylindrischen Behälter mit einer Höhe (H) und einer Querschnittsfläche (A) gegeben, der einen beweglichen Kolben mit einer Masse m hat. Durch das Hinzufügen von Gewicht (mg) oben auf dem Kolben erhöht sich der Druck oben um mg/A, da das zusätzliche Gewicht auch über die Fläche (A) des Deckels wirkt.

Gemäß Pascals Prinzip ändert sich der Druck an allen Stellen im Wasser um den gleichen Betrag, mg/A. Daher erhöht sich der Druck auch am Boden um mg/A. Somit ist der Druck am Boden des Behälters gleich der Summe aus dem Luftdruck, dem Druck durch die Flüssigkeit und dem Druck, der durch die Masse bereitgestellt wird.

Dieser Text ist angepasst von <a href="https://openstax.org/books/university-physics-volume-1/pages/14-3-pascals-principle-and-hydraulics">Openstax, University Physics Volume 1, Abschnitt 14.3: Pascals Prinzip und Hydraulik.</a>

Pascal'sches Gesetz

Im Jahr 1653 veröffentlichte der französische Philosoph und Wissenschaftler Blaise Pascal eine "Abhandlung über das Gleichgewicht der Flüssigkeiten", in der er die ...

Education

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Physik

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Einheit 1

Fluid Mechanics

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KEY TERMS AND CONCEPTS

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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

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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...

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excess pressure inside a drop and a bubble

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buoyancy

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contact angle

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rise of liquid in a capillary tube

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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

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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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