Name: how depth changes fluid pressure
Uploaded: 2023-09-22T11:49:33.000Z
Duration: 1 min 14 s
Channel: JoVE

Der Druck ist definiert als die Größe der Kraft pro Flächeneinheit. Bei einem inkompressiblen Fluid kann die Kraft in Form eines spezifischen Gewichts oder einer Fluiddichte ausgedrückt werden.
Betrachten Sie vier Punkte im Wasser. Der Druck ist für alle Punkte in der gleichen Tiefe von der Oberfläche gleich, aber in geringen Tiefen geringer. Der Druck nimmt linear mit der Tiefe von der Oberfläche zu.
Nach dem Pascalschen Gesetz ist die Druckintensität an einem bestimmten Punkt in einem inkompressiblen statischen Fluid in alle Richtungen gleich.
Nehmen wir ein keilförmiges infinitesimales Fluidelement mit einer Breiteneinheit an. Die Kraft auf jeder Seite wird als Produkt aus Druck und Fläche ausgedrückt.
Da sich die Flüssigkeit in Ruhe befindet, sollte die Summe der horizontalen und vertikalen Komponenten der Kräfte Null sein.
Unter Verwendung der horizontalen Komponenten und unter Verwendung trigonometrischer Beziehungen werden die Gleichungen vereinfacht, um px gleich ps zu erhalten.
In ähnlicher Weise werden die Gleichungen unter Berücksichtigung der vertikalen Komponenten vereinfacht, um py gleich ps zu erhalten. 
Der Druck ist also an jedem Punkt in alle Richtungen gleich.

<ol>
	<li>Hibbeler, R.C. (2016). Technische Mechanik: Statik. Vierzehnte Auflage, New Jersey: Pearson. S. 512.</li>
</ol>

flüssigkeitsdruck

In der Maschinenbau spielen Flüssigkeitsdrücke eine entscheidende Rolle bei der Konstruktion von Systemen, die den Flüssigkeitsfluss nutzen, wie z.B. hydraulische Systeme, Pumpen und Ventile. Bei der Konstruktion dieser Systeme müssen Ingenieure sicherstellen, dass sie den durch den Flüssigkeitsdruck erzeugten Kräften standhalten können, um Schäden oder Ausfälle zu vermeiden. Gemäß dem Pascal'schen Gesetz erzeugt eine in Ruhe befindliche Flüssigkeit einen gleichmäßigen Druck in alle Richtungen. Dieser Druck wird als Kraft pro Fläche gemessen und seine Stärke hängt von der spezifischen Gewichtskraft oder Dichte der Flüssigkeit und der Tiefe des Messpunkts von der Flüssigkeitsoberfläche ab. Diese Beziehung lässt sich mathematisch ausdrücken als p = ρgz, wobei ρ die Flüssigkeitsdichte, g die Erdbeschleunigung und z die Tiefe ist. Es sollte beachtet werden, dass die oben genannte Gleichung für inkompressible Flüssigkeiten, wie die meisten Flüssigkeiten, gültig ist, aber nicht für Gase, deren Dichte sich sowohl mit Temperatur als auch mit Druck erheblich verändert. Um zu verstehen, wie diese Gleichung auf Flüssigkeiten zutrifft, betrachten wir drei Punkte, die sich im Wasser befinden. Bei gleicher Tiefe von der Oberfläche ist der Druck für alle drei Punkte identisch. Allerdings ist der Druck in geringer Tiefe niedriger. Der Druck nimmt linear mit der Tiefe zu, wenn man sich weiter von der Oberfläche entfernt.

Flüssigkeitsdruck

Im Maschinenbau spielt der Flüssigkeitsdruck eine entscheidende Rolle bei der Konstruktion von Systemen, die einen Flüssigkeitsstrom nutzen, wie z. B. Hydrauliksysteme, Pumpen und ...

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JoVE Core

Mechanical Engineering

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Unit 1

Einheit 1

Center of Gravity and Centroid

Schwerpunkt und Flächenschwerpunkt

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Fluid Pressure

how depth changes fluid pressure

Fluid pressure changes with depth in liquids used in engineering systems. It matters in hydraulic systems, pumps, and valves, where the forces from moving and resting fluid must be considered to prevent damage or failure.

For a fluid at rest, Pascal’s law says the pressure is equal in all directions. Pressure is force per unit area. Its size depends on the fluid’s specific weight, or mass density, and on how deep the measurement point is below the fluid surface.

This relationship can be written as p = ρgz. In this equation, ρ is fluid density, g is the acceleration due to gravity, and z is depth. The equation applies to incompressible fluids, such as most liquids, but not to gases, because gas density can change greatly with temperature and pressure.

The pattern is easy to see in water. If three points are at the same depth, their pressure is the same. A point closer to the surface has lower pressure. As depth increases, pressure rises in a linear way.

How Depth Changes Fluid Pressure

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fluid pressure

Fluid pressure changes with depth in liquids used in engineering systems. It matters in hydraulic systems, pumps, and valves, where the forces from moving and resting fluid must be considered to prevent damage or failure. For a fluid at rest, Pascal’s law says the pressure is equal in all directions. Pressure is force per unit area. Its size depends on the fluid’s specific weight, or mass density, and on how deep the measurement point is below the fluid surface. This relationship can be...

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key terms and concepts

Explore how fluid pressure changes with depth, why Pascal’s law matters, and how the equation p = ρgz describes pressure in liquids like water.

How Depth Changes Fluid Pressure | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

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How Depth Changes Fluid Pressure

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