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

Pressure is defined as the magnitude of force per unit area. Considering an incompressible fluid, the force can be expressed in terms of specific weight or fluid density.
Consider four points in water. The pressure is the same for all points at the same depth from the surface, but less at shallow depths. The pressure increases linearly with depth from the surface.
According to Pascal&#39;s law, the pressure intensity at any given point in an incompressible static fluid is the same in all directions.
Assume a wedge-shaped infinitesimal fluid element of unit width. The force on each side is expressed as the product of pressure and area.
As the liquid is at rest, the sum of the horizontal and vertical components of the forces should be zero.
Taking the horizontal components and using trigonometric relations, the equations are simplified to obtain px equal to ps.
Similarly, considering the vertical components, the equations are simplified to obtain py equal to ps.&#160;
So, the pressure at any point is the same in all directions.

vloeistofdruk

In de werktuigbouwkunde speelt vloeistofdruk een cruciale rol bij het ontwerpen van systemen die gebruik maken van vloeistofstroom, zoals hydraulische systemen, pompen en kleppen. Bij het ontwerpen van deze systemen moeten ingenieurs ervoor zorgen dat ze bestand zijn tegen de krachten die worden veroorzaakt door vloeistofdruk om schade of falen te voorkomen. Volgens de wet van Pascal zal een stilstaande vloeistof gelijke druk in alle richtingen genereren. Deze druk wordt gemeten als een kracht per oppervlakte-eenheid, en de grootte ervan hangt af van het soortelijk gewicht of massa-dichtheid van de vloeistof en de diepte van het meetpunt vanaf het oppervlak van de vloeistof. We kunnen deze relatie wiskundig uitdrukken als p = ρgz, waarbij ρ de vloeistofdichtheid is, g de versnelling van de zwaartekracht is, en z de diepte is. Het moet worden opgemerkt dat de vergelijking, zoals hierboven vermeld, geldig is voor onsamendrukbare vloeistoffen, zoals de meeste vloeistoffen, maar niet voor gassen, waarvan de dichtheid aanzienlijk verandert met zowel temperatuur als druk. Om te begrijpen hoe deze vergelijking van toepassing is op vloeistoffen, overweeg drie punten gelegen binnenin water. Op dezelfde diepte vanaf het oppervlak is de druk identiek voor alle drie de punten. Echter, de druk is lager op geringe dieptes. De druk neemt lineair toe met de diepte naarmate men verder van het oppervlak gaat.

Vloeistofdruk

In mechanical engineering, fluid pressure plays a critical role in designing systems that utilize liquid flow, such as hydraulic systems, pumps, and ...

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Mechanical Engineering

Werktuigbouwkunde

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Center of Gravity and Centroid

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KEY TERMS AND CONCEPTS

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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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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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