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

圧力は、単位面積あたりの力の大きさとして定義されます。非圧縮性流体を考慮すると、力は比重量または流体密度で表すことができます。
水中の4つのポイントを考えてみましょう。圧力は、サーフェスから同じ深さにあるすべてのポイントで同じですが、浅い深さでは低くなります。圧力は、表面からの深さに比例して増加します。
パスカルの法則によれば、非圧縮性静的流体の任意の点での圧力強度は、すべての方向で同じです。
単位幅のくさび形の無限小流体要素を仮定します。各辺の力は、圧力と面積の積として表されます。
液体が静止しているため、力の水平成分と垂直成分の合計はゼロになるはずです。
水平成分を取り、三角関数の関係を使用して、方程式を簡略化して px を ps に等しくします。
同様に、垂直成分を考慮すると、方程式は単純化されてpyがpsに等しくなります。 
したがって、どの点でも圧力はすべての方向で同じです。

<ol>
	<li>ヒベラー、RC(2016)。エンジニアリングメカニクス:静力学。第14版、ニュージャージー州:ピアソン。512ページ。</li>
</ol>

流体圧力

機械工学では、流体圧力は液体の流れを利用するシステム、例えば油圧システム、ポンプ、バルブの設計において重要な役割を果たします。これらのシステムを設計する際、エンジニアは流体圧力によって生じる力に耐えられるようにし、損傷や故障を防止しなければなりません。

パスカルの法則によれば、静止した流体は全ての方向で等しい圧力を生成します。この圧力は単位面積当たりの力として測定され、その大きさは流体の比重や密度、盤測点の深さによって異なります。この関係は数学的に p = ρgzと表すことができます。ここで、ρは流体の密度、gは重力加速度、zは深さを示します。

上記の式は圧縮できない流体（ほとんどの液体）に対して有効ですが、温度と圧力の両方で密度が大幅に変化する気体には適用できません。この式が液体にどのように適用されるかを理解するために、水中に位置する3つの点を考えてみましょう。表面からの同じ深さで、全ての点での圧力は同じです。しかし、浅い深さでは圧力が低くなります。表面から遠ざかるにつれて圧力は深さに比例して上昇します。

機械工学では、油圧システム、ポンプなど、液体の流れを利用するシステムを設計する上で、流体圧力が重要な役割を果たします。

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Center of Gravity and Centroid

重心と図心

KEY TERMS AND CONCEPTS

主要用語と概念

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

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mechanical engineering

How Depth Changes Fluid Pressure

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