Name: fluid pressure at one point
Uploaded: 2025-02-13T15:43:11.000Z
Duration: 1 min 15 s
Channel: JoVE

エッジ寸法が定義された小さな三角形のくさびを、任意の位置の流体質量から抽出することを考えてみます。
ウェッジに作用する力は、周囲の流体が平面に加える垂直圧力力と、流体要素自体の重量だけです。
せん断応力を考慮せずに加速運動を経験すると仮定する流体要素の y 方向と z 方向の運動方程式は 0 に等しくなります。
圧力は、圧力によって生成される力を計算するために作用する領域で乗算されます。
垂直寸法と水平寸法は、幾何学的関係に基づいて傾斜面の長さで表すことができます。
これらの値を運動方程式に代入することにより、三角形のくさびの平面に作用する力の式は、ジオメトリに関与する辺の長さに関して簡略化されます。
長さがゼロに近づくと、結果は流体内の各表面に作用する圧力が互いに等しいことを示します。この重要な発見は、パスカルの法則と呼ばれます。

点における圧力の概念

流体内の点における圧力の概念は、流体内の圧力が特定の場所では全方向で均一であることを示しています。この均一性は、流体分子が流体内でのランダムな動きと継続的な衝突により、どの点でも均等に力を及ぼすために生じます。点における圧力は周囲の流体分子によって決定され、形状や方向ではなく、深さや密度などの要因によって影響を受けます。

 静止状態の流体では、方向とは無関係な分子相互作用により、圧力はすべての方向に均等に作用します。流体内の深さが増すと、圧力は比例して上昇します。これは、特定の点における圧力がその点より上の流体柱の高さと流体の密度のみに依存するという原則に従います。これはパスカルの法則につながります。パスカルの法則は、非圧縮性流体内の 1 点における圧力の変化は、流体内のすべての点に均等に伝わると主張しています。

 この均一な圧力分布の基本原則は、土木工学の用途において非常に重要です。たとえば、ダムを設計する場合、水深に応じて水圧が増し、ダムの構造的完全性に影響を与えるため、水深によって生じる圧力を慎重に考慮する必要があります。

エッジ寸法が定義された小さな三角形のくさびを、任意の位置の流体質量から抽出することを考えてみます。
くさびに作用する唯一の力...

Education

JoVE Core

Civil Engineering

土木工学

Unit 1

ユニット1

Fluid Statics

流体静力学

KEY TERMS AND CONCEPTS

主要用語と概念

Concept of Pressure at a Point

fluid pressure at one point

Fluid pressure at one point is the focus of this lesson. It shows that pressure in a fluid is the same in every direction at a single location. This happens because fluid molecules move randomly and collide with nearby molecules in a balanced way.

At a given point, the pressure depends on the surrounding fluid molecules. It is affected by depth and density, not by the shape of the container or the way the fluid is oriented. In a fluid at rest, the pressure acts equally in all directions because the molecular motion does not favor one direction over another.

Pressure also increases as depth increases. The pressure at a specific point depends on the height of the fluid column above that point and on the fluid’s density. This idea leads to Pascal’s law, which says that a pressure change at one point in an incompressible fluid is transmitted equally throughout the fluid.

This principle is important in civil engineering. When engineers design dams, they must account for water pressure at different depths. Water pressure rises with depth, and that increase affects the dam’s structural strength.

Fluid Pressure at One Point

concept of pressure at a point

Fluid pressure at one point is the focus of this lesson. It shows that pressure in a fluid is the same in every direction at a single location. This happens because fluid molecules move randomly and collide with nearby molecules in a balanced way. At a given point, the pressure depends on the surrounding fluid molecules. It is affected by depth and density, not by the shape of the container or the way the fluid is oriented. In a fluid at rest, the pressure acts equally in all directions...

basic equation for pressure field

Pressure Balance in a Fluid Element

The pressure field equation describes how forces stay balanced inside a small fluid element. In fluid mechanics, this balance helps explain how pressure changes from one place to another within a fluid. Two main force types act on a fluid segment: surface forces and body forces. Surface forces come from pressure differences across nearby points in the fluid, so they depend on the local pressure gradient, which is the rate of pressure change with position. Body forces are spread through the...

pressure variation in a fluid at rest

Hydrostatic Pressure and Fluid Depth

Hydrostatic pressure describes how pressure changes with depth in a fluid at rest. In a stationary fluid, the fluid acceleration is zero, so the forces inside the fluid balance. That means pressure at a point below the surface depends on depth, not on the container’s shape or size. Only vertical forces affect the pressure change in this situation. These forces come from the weight of the fluid above a point. When pressure is compared at two different levels, the difference in pressure equals...

measurement of fluid pressure

Manometers and Gauges for Fluid Pressure

Fluid pressure is measured with manometers and related gauges. These tools use a liquid column to show pressure differences. The height of the column gives a simple reading of the force the fluid exerts. A basic manometer is the piezometer. It is a vertical tube that is open at the top and filled with the same fluid being measured. When the tube connects to a container, the fluid height in the tube matches the pressure inside that container. For more detailed measurements, the U-tube...

hydrostatic pressure force on a plane surface

hydrostatic-pressure-force-on-a-plane-surface

Hydrostatic Pressure on Submerged Surfaces

Hydrostatic pressure creates force on submerged plane surfaces. The force depends on the fluid pressure and the area of the surface. The way that force acts changes with the surface position. For a horizontal surface, the depth stays the same across the whole area. That means the pressure is uniform. The resultant force equals the pressure at that depth multiplied by the surface area, and it acts through the centroid of the surface. For a vertical surface, pressure increases as depth...

hydrostatic pressure force on a curved surface

hydrostatic-pressure-force-on-a-curved-surface

Finding the Force on Curved Fluid Surfaces

Hydrostatic pressure on curved surfaces is an important idea in fluid mechanics. It helps explain how water pushes on curved structures in civil engineering. Examples include reservoirs, dams, and storage tanks. The pressure changes in both size and direction along the curve. To find the total hydrostatic force on a curved surface, engineers isolate the fluid volume next to that surface. They then study the forces on imaginary horizontal and vertical planes that cut through the volume. The...

buoyancy and stability for submerged and floating bodies

buoyancy-and-stability-for-submerged-and-floating-bodies

How Buoyancy Keeps Bodies Stable in Water

Buoyancy and stability explain how submerged and floating bodies behave in a fluid. When a body is fully or partly under water and stays still, the fluid pushes upward on it. That upward push is called the buoyant force. The buoyant force acts through the center of buoyancy. This is the center of the displaced fluid volume. Archimedes’ principle says the buoyant force equals the weight of the fluid displaced by the body. Stability describes whether a body can return to its original position...

design example: application of archimedes' principle

design-example-application-of-archimedes-principle

Floating Block Buoyancy and Center of Buoyancy

Archimedes' principle is used to analyze the buoyant force on a wooden block that floats in seawater. The block has a rectangular section, and its dimensions, specific gravity, and the specific weight of seawater are used in the calculation. This setup shows how floating bodies stay in equilibrium. The first step is to find the weight of the block from its volume and specific gravity. Then Archimedes' principle is applied. The weight of the displaced water must equal the weight of the block.

key terms and concepts

Explore how fluid pressure acts at a single point, why it is equal in all directions, and how depth, density, and Pascal’s law apply to dams.

Fluid Pressure at One Point | JoVE K12

JoVE Core Civil Engineering provides a foundational exploration of essential construction materials in civil engineering, focusing on bricks, stones, steel, wood, and concrete through easy-to-understand animated videos. This collection covers the properties, manufacturing processes, and practical applications of these materials. Additionally, the accompanied science-in-action videos demonstrate the research experiments performed in laboratories.

civil engineering

Fluid Pressure at One Point

Description

Transcript