Name: finding the force on curved fluid surfaces
Uploaded: 2025-02-13T15:43:11.000Z
Duration: 1 min 4 s
Channel: JoVE

底部に曲面がある既知の比重の流体があるスイミングプールを考えてみましょう。
曲面の周囲の体積が単位長に沿って水平面と垂直面で分離されている場合、水平面面と垂直面面は、流体によりそれらの平面に垂直な力を受けます。
密閉された体積内の流体の自重は、流体の比重と密閉された空間の体積の積であり、体積の重心を通じて作用します。
曲面が流体に及ぼす力成分は、水平方向と垂直方向の両方で、水平面と垂直面に発生する力と、分離された体積内の流体の自重によって表すことができます。
最後に、曲面に作用する静水圧は、スイミングプールの曲面が流体に及ぼす力成分の二乗の合計の平方根によって与えられます。

曲面上の静水圧力

曲面上の静水圧は、土木工学の分野で幅広く応用されている流体力学の基本概念です。貯水池、ダム、貯蔵タンクなどの曲面と流体が接触すると、曲面に沿って大きさと方向が変化する圧力がかかります。曲面構造に流体が及ぼす静水力の合計を評価するために、エンジニアは通常、表面に隣接する流体体積を分離し、この体積と交差する仮想の水平面と垂直面に作用する力を分析します。

 水平力と垂直力は、各平面に垂直に作用する流体圧力から生じ、その大きさは流体の特定の重量と深さに依存します。さらに、分離された体積内の流体の自重は、その重心を介して作用し、曲面上の全体的な力に寄与します。水平成分と垂直成分の二乗を合計し、平方根を求めることで、エンジニアは曲面上の静水力の合計を計算できます。

 これらの力を理解することは、ダム、パイプライン、格納容器などの安全で効率的な水力構造物を設計するために不可欠です。曲面上の静水圧を適切に評価することで、エンジニアはさまざまな流体負荷の下で構造の安定性を確保し、重要なインフラの長期的な耐久性と安全性に貢献できます。

底部に曲面がある既知の比重の流体があるスイミングプールを考えてみましょう。
曲面周りのボリュームが...

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

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

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 fluid pressure acts perpendicular to each plane. The size of each force depends on the fluid’s specific weight and depth.

The weight of the fluid inside the isolated volume also matters. This self-weight acts through the volume’s center of gravity. Engineers combine the horizontal and vertical force components to get the total hydrostatic force. They do this by squaring the two components, adding them, and taking the square root.

This method is useful for designing safe hydraulic structures. It supports the analysis of dams, pipelines, and containment vessels. Accurate force calculations help these structures stay stable under fluid loads. They also improve long-term durability and safety in essential infrastructure.

Finding the Force on Curved Fluid Surfaces

finding-the-force-on-curved-fluid-surfaces

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...

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 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

See how hydrostatic pressure on curved surfaces is analyzed using horizontal and vertical force components, fluid weight, and depth in civil engineering examples.

Finding the Force on Curved Fluid Surfaces | 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.

Finding the Force on Curved Fluid Surfaces

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