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

Considérons une piscine avec un fluide d’un poids spécifique connu ayant une surface incurvée au fond.
Si le volume autour de la surface courbe est isolé par un plan horizontal et vertical le long d’une unité de longueur, la surface plane horizontale et la surface plane verticale subiront des forces perpendiculaires à leurs plans en raison du fluide.
Le poids propre du fluide dans le volume clos est le produit du poids spécifique du fluide et du volume de l'espace clos, agissant par l'intermédiaire du centre de gravité du volume.
Les composantes de force exercées par la surface incurvée sur le fluide, dans les directions horizontales et verticales, peuvent être exprimées par les forces développées sur les plans horizontal et vertical, ainsi que par le poids propre du fluide dans le volume isolé.
Enfin, la force hydrostatique agissant sur la surface incurvée est donnée par la racine carrée de la somme des carrés des composantes de la force exercée par la surface courbe de la piscine sur le fluide.

force de pression hydrostatique sur une surface courbe

La pression hydrostatique sur les surfaces courbes est un concept fondamental de la mécanique des fluides avec de larges applications dans le domaine du génie civil. Lorsque le fluide est en contact avec une surface courbe, comme dans un réservoir, un barrage ou un réservoir de stockage, il exerce une pression dont l'amplitude et la direction varient le long de la surface courbe. Pour évaluer la force hydrostatique totale exercée par le fluide sur une structure courbe, les ingénieurs isolent généralement le volume de fluide adjacent à la surface et analysent les forces agissant sur des plans horizontaux et verticaux imaginaires coupant ce volume.

Les forces horizontales et verticales résultent de la pression du fluide agissant perpendiculairement à chaque plan, et leurs amplitudes dépendent du poids et de la profondeur spécifiques du fluide. De plus, le poids propre du fluide dans le volume isolé agit par l'intermédiaire de son centre de gravité, contribuant à la force globale sur la surface courbe. En additionnant les carrés des composantes horizontales et verticales et en trouvant la racine carrée, les ingénieurs peuvent calculer la force hydrostatique totale sur la surface courbe.

Il est essentiel de comprendre ces forces pour concevoir des structures hydrauliques sûres et efficaces, telles que des barrages, des pipelines et des cuves de confinement. Une évaluation correcte de la pression hydrostatique sur des surfaces courbes aide les ingénieurs à garantir la stabilité structurelle sous des charges de fluides variables, contribuant ainsi à la durabilité et à la sécurité à long terme des infrastructures essentielles.

Force de pression hydrostatique sur une surface courbe

Considérons une piscine avec un fluide d’un poids spécifique connu ayant une surface incurvée au fond.
Si le volume autour de la surface incurvée est ...

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

Education

Enseignement

JoVE Core

Civil Engineering

Génie civil

Unit 1

Unité 1

Fluid Statics

Statique des fluides

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

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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