Name: pressure balance in a fluid element
Uploaded: 2025-02-13T15:43:11.000Z
Duration: 1 min 13 s
Channel: JoVE

Considere um pequeno elemento fluido retangular com os comprimentos das arestas assumidos como retirados de qualquer local arbitrário dentro da massa fluida de interesse.
Dois tipos de forças atuam sobre este elemento, incluindo forças de superfície causadas pela pressão e uma força corporal igual ao peso do elemento.
Se a pressão é denotada no centro do elemento como p, a pressão média nas diferentes faces pode então ser descrita em termos de p e suas derivadas.
Para entender o efeito das forças no elemento fluido, a força superficial resultante na direção y pode ser expressa e, da mesma forma, para as superfícies x e z.
A força de superfície resultante que atua no elemento agora pode ser representada em forma de vetor e posteriormente expressa como a força de superfície resultante por unidade de volume.
O peso do elemento pode ser expresso usando o peso específico do fluido.
A segunda lei de Newton para o elemento fluido pode ser expressa usando a força superficial resultante por unidade de volume e o peso do elemento.
Com isso, a equação do campo de pressão pode ser obtida.

equação básica para campo de pressão

A equação básica para um campo de pressão na mecânica dos fluidos captura o equilíbrio de forças dentro de qualquer segmento de fluido, fornecendo uma compreensão fundamental de como a pressão muda em fluidos sob várias forças. Geralmente, dois tipos principais de forças atuam em qualquer parte de um fluido: forças de superfície e forças de corpo. As forças de superfície surgem de diferenças de pressão entre pontos no fluido, resultando em forças líquidas que podem variar dependendo do gradiente de pressão local. As forças de corpo, por outro lado, são distribuídas por todo o fluido e surgem principalmente da gravidade agindo sobre a massa do fluido.

A equação do campo de pressão é derivada pela análise dessas forças em combinação com a segunda lei de Newton, que vincula a força à aceleração da massa do fluido. Esta equação oferece uma visão simplificada de como as forças interagem para criar variações de pressão em um fluido. Quando a pressão aumenta ou diminui em um fluido, isso geralmente leva ao movimento ou aceleração, impulsionado por esse equilíbrio de forças.

A equação do campo de pressão é essencial para entender o comportamento do fluido, desde o fluxo em rios e canos até mudanças na pressão atmosférica e padrões climáticos. Ao entender como a pressão é distribuída em um fluido, o movimento do fluido pode ser previsto, e sistemas podem ser projetados para gerenciar o fluxo em aplicações que vão desde máquinas hidráulicas até redes de distribuição de água e até mesmo aerodinâmica.

Equação básica para campo de pressão

Considere um pequeno elemento fluido retangular com os comprimentos das arestas assumidos como retirados de qualquer local arbitrário dentro da massa fluida de ...

Education

JoVE Core

Civil Engineering

Engenharia Civil

Unit 1

Unidade 1

Fluid Statics

Estática dos Fluidos

KEY TERMS AND CONCEPTS

TERMOS E CONCEITOS-CHAVE

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 fluid, and gravity is the main example because it acts on the fluid’s mass.

The pressure field equation is derived by combining these forces with Newton’s second law, which connects force and acceleration. The result gives a simplified way to see how pressure variations form in a fluid. When pressure increases or decreases across the fluid, the force balance can lead to motion or acceleration.

This idea is useful for understanding fluid behavior in rivers and pipes, as well as atmospheric pressure changes and weather patterns. It also helps predict fluid movement and support the design of systems such as hydraulic machinery, water distribution networks, and aerodynamics applications.

Pressure Balance in a Fluid Element

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

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

Learn how surface forces, body forces, and Newton’s second law combine to explain pressure changes in fluids, from pipes to weather patterns.

Pressure Balance in a Fluid Element | 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

Pressure Balance in a Fluid Element

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