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

Рассмотрим извлечение небольшого треугольного клина с определенными размерами ребер из массы жидкости в произвольном месте.
Единственными силами, действующими на призму, являются силы нормального давления, оказываемые окружающей жидкостью на плоские поверхности, и вес самого элемента жидкости.
Уравнения движения в направлениях y и z для жидкостного элемента, который, как предполагается, испытывает ускоренное движение без учета касательных напряжений, равны нулю.
Давление умножается на площадь, на которую оно действует, чтобы рассчитать силу, создаваемую давлением.
Вертикальные и горизонтальные размеры могут быть выражены в терминах длины наклонной плоскости на основе геометрических соотношений.
Подставляя эти величины в уравнения движения, выражения сил, действующих на плоскости треугольного клина, упрощаются в терминах длин сторон, участвующих в геометрии.
Если длины близки к нулю, результат указывает на то, что давление, действующее на каждую поверхность в жидкости, равно друг другу. Этот ключевой вывод называется законом Паскаля.

Концепция давления в точке

Концепция давления в точке жидкости утверждает, что давление внутри жидкости одинаково во всех направлениях в определенной точке. Эта однородность возникает, потому что молекулы жидкости равномерно прикладывают силу в любой точке из-за их случайного движения и непрерывных столкновений внутри жидкости. Давление в точке определяется окружающими молекулами жидкости и зависит от таких факторов, как глубина и плотность, а не от формы или ориентации.

 В покоящейся жидкости давление действует одинаково во всех направлениях из-за молекулярных взаимодействий, которые не зависят от направления. По мере увеличения глубины давление внутри жидкости пропорционально увеличивается, следуя принципу, согласно которому давление в определенной точке зависит исключительно от высоты столба жидкости над этой точкой и плотности жидкости. Это приводит к закону Паскаля, который утверждает, что любое изменение давления в одной точке несжимаемой жидкости передается одинаково во все точки жидкости.

 Этот основополагающий принцип равномерного распределения давления имеет решающее значение в приложениях гражданского строительства. Например, при проектировании плотин необходимо тщательно учитывать давление, оказываемое водой на разных глубинах, поскольку давление увеличивается с глубиной и влияет на структурную целостность плотины.

Рассмотрим извлечение небольшого треугольного клина с определенными размерами ребер из массы жидкости в произвольном месте.
Единственные силы, действующие на клин...

Education

JoVE Core

Civil Engineering

Unit 1

Раздел 1

Fluid Statics

Гидростатика

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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

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