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

모서리의 길이가 관심 유체 질량 내의 임의의 위치에서 취해지는 것으로 가정되는 작은 직사각형 유체 요소를 고려하십시오.
이 요소에는 압력으로 인한 표면력과 요소의 무게와 동일한 몸체력을 포함하여 두 가지 유형의 힘이 작용합니다.
압력이 요소의 중심에서 p로 표시되는 경우, 다른 면에 대한 평균 압력은 p와 그 도함수로 설명할 수 있습니다.
유체 요소에 대한 힘의 효과를 이해하기 위해 y 방향의 결과 표면력을 표현할 수 있으며, 마찬가지로 x 및 z 표면에 대해서도 표현할 수 있습니다.
요소에 작용하는 결과적인 표면력은 이제 벡터 형태로 표현될 수 있으며 단위 부피당 결과 표면력으로 더 표현될 수 있습니다.
요소의 무게는 유체의 특정 무게를 사용하여 표현할 수 있습니다.
유체 요소에 대한 뉴턴의 제2법칙은 단위 부피당 결과 표면력과 요소의 무게를 사용하여 표현할 수 있습니다.
이를 통해 압력장의 방정식을 얻을 수 있습니다.

압력장에 대한 기본 방정식

유체 역학에서 압력장에 대한 기본 방정식은 유체의 모든 마디 내에서 힘의 균형을 포착하여 다양한 힘 하에서 유체 내에서 압력이 어떻게 변하는지에 대한 기초적인 이해를 제공합니다. 일반적으로 두 가지 주요 유형의 힘은 유체의 모든 부분에 작용합니다. 표면력과 체적력입니다. 표면력은 유체 내의 지점 간 압력 차이에서 발생하며, 이는 국소 압력 기울기에 따라 달라질 수 있는 순 힘을 초래합니다. 반면 체적력은 유체 전체에 분포하며 주로 유체의 질량에 작용하는 중력에서 발생합니다.

압력장 방정식은 이러한 힘을 뉴턴의 제2 법칙과 결합하여 분석하여 도출되며, 이는 힘을 유체 질량의 가속도에 연결합니다. 이 방정식은 힘이 유체 내에서 압력 변화를 생성하는 상호 작용 방식에 대한 단순화된 관점을 제공합니다. 유체에서 압력이 증가하거나 감소하면 종종 이러한 힘의 균형에 의해 움직이는 움직임이나 가속으로 이어집니다.

압력장 방정식은 강과 파이프의 흐름에서 대기압 변화 및 기상 패턴에 이르기까지 유체 거동을 이해하는 데 필수적입니다. 유체 내에서 압력이 어떻게 분포되는지 이해하면 유체의 움직임을 예측할 수 있으며, 유압 장치부터 물 분배 네트워크, 심지어 공기 역학에 이르기까지 다양한 응용 분야에서 흐름을 관리하도록 시스템을 설계할 수 있습니다.

가장자리의 길이가 유체 질량 내의 임의의 위치에서 취해지는 것으로 가정되는 작은 직사각형 유체 요소를 고려하십시오.

Education

교육

JoVE Core

Civil Engineering

토목공학

Unit 1

제1단원

Fluid Statics

유체 정역학

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 offers a foundational exploration of essential construction materials such as bricks, stones, steel, wood, and concrete, along with fluid mechanics topics like flow over immersed bodies, open channel flow, and dimensional modeling. It also covers key surveying concepts, including leveling, traverse adjustments, curve design, topographic mapping, and geospatial technologies (GPS & GIS). Science-in-action videos showcase laboratory research on materials, fluids, and surveying practices in real-world engineering systems.

civil engineering

Pressure Balance in a Fluid Element

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