Name: how depth changes fluid pressure
Uploaded: 2023-09-22T11:49:33.000Z
Duration: 1 min 14 s
Channel: JoVE

압력은 단위 면적당 힘의 크기로 정의됩니다. 비압축성 유체를 고려할 때 힘은 특정 중량 또는 유체 밀도로 표현할 수 있습니다.
물에 있는 네 가지 점을 생각해 보십시오. 압력은 표면에서 동일한 깊이에 있는 모든 점에 대해 동일하지만 얕은 깊이에서는 더 적습니다. 압력은 표면의 깊이에 따라 선형으로 증가합니다.
파스칼의 법칙에 따르면 비압축성 정적 유체의 주어진 지점에서의 압력 강도는 모든 방향에서 동일합니다.
단위 너비의 쐐기 모양의 극소 유체 요소를 가정합니다. 각 측면의 힘은 압력과 면적의 곱으로 표현됩니다.
액체가 정지해 있기 때문에 힘의 수평 및 수직 구성 요소의 합은 0이어야 합니다.
수평 구성 요소를 취하고 삼각 관계를 사용하면 방정식이 단순화되어 ps와 동일한 px를 얻습니다.
유사하게, 수직 성분을 고려할 때, 방정식은 ps와 동일한 py를 얻기 위해 단순화됩니다. 
따라서 모든 지점의 압력은 모든 방향에서 동일합니다.

<ol>
	<li>히벨러, R.C. (2016). 엔지니어링 역학: 정적. 14판, 뉴저지: 피어슨. 512쪽.</li>
</ol>

유체 압력

기계공학에서 유체 압력은 유압 시스템, 펌프 및 밸브와 같은 액체 흐름을 사용하는 시스템을 설계하는 데 중요한 역할을 합니다. 이러한 시스템을 설계할 때 엔지니어는 손상 또는 고장을 피하기 위해 유체 압력에 의해 생성된 힘을 견딜 수 있는지 확인해야 합니다.
파스칼의 법칙에 따르면 정지한 유체는 모든 방향에 동일한 압력을 발생시킬 것입니다. 이 압력은 단위면적당 힘으로 측정되며, 그 크기는 유체의 비중이나 질량밀도, 유체표면에서 측정되는 지점의 깊이에 따라 달라집니다. 이 관계식을 수학적으로 p = ρ gz으로 표현할 수 있는데, 여기서 ρ 은 유체밀도, g은 중력에 의한 가속도, z은 깊이입니다.
위에서 언급한 바와 같이 이 식은 대부분의 액체와 같은 비압축성 유체에는 유효하지만 온도와 압력에 따라 밀도가 상당히 변하는 기체에는 유효하지 않습니다. 이 방정식이 액체에 어떻게 적용되는지 알기 위해서는 물 속에 위치한 세 개의 점을 고려해야 합니다. 표면에서 같은 깊이에서 압력은 세 개의 점 모두에서 동일합니다. 그러나 압력은 얕은 깊이에서 더 낮습니다. 압력은 표면에서 멀어질수록 깊이에 따라 선형적으로 증가합니다.

기계 공학에서 유체 압력은 유압 시스템, 펌프 및 ...

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Center of Gravity and Centroid

무게중심과 도심

KEY TERMS AND CONCEPTS

주요 용어 및 개념

Fluid Pressure

how depth changes fluid pressure

Fluid pressure changes with depth in liquids used in engineering systems. It matters in hydraulic systems, pumps, and valves, where the forces from moving and resting fluid must be considered to prevent damage or failure.

For a fluid at rest, Pascal’s law says the pressure is equal in all directions. Pressure is force per unit area. Its size depends on the fluid’s specific weight, or mass density, and on how deep the measurement point is below the fluid surface.

This relationship can be written as p = ρgz. In this equation, ρ is fluid density, g is the acceleration due to gravity, and z is depth. The equation applies to incompressible fluids, such as most liquids, but not to gases, because gas density can change greatly with temperature and pressure.

The pattern is easy to see in water. If three points are at the same depth, their pressure is the same. A point closer to the surface has lower pressure. As depth increases, pressure rises in a linear way.

How Depth Changes Fluid Pressure

center of gravity

Center of Gravity in Balance and Design

The center of gravity is the point where an object’s weight appears to act. It is the spot used to balance the object most evenly. In mechanics, this point helps explain stability and moments of inertia. The center of gravity does not always sit inside the object’s shape. In some cases, it can lie outside the body. That is why the idea is useful for both simple and more complex shapes. Its location can be found with the principle of moments. The object is divided into very small parts, and...

center of mass

Center of Mass in Motion

The center of mass helps explain how an object moves through space. It is the point where the total mass of an object can be treated as concentrated. This idea applies to objects of different shapes and sizes. The center of mass is related to the center of gravity, but they are not the same. The center of gravity is the point where an object’s weight seems to be concentrated. It can be used to balance an object perfectly. Knowing the center of mass also helps predict motion. When a ball is...

centroid of a body

Finding the Center of a Body

The centroid is the geometric center of a body. It is an important idea in engineering, physics, and mechanics. For many objects, it lies inside the body. A body with holes or cavities can be an exception. For a homogeneous body, the centroid matches the center of mass or the center of gravity. Homogeneous means the material has a uniform density. In that case, the centroid can often be found by balancing the moments of the body’s volume. Symmetry can also help locate the centroid. If a...

centroid of a body: problem solving

Centroid of a Quarter Circle Wire

The centroid of a quarter circle wire shows how balance points can be found for curved shapes. In physics and engineering, the centroid helps describe stability, balance, and design. For a thin wire bent into a quarter circular arc, the goal is to find the centroid coordinates of the arc itself. Polar coordinates are used to solve this centroid problem. The wire is divided into small differential elements, and each element has a length equal to the radius times the differential angle. The x-...

centroid for the paraboloid of revolution

centroid-for-the-paraboloid-of-revolution

Centroid and Uses of a Paraboloid Shape

The centroid of a paraboloid of revolution is the point where its mass is balanced. A paraboloid of revolution is an axially symmetric surface made by rotating a parabola around its axis. In engineering, this location matters because it helps show how forces spread across the shape. Knowing the centroid can help when building parts that must handle stress and pressure reliably. The paraboloid shape has useful structural properties, including rotational symmetry and strength against stress...

composite bodies

Center of Gravity in Composite Bodies

Composite bodies are made of multiple connected parts that act as one larger object. Each part still has its own weight and center of gravity. To find the center of gravity of the whole body, engineers must account for every part. When the density or specific weight is constant, the center of gravity matches the centroid. The centroid is the geometric center of a shape. This idea is useful when analyzing parts that behave as a single unit. Composite bodies are common in mechanical engineering.

theorems of pappus and guldinus

Surface Area and Volume by Centroid Paths

Pappus and Guldinus theorems help find the surface area and volume of bodies of revolution. A body of revolution is formed when a plane curve or plane area is turned around an axis that does not intersect it. For surface area, a curve is revolved around a non-intersecting axis. A small line element on the curve creates a thin ring as it moves. Adding these ring areas gives the total surface area of the solid. The first theorem says that this surface area equals the length of the generating...

theorems of pappus and guldinus: problem solving

theorems-of-pappus-and-guldinus-problem-solving

Pappus and Guldinus Theorems for Surface Area

Pappus and Guldinus's theorems help find the surface area and volume of composite shapes. These rules are useful when a solid is made from simple parts that are hard to measure directly. A cylindrical storage tank with a conical top is one example. The tank can be split into two simple shapes: a cylinder and a cone. To find surface area, the first theorem is used for the solid formed by revolving each generating curve around a non-intersecting axis. The calculation uses the length of the...

resultant of a general distributed loading

resultant-of-a-general-distributed-loading

Finding the Resultant of Distributed Loads

Distributed loads create a force that is spread over a surface instead of acting at one point. To analyze this kind of loading, engineers use a single resultant force. That force represents the net effect of the entire load. This idea is important in structures that face non-uniform loads. Wind can push on buildings and towers with changing speed and direction, so the load is not evenly spread. Bridges also experience non-uniform loading from vehicles, and some parts of the bridge can feel...

fluid pressure

Fluid pressure changes with depth in liquids used in engineering systems. It matters in hydraulic systems, pumps, and valves, where the forces from moving and resting fluid must be considered to prevent damage or failure. For a fluid at rest, Pascal’s law says the pressure is equal in all directions. Pressure is force per unit area. Its size depends on the fluid’s specific weight, or mass density, and on how deep the measurement point is below the fluid surface. This relationship can be...

fluid pressure over flat plate of constant width

fluid-pressure-over-flat-plate-of-constant-width

Center of Pressure on a Submerged Plate

Fluid pressure on a submerged flat plate depends on depth and shape. A plate under water experiences pressure acting normal to its surface, and the force is spread across the whole area. For a rectangular plate of constant width, this pressure increases from the top edge to the bottom edge. Because the pressure rises with depth, the loading forms a trapezoidal distribution. The resultant force on the plate comes from the trapezoidal volume of water with a specific weight. The line of action of...

fluid pressure over curved plate of constant width

fluid-pressure-over-curved-plate-of-constant-width

Finding Force on a Curved Plate in Water

Fluid pressure on a curved plate of constant width changes in both size and direction. That makes the total force hard to find directly. A common method is to split the force into horizontal and vertical parts and then combine them. The calculation becomes simpler by replacing the distributed load with an equivalent two-dimensional loading. The first step is to include the weight of the liquid inside the block. That force equals the specific weight of the liquid times the plate thickness and...

fluid pressure over flat plate of variable width

fluid-pressure-over-flat-plate-of-variable-width

A submerged flat plate experiences fluid pressure that changes with depth. This pressure can create effects such as drag and buoyancy. To study a flat plate with variable width, the pressure distribution across the plate must be analyzed first. The force on a small strip of the plate is found by multiplying the pressure by the strip’s differential area. The pressure can also be written using the fluid’s specific weight and the depth of that strip below the surface. To find the total, or...

key terms and concepts

Explore how fluid pressure changes with depth, why Pascal’s law matters, and how the equation p = ρgz describes pressure in liquids like water.

How Depth Changes Fluid Pressure | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

How Depth Changes Fluid Pressure

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