Name: how flow changes affect particle motion
Uploaded: 2025-02-13T15:43:18.000Z
Duration: 1 min 11 s
Channel: JoVE

흐름에서 유적선을 따라 이동하는 유체 입자를 생각해 보십시오. 입자의 속도는 위치와 시간의 함수로 표시됩니다.
이제 입자의 가속도는 시간에 대한 속도의 표현을 구별하여 결정할 수 있습니다.
이 속도가 어떤 지점으로 일반화되면 가속도도 일반적으로 표현될 수 있습니다.
또한, 가속도의 구성 요소는 세 개의 수직 방향으로 표시될 수 있으며, 이는 시간이 지남에 따라 물체의 속도가 어떻게 변하는지 나타냅니다.
마지막으로, 가속도는 시간에 대한 속도의 도함수로 표현할 수 있습니다.
이 방정식에서 시간 도함수는 국소 도함수로 표시되며 정상 흐름에서 0과 같으며 이 경우 국소 효과는 사라집니다.
불안정한 흐름에서는 속도, 온도 및 밀도와 같은 매개변수가 지정된 위치에서 시간이 지남에 따라 변할 수 있습니다.
즉, 공간 도함수는 0으로 감소하고 가속도는 시간에 대한 속도의 편도함수로 감소합니다.

정상 및 비정상 흐름에서의 속도 및 가속도

유체 역학에서 속도와 가속도는 정상 및 비정상 흐름에서 입자 운동을 분석하는 데 중요한 개념입니다. 경로선을 따라 움직이는 유체 입자를 생각해 보세요. 여기서 속도는 위치와 시간에 따라 달라집니다. 입자의 가속도는 속도를 시간에 따라 미분하여 얻습니다.

가속도는 흐름의 모든 지점으로 일반화할 수 있으며, 시간에 따른 속도 변화를 나타내는 세 개의 수직 방향을 따라 성분으로 표현할 수 있습니다. 이러한 성분은 입자의 속도가 다른 공간 방향에서 어떻게 진화하는지 반영합니다.

정상 흐름에서 각 지점의 속도는 시간에 따라 일정하게 유지되므로 속도의 로컬 시간 미분인 로컬 미분이 0입니다. 결과적으로 입자의 속도에는 시간에 따른 변화가 없으며 가속도는 속도의 공간적 변화에 의해서만 지배됩니다.

반면 비정상 흐름은 주어진 위치에서 시간에 따른 속도, 온도 및 밀도의 변화를 포함합니다. 이 경우 로컬 시간 미분이 0이 아니므로 입자의 가속에 기여합니다. 따라서 비정상 유동에서 가속도는 시간에 대한 속도의 편미분으로 주어지며, 이는 유동의 시간에 따른 본질을 강조합니다.

흐름에서 유적선을 따라 이동하는 유체 입자를 생각해 보십시오. 입자의 속도는 위치와 시간의 함수로 표시됩니다.
자, ...

velocity-and-acceleration-in-steady-and-unsteady-flow

Education

교육

JoVE Core

Civil Engineering

토목공학

Unit 1

제1단원

Fluid Kinematics

유체 운동학

KEY TERMS AND CONCEPTS

주요 용어 및 개념

Velocity and Acceleration in Steady and Unsteady Flow

how flow changes affect particle motion

Velocity and acceleration help describe how a fluid particle moves in steady and unsteady flow. A fluid particle follows a pathline, and its velocity depends on both position and time. Acceleration is found by differentiating velocity with respect to time, so it shows how the particle’s motion changes.

In a flow field, acceleration can be written using three perpendicular components. These components show how velocity changes over time in different spatial directions. This gives a general way to track motion at any point in the flow.

Steady flow means the velocity at each point stays constant with time. In that case, the local time derivatives of velocity, called local derivatives, are zero. That means there is no time-based change in the particle’s velocity, and acceleration comes only from spatial changes in velocity.

Unsteady flow is different because velocity, temperature, and density can change with time at a fixed location. Here, the local time derivatives are not zero, so they add to the particle’s acceleration. In this case, acceleration is given by the partial derivative of velocity with respect to time, which highlights the time-dependent nature of the flow.

How Flow Changes Affect Particle Motion

eulerian and lagrangian flow descriptions

eulerian-and-lagrangian-flow-descriptions

Tracking Fluid Motion in Space and Time

Fluid flow can be described with the Eulerian and Lagrangian methods. These two approaches give different views of the same moving fluid. They are useful in science and engineering because the best method depends on the problem being studied. The Eulerian method looks at fixed points in space. At each location, it measures fluid properties such as velocity, pressure, and temperature as the fluid moves past. This stationary view is useful when studying how a fluid interacts with a solid object.

introduction to types of flows

Flow Patterns by Direction and Time

Fluid flow can be grouped by direction and by how it changes over time. The simplest case is one-dimensional flow. In this type, properties such as velocity and pressure change along only one axis. Water moving through a straight pipe is a common example, because changes in other directions are very small. Two-dimensional flow changes in two directions. It varies in both length and height, so the analysis is more complex than one-dimensional flow. Air moving over a flat surface, such as a...

streamlines, streaklines, and pathlines

Tracing Fluid Motion: Three Flow Paths

Streamlines, streaklines, and pathlines are three ways to describe fluid motion. Each one shows flow from a different angle. Together, they help students compare how a fluid moves in steady and unsteady flow. A streamline is a line that stays tangent to the fluid’s velocity vector at each point. That means the fluid velocity points along the streamline. Streamlines give an instant picture of the flow field, so they are useful for showing the overall direction of flow in a fluid system. In...

control volume and system representations

control-volume-and-system-representations

Tracking Fluid Through Space or Mass

Fluid analysis often uses two linked ideas: the control volume approach and the system approach. Both help describe mass, energy, and momentum transfer, but they focus on different things. One follows a region in space. The other follows a fixed mass of fluid over time. The control volume approach looks at a stationary area in space through which fluid moves. That area is bounded by a control surface, which is the outer edge of the region. A pipe with water flowing through it is a clear...

velocity and acceleration in steady and unsteady flow

Velocity and acceleration help describe how a fluid particle moves in steady and unsteady flow. A fluid particle follows a pathline, and its velocity depends on both position and time. Acceleration is found by differentiating velocity with respect to time, so it shows how the particle’s motion changes. In a flow field, acceleration can be written using three perpendicular components. These components show how velocity changes over time in different spatial directions. This gives a general way...

reynolds transport theorem

Reynolds Transport and Control Volumes

Reynolds transport theorem links a fluid system to a control volume. It helps explain how the time rate of change of a property can be tracked in fluid dynamics. The theorem uses extensive properties, such as mass, velocity, acceleration, temperature, and momentum. These properties depend on the size of the system. Their intensive forms are the values per unit mass. The total amount of an extensive property in a system at any instant is the sum of the amounts carried by each tiny fluid...

design example: flow through a fire extinguisher

design-example-flow-through-a-fire-extinguisher

Fire Extinguisher Nozzle Flow and Pressure

A pressurized water fire extinguisher uses fluid dynamics to create a fast stream of water. The water is stored at a much higher pressure inside the extinguisher than the surrounding air. When the extinguisher is activated, that pressure difference forces water to flow out quickly. Bernoulli's equation helps predict the exit speed of the water. This equation links pressure and velocity. As pressure drops, velocity increases. In the extinguisher, the high internal pressure is converted into the...

key terms and concepts

See how velocity and acceleration describe fluid particle motion in steady and unsteady flow, including local derivatives and time-dependent changes.

How Flow Changes Affect Particle Motion | 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.

How Flow Changes Affect Particle Motion

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