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

流れのパスラインに沿って移動する流体粒子を考えてみましょう。粒子の速度は、その位置と時間の関数で表されます。
さて、粒子の加速度は、速度の表現を時間に対して微分することによって決定できます。
この速度を任意の点に一般化すると、加速度も一般的に表すことができます。
さらに、加速度の成分は、物体の速度が時間とともにどのように変化するかを表す3つの垂直方向で示すことができます。
最後に、加速度は、時間に対する速度の微分として表すことができます。
これらの方程式では、時間微分は局所微分として表され、定常流れではゼロに等しく、この場合、局所効果は消失します。
非定常流れでは、速度、温度、密度などのパラメータは、任意の位置で時間とともに変化する可能性があります。
つまり、空間微分は 0 に減少し、加速度は時間に対する速度の偏微分に減少します。

定常および非定常流における速度と加速度

流体力学では、速度と加速度は、定常および非定常流の両方における粒子の動きを分析するための重要な概念です。流跡線に沿って移動する流体粒子を考えてみましょう。その速度は位置と時間に依存します。粒子の加速度は、速度を時間に関して微分することによって得られます。

 加速度は、流れの任意の点に一般化でき、時間の経過に伴う速度の変化を表す 3 つの垂直方向に沿った成分として表すことができます。これらの成分は、粒子の速度がさまざまな空間方向でどのように変化するかを反映しています。

 定常流では、各点の速度は時間の経過に伴って一定であり、つまり、局所微分と呼ばれる速度の局所時間微分はゼロです。その結果、粒子の速度には時間依存の変化はなく、加速度は速度の空間的変化によってのみ左右されます。

 対照的に、非定常流では、任意の場所での速度、温度、密度の時間経過に伴う変化が伴います。この場合、局所時間微分はゼロではなく、粒子の加速に寄与します。したがって、非定常流れでは、加速度は時間に対する速度の偏微分によって与えられ、流れの時間依存の性質が強調されます。

流れのパスラインに沿って移動する流体粒子を考えてみましょう。粒子の速度は、その位置と時間の関数で表されます。
さて、...

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

Education

JoVE Core

Civil Engineering

土木工学

Unit 1

ユニット1

Fluid Kinematics

流体運動学

KEY TERMS AND CONCEPTS

主要用語と概念

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 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.

How Flow Changes Affect Particle Motion

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