Name: tracing fluid motion: three flow paths
Uploaded: 2025-02-13T15:43:18.000Z
Duration: 1 min 18 s
Channel: JoVE

K12 Standards

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

9-12

Physical Geology

igneous-metamorphic-and-sedimentary-rocks

Igneous, Metamorphic And Sedimentary Rocks

Ocean

Streamlines, Streaklines, and Pathlines

考虑水稳定地流过一段弯曲的管道。管道内流动的方向可以通过流线来可视化。
流线表示一条在每一点上始终与流体速度相切的路径。
当流体微粒沿流线运动时，其在任意点的速度方向均与该点流线的切线方向一致。这种速度方向的对齐确保了微粒在每一时刻都沿着流线所定义的流动方向运动。
当将染料注入同一管道的某一固定点时，染料颗粒会随之流动，并持续标记流经该点的流体颗粒。
这条迹线形成了一条迹线，显示了在任意时刻经过某一特定点的粒子所在的位置。
流线表示单个流体粒子随时间变化所经过的实际路径。
设想一片树叶沿着河流漂浮，遵循其独特的路径。树叶在顺流而下过程中所经过的路径称为迹线。
在定常流动中，迹线与流线和脉线重合。然而，在非定常流动中，由于每个质点遵循其动态路径，迹线则有所不同。

流线、脉线和迹线

流线表示在任何给定点始终与流体速度矢量相切的轨迹。流体粒子的速度始终沿着流线方向，确保粒子持续遵循流线的路径。流线对于可视化流体系统中的整体流动方向特别有用，它们提供流动速度场的瞬时表示。在稳定流中，即条件不随时间而变化，流线提供了流动模式的一致图像。 相反，脉线追踪随时间经过特定点的粒子的位置。当在流中固定位置引入染料时，它会显示流体粒子在通过该点时所走的路径，从而有效地显示其位置的时间积分历史。脉线与非稳定流中的流线不同，因为它们随时间跟踪粒子，而流线是瞬时的。 迹线是单个流体粒子随时间在空间中移动的轨迹。例如，一片树叶在河流中顺流而下的路径代表着一条迹线。在稳定流中，迹线与流线和脉线重合，因为稳定流中的条件是恒定的，因此很难区分它们。然而，在非稳定流中，速度和流向会随时间变化，迹线可能会与流线和脉线不同，因为每个粒子在流体中都会遵循一条独特的路径。这些区别对于分析不同流动条件下的流体运动非常重要。

考虑水稳态流过一段弯曲的管道。管道内流动方向可通过流线来可视化。  
流线表示……

Education

教育

JoVE Core

Civil Engineering

土木工程

Unit 1

第一单元

Fluid Kinematics

流体运动学

KEY TERMS AND CONCEPTS

关键术语与概念

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 steady flow, where conditions do not change with time, streamlines give a consistent pattern.

A streakline shows the particles that have passed through one fixed point over time. A common way to see a streakline is to inject dye at a set location in the flow. The dye marks the history of particles that move through that point. Because streaklines track particles over time, they can look different from streamlines in unsteady flow.

A pathline traces the route of one fluid particle as it moves through space and time. A leaf floating downstream in a river is a simple example of a pathline. In steady flow, pathlines, streamlines, and streaklines match and look the same. In unsteady flow, where velocity and flow direction change over time, each particle can follow a different path, so the three lines may no longer coincide.

Tracing Fluid Motion: Three Flow Paths

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

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-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...

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

Compare streamlines, streaklines, and pathlines in fluid flow. Learn how each one shows motion, from instant direction to time-based particle paths.

Tracing Fluid Motion: Three Flow Paths | 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

Igneous Intrusive Rock

Source: Laboratory of Alan Lester - University of Colorado Boulder
Igneous rocks are products of the cooling and crystallization of high temperature ...

Igneous Volcanic Rock

Source: Laboratory of Alan Lester - University of Colorado Boulder
Igneous rocks are the products of cooling and crystallization of magma. Volcanic rocks ...

determining-spatial-orientation-rock-layers-with-brunton

Determining Spatial Orientation of Rock Layers with the Brunton Compass

Source: Laboratory of Alan Lester - University of Colorado Boulder
Most rock units exhibit some form of planar surfaces or linear features. Examples ...

using-topographic-maps-to-generate-topographic-profiles

Using Topographic Maps to Generate Topographic Profiles

Source: Laboratory of Alan Lester - University of Colorado Boulder
Topographic maps are &#34;plan-view&#34; representations of Earth&#39;s ...

Making a Geologic Cross Section

Source: Laboratory of Alan Lester - University of Colorado Boulder
Geologic maps were first made and utilized in Europe, in the mid-to-late 18th century. ...

Igneous
• Mafic and felsic rocks and minerals
• Intrusive (igneous structures: dikes, sills, batholiths, pegmatites)
• Earth's interior (inner core, outer core, lower mantle, upper mantle, Mohorovicic discontinuity, crust)
• Magnetic reversals and Earth's magnetic field
• Thermal energy within the Earth
• Extrusive (volcanic activity, volcanoes: cinder cones, composite, shield)
• Bowen's Reaction Series (continuous and discontinuous branches)

Content elaboration: This unit builds upon a variety of topics studied in middle school. In the Earth and Space Science strand, sedimentary, igneous and metamorphic rocks are introduced. Rocks and minerals are tested and classified. Plate tectonics, seismic waves and the structure of Earth are studied and the geologic record is introduced (including the evidence of climatic variances through Earth's history). In the Life Science strand, fossils and depositional environments are included as they relate to the documented history of life in the geologic record. In the Physical Science strand, waves, thermal energy, currents, pressure and gravity are presented. In this course, geologic, topographic, seismic and aerial maps are used to locate and recognize igneous, metamorphic and sedimentary structures and features. Technological advances permit the investigation of intrusive structures and the interior of Earth. Connections between the minerals present within each type of rock and the environment formed are important. The processes and environmental conditions that lead to fossil fuel formation (Note: this links to the energy resources section below) includes the fossil fuels found in Ohio, nationally and globally. Bowen's Reaction Series is used to develop an understanding of the relationship of cooling temperature, formation of specific igneous minerals and the resulting igneous environment. The focus is on knowing how to use Bowen's Reaction Series, not to memorize it. Virtual demonstrations and simulations of cooling magma and crystallization of the igneous minerals found on the series can be helpful in conceptualizing the chart. The magnetic properties of Earth are examined through the study of real data and evidence. The relationship of polar changes, magnetic striping, grid north, true north and the North Pole are included in the study of Earth's magnetic properties. Features found in the ocean include all types of environments (igneous, metamorphic or sedimentary). Using models (3-D or virtual) with real-time data to simulate waves, tides, currents, feature formation and changing sea levels to explore and investigate the ocean fully is recommended. Interpreting sections of the geologic record to determine sea level changes and depositional environments, including relative age, is also recommended. Technological advances can be used to observe and record the physical features of the Earth, including the ocean floor. Interpreting geologic history using maps of local cross-sections of bedrock can be related to the geologic history of Ohio, the United States and Earth.

Igneous

physical-properties-of-minerals-ii-polymineralic-analysis

Physical Properties Of Minerals II: Polymineralic Analysis

Source: Laboratory of Alan Lester - University of Colorado Boulder
The physical properties of minerals include various measurable and discernible ...

physical-properties-of-minerals-i-crystals-and-cleavage

Physical Properties Of Minerals I: Crystals and Cleavage

Source: Laboratory of Alan Lester - University of Colorado Boulder
The physical properties of minerals comprise various measurable and discernible ...

Metamorphic
• Pressure, stress, temperature and compressional forces
• Foliated (regional), non-foliated (contact)
• Parent rock and degrees of metamorphism
• Metamorphic zones (where metamorphic rocks are found)

Content elaboration: This unit builds upon a variety of topics studied in middle school. In the Earth and Space Science strand, sedimentary, igneous and metamorphic rocks are introduced. Rocks and minerals are tested and classified. Plate tectonics, seismic waves and the structure of Earth are studied and the geologic record is introduced (including the evidence of climatic variances through Earth's history). In the Life Science strand, fossils and depositional environments are included as they relate to the documented history of life in the geologic record. In the Physical Science strand, waves, thermal energy, currents, pressure and gravity are presented. In this course, geologic, topographic, seismic and aerial maps are used to locate and recognize igneous, metamorphic and sedimentary structures and features. Technological advances permit the investigation of intrusive structures and the interior of Earth. Connections between the minerals present within each type of rock and the environment formed are important. The processes and environmental conditions that lead to fossil fuel formation (Note: this links to the energy resources section below) includes the fossil fuels found in Ohio, nationally and globally. Bowen's Reaction Series is used to develop an understanding of the relationship of cooling temperature, formation of specific igneous minerals and the resulting igneous environment. The focus is on knowing how to use Bowen's Reaction Series, not to memorize it. Virtual demonstrations and simulations of cooling magma and crystallization of the igneous minerals found on the series can be helpful in conceptualizing the chart. The magnetic properties of Earth are examined through the study of real data and evidence. The relationship of polar changes, magnetic striping, grid north, true north and the North Pole are included in the study of Earth's magnetic properties. Features found in the ocean include all types of environments (igneous, metamorphic or sedimentary). Using models (3-D or virtual) with real-time data to simulate waves, tides, currents, feature formation and changing sea levels to explore and investigate the ocean fully is recommended. Interpreting sections of the geologic record to determine sea level changes and depositional environments, including relative age, is also recommended. Technological advances can be used to observe and record the physical features of the Earth, including the ocean floor. Interpreting geologic history using maps of local cross-sections of bedrock can be related to the geologic history of Ohio, the United States and Earth.

Metamorphic

Magnetism

Magnets are commonly found in everyday objects, such as toys, hangers, elevators, doorbells, and computer devices. Experimentation on these magnets shows ...

Magnetic Field Lines

The representation of magnetic fields by magnetic field lines is very useful in visualizing the strength and direction of the magnetic field. Each of the ...

Meridians

In surveying, meridians are vital reference lines to measure directions and establish accurate land orientations. Meridians run from the north to the ...

Compass

The compass is a fundamental instrument that operates by aligning its magnetic needle with Earth's magnetic field. This alignment facilitates navigation ...

Magnetic Fields

Source: Yong P. Chen, PhD, Department of Physics &#38; Astronomy, College of Science, Purdue University, West Lafayette, IN
Magnetic fields can be ...

Sedimentary
• Division of sedimentary rocks and minerals (chemical, clastic/physical, organic)
• Depositional environments

Content elaboration: This unit builds upon a variety of topics studied in middle school. In the Earth and Space Science strand, sedimentary, igneous and metamorphic rocks are introduced. Rocks and minerals are tested and classified. Plate tectonics, seismic waves and the structure of Earth are studied and the geologic record is introduced (including the evidence of climatic variances through Earth's history). In the Life Science strand, fossils and depositional environments are included as they relate to the documented history of life in the geologic record. In the Physical Science strand, waves, thermal energy, currents, pressure and gravity are presented. In this course, geologic, topographic, seismic and aerial maps are used to locate and recognize igneous, metamorphic and sedimentary structures and features. Technological advances permit the investigation of intrusive structures and the interior of Earth. Connections between the minerals present within each type of rock and the environment formed are important. The processes and environmental conditions that lead to fossil fuel formation (Note: this links to the energy resources section below) includes the fossil fuels found in Ohio, nationally and globally. Bowen's Reaction Series is used to develop an understanding of the relationship of cooling temperature, formation of specific igneous minerals and the resulting igneous environment. The focus is on knowing how to use Bowen's Reaction Series, not to memorize it. Virtual demonstrations and simulations of cooling magma and crystallization of the igneous minerals found on the series can be helpful in conceptualizing the chart. The magnetic properties of Earth are examined through the study of real data and evidence. The relationship of polar changes, magnetic striping, grid north, true north and the North Pole are included in the study of Earth's magnetic properties. Features found in the ocean include all types of environments (igneous, metamorphic or sedimentary). Using models (3-D or virtual) with real-time data to simulate waves, tides, currents, feature formation and changing sea levels to explore and investigate the ocean fully is recommended. Interpreting sections of the geologic record to determine sea level changes and depositional environments, including relative age, is also recommended. Technological advances can be used to observe and record the physical features of the Earth, including the ocean floor. Interpreting geologic history using maps of local cross-sections of bedrock can be related to the geologic history of Ohio, the United States and Earth.

Sedimentary

measuring-structure-composition-change-underwater-environments-with

Measuring the Structure, Composition, and Change of Underwater Environments with Large-area Imaging

Digital imaging and processing technology have evolved to facilitate the expansion of large-area imaging surveys, which increase our capacity to study the ...

a-field-primer-for-monitoring-benthic-ecosystems-using-structure-from

A Field Primer for Monitoring Benthic Ecosystems Using Structure-From-Motion Photogrammetry

Structure-from-motion (SfM) photogrammetry is a technique used to generate three-dimensional (3D) reconstructions from a sequence of two-dimensional (2D) ...

Thermal Expansion

The expansion of alcohol in a thermometer is one of many commonly encountered examples of thermal expansion, which is the change in size or volume of a ...

Density

Density is an important characteristic of substances, crucial in determining whether an object sinks or floats in a fluid. Its SI unit is kg/m3, and its ...

Tidal Forces

The origin of Earth&#39;s ocean tides has been a subject of continuous investigation for over 2000 years. However, the work of Newton is considered to be ...

The Water Cycle

The Earth&rsquo;s hydrosphere includes all of the areas where the storage and movement of water occurs. Since water is the basis of all living processes, ...

Climate Change

The certainty of climate change remains a public controversy despite the consensus among approximately 97% of active climate researchers, who not only ...

Gradually Varying Flow

Gradually varying flow (GVF) in open channels describes situations where water depth changes slowly along the channel due to factors like non-uniform bed ...

Consider water flowing steadily through a curved pipe. The direction of flow inside the pipe can be visualized using streamlines.
A streamline represents ...

Hydraulic Jumps

Source: Alexander S Rattner and Mahdi Nabil; Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA
When ...

design-example-analyzing-capacity-contours-for-flood-risk-assessment

Design Example: Analyzing Capacity Contours for Flood Risk Assessment

Flood risk assessment involves careful planning and analysis to ensure the safety of communities near water retention structures. Capacity contours are a ...

Ocean
• Tides (daily, neap and spring)
• Currents (deep and shallow, rip and longshore)
• Thermal energy and water density
• Waves
• Ocean features (ridges, trenches, island systems, abyssal zone, shelves, slopes, reefs, island arcs)
• Passive and active continental margins
• Transgressing and regressing sea levels
• Streams (channels, streambeds, floodplains, cross-bedding, alluvial fans, deltas)

Content elaboration: This unit builds upon a variety of topics studied in middle school. In the Earth and Space Science strand, sedimentary, igneous and metamorphic rocks are introduced. Rocks and minerals are tested and classified. Plate tectonics, seismic waves and the structure of Earth are studied and the geologic record is introduced (including the evidence of climatic variances through Earth's history). In the Life Science strand, fossils and depositional environments are included as they relate to the documented history of life in the geologic record. In the Physical Science strand, waves, thermal energy, currents, pressure and gravity are presented. In this course, geologic, topographic, seismic and aerial maps are used to locate and recognize igneous, metamorphic and sedimentary structures and features. Technological advances permit the investigation of intrusive structures and the interior of Earth. Connections between the minerals present within each type of rock and the environment formed are important. The processes and environmental conditions that lead to fossil fuel formation (Note: this links to the energy resources section below) includes the fossil fuels found in Ohio, nationally and globally. Bowen's Reaction Series is used to develop an understanding of the relationship of cooling temperature, formation of specific igneous minerals and the resulting igneous environment. The focus is on knowing how to use Bowen's Reaction Series, not to memorize it. Virtual demonstrations and simulations of cooling magma and crystallization of the igneous minerals found on the series can be helpful in conceptualizing the chart. The magnetic properties of Earth are examined through the study of real data and evidence. The relationship of polar changes, magnetic striping, grid north, true north and the North Pole are included in the study of Earth's magnetic properties. Features found in the ocean include all types of environments (igneous, metamorphic or sedimentary). Using models (3-D or virtual) with real-time data to simulate waves, tides, currents, feature formation and changing sea levels to explore and investigate the ocean fully is recommended. Interpreting sections of the geologic record to determine sea level changes and depositional environments, including relative age, is also recommended. Technological advances can be used to observe and record the physical features of the Earth, including the ocean floor. Interpreting geologic history using maps of local cross-sections of bedrock can be related to the geologic history of Ohio, the United States and Earth.

Tracing Fluid Motion: Three Flow Paths

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