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

Consider water flowing steadily through a curved pipe. The direction of flow inside the pipe can be visualized using streamlines.
A streamline represents a path always tangent to the fluid&#39;s velocity at every point.
When a fluid particle moves along the streamline, its velocity at any point is directed along the path of the streamline. This velocity alignment ensures that the particle follows the flow direction defined by the streamline at every moment.
When a dye is injected into the same pipe at one fixed point, the dye particles flow through and continuously trace the fluid particles passing through that point.
This trace forms a streakline, which shows where particles that have passed through a particular point are located at any moment.
A pathline shows the actual path that a single fluid particle takes over time.
Consider a leaf floating along a river, following its unique path. The path taken by the leaf as it moves downstream represents a pathline.
In steady flow, pathlines align with streamlines and streaklines. However, in unsteady flow, pathlines differ as each particle follows its dynamic route.

streamlines, streaklines, and pathlines

A streamline represents the trajectory that is always tangent to the fluid&#39;s velocity vector at any given point. The velocity of a fluid particle is always directed along the streamline, ensuring the particle continuously follows the streamline&#39;s path. Streamlines are particularly useful for visualizing the overall direction of flow in a fluid system, and they provide an instantaneous representation of the flow&#39;s velocity field. In steady flow, where conditions do not change over time, streamlines offer a consistent picture of the flow pattern.
Streaklines, in contrast, trace the position of particles that have passed through a specific point over time. When a dye is introduced at a fixed location in the flow, it reveals the path fluid particles take as they move through that point, effectively showing a time-integrated history of their positions. Streaklines can differ from streamlines in unsteady flow because they track particles over time, whereas streamlines are instantaneous.
A pathline is a single fluid particle&#39;s trajectory as it moves through space over time. For example, the path of a leaf floating downstream in a river represents a pathline. Pathlines coincide with streamlines and streaklines in a steady flow, where conditions are constant, making them indistinguishable. However, in unsteady flow, where velocity and flow direction change over time, pathlines can diverge from streamlines and streaklines as each particle follows a unique path through the fluid. These distinctions are important for analyzing fluid motion under varying flow conditions.

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

Education

JoVE Core

Civil Engineering

Unit 1

Fluid Kinematics

KEY TERMS AND CONCEPTS

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 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 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

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 ...

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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