For example, the streaklines in Figure 4a show more structure further downstream than directly behind the cylinder. Open ParaView. 11 B. Contents 1 The challenge of fluid mechanics is mainly the kinematics of fluid flow. However, increasing Re above ≈1200 significantly distorts the streaklines and leads to small convective cells associated with unsteady flow. Streamlines are useful for visualizing and understanding the overall flow pattern in a flow field. A streamline is a line which smoothly connects velocity vectors at an instance in time. Mechanical Engineering questions and answers. Dye steadily injected into the fluid at a fixed point (as in dye tracing) extends along a streakline. The. Cross-sectional areas of the streaklines are calculated at various points along flow to investigate morphological evolution. Explain. Plot. 3D. Streaklines Timelines Refractive flow visualization techniques Surface flow visualization techniques Profile plots Vector plots Contour plots 4. 1 Physical properties of materials; what distinguishes fluids from solids. Streaklines show the path history of fluid particles that have passed through a particular location. 2 Continuity Equation 59 4. Analyze the graph of each function. The equation for the pathline can be found parametrically using Eqns. For the toxic cloud release, one would be most interested in determining the streakline passing through the location of the damaged reactor. 3. Southampton Shoal Channel LB 6. Streamlines, Streaklines, Pathlines [edit | edit source] If in a flow field a curve is drawn in such a way that the tangent to the curve at any point represents the velocity to that point. 001 in. ParaView Tutorials. Module 4: Fluid KinematicsThis module i. Streaklines are traced in a fluid flow by injecting color material, such as smoke or dye, which is transported with the flow and used for visualization. b) Consider the visualization of ground vortex flow in the figure. A streamline is a path traced out by a massless particle as it moves with the flow. Name an application where timelines are more useful than streaklines. pΔA −(p + ∂p ∂sΔs) ΔA = −∂p ∂sΔsΔA (3. Final Answer: Streamlines, streaklines, and pathlines are concepts in fluid dynamics used to describe the behavior of fluid particles over time. zero d. Task Requirement Students are required to evaluate the visualization effects of streamlines, streaklines and pathlines based on following two dimensional velocity field equation V= (uˉ,vˉ)= (2. The resulting trajectories, streaklines, and streamlines are seen in figures 4. Streaklines can be used to study the spreading of pollutants in the environment or the mixing of different fluids. Mechanical Engineering questions and answers. 7. Correct option with explanat. In this segment, we cover streamline (including deriving streamline equation), streakline, and pathline. . Fluid can be divided into two parts: Newtonian and non-Newtonian fluid. 流線型的起源可以追溯到19世紀對自然生命的研究，以及對於魚、鳥等有機形態的效能的欣賞。. The relevant thread on the user's list is here, and there's also another similar code snippet by Ray Speth that does things slightly differently. , 2016), which appears to validate the hypothesis that θ ≈ 0 particles behave similarly to. In symbols, this is written as. Engineering; Mechanical Engineering; Mechanical Engineering questions and answers; Some students want to visualize flow over a spinning baseball. Their fluids laboratory has a nice water tunnel into which they can inject multicolored dye streaklines, so they decide to test a spinning baseball in the water tunnel as shown in the figure. First, the flow lines embracing streamlines, pathlines, and streaklines are discussed. For information on missing data, go to the PORTS Stations Status Page or call (301) 713-2540. •In experimental analysis, typically a tracer is released from a fixed point to visualize the motion of the fluid. One example of a pathline is the path defined by a balloon floating in the air. density linearly scales this grid. 3. Intuitively, if we place multiple small balls into the water flow at the same position but at different time steps, the streakline is the path by connecting all the balls in the placement order. related to rate of strain by the dynamic viscosity ii. 1 Flow Patterns: Streamlines, Pathlines, Streaklines 1) A streamline ð k T, o is a line that is everywhere tangent to the velocity vector at a given instant. The theory requires the firing angle to be less than about 40 degrees or so, which is fine in most instances. 3. 3 m wind tunnel with a 0. 8x) + (0. Their fluids laboratory has a nice water tunnel into which they can inject multicolored dye streaklines, so they decide to test a spinning baseball in the water tunnel (Fig. For unsteady flows the streamlines may change shape with time. A. A region bounded by streamlines is called a streamtube. 1 - Streamlines, Streaklines, and Pathlines 1) At time t 0, a dye streak was started at point A in a flow field of liquid. At a Re = 1211, transitional flow was. Streaklines are cre-ated by tracking individual particles of ‘numerical dye,’ released at a constant rate from X= 0. 4. Are we seeing streamlines, streaklines, pathlines, or timelines?3. Engineering. Pathlines are the trajectories that individual fluid particles follow. P7-41E). Pathlines and streaklines provide ways to visualize flows. The net force on the stream tube in the flow direction is then. 4. 1 Flow Patterns: Streamlines, Pathlines, Streaklines. 1 Flow Patterns: Streamlines, Pathlines, Streaklines 1) A streamline ð k T, o is a line that is everywhere tangent to the velocity vector at a given instant. • Streamlines, streaklines, and pathlines Streamline: a line that is everywhere tangent to the velocity field. Visualization of streamlines for the original vector field in the left image yields. What follows is a lightly edited transcription of the video. Some students want to visualize flow over a spinning baseball. . f (x)=2 x+\frac {9} {x^ {3}} f (x)= 2x+ x39. Dye steadily injected into the fluid at a fixed point extends along a streakline. Rendering the streaklines as tubes allows rendering with surface shading – which helps our eyes see thire orientations more accurately. Organized by textbook: example that demonstrates how to sketch streamlines within the flow using the velocity components and the st. The streaklines near the heated wire indicate that the fluid near the heated wire flows towards the heated section of the wire with circulation. 2) (3. the flow is steady iv. Aerospace Engineering In aerospace engineering, both streaklines and streamlines are commonly used to describe the behavior of fluids around aircraft. (Do not consider move or wiggle to mean growing longer. By studying streamlines, streaklines, and pathlines, engineers can gain insights. Streaklines. Hi all, For the couple of weeks I am trying to plot the streaklines from my 3D simulations that I have performed using OpenFOAM. 1, p. Martinez-AMORCO Pier Currents. As illustrated in Figure 1b , according to mass balance, the change in SSC of a depth-averaged fluid parcel as it travels downstream. D. Practically, such sediment plumes can be understood as diffusing streaklines, i. • Streaklines: Streaklines are defined as the locus of the path from where all the particles havepassed through in the past. \%-50timelines c. Pathlines are unique to each particle and do not cross, providing a clear trajectory for each. Considering a velocity vector field in three-dimensional space in the framework of continuum mechanics, we have that: By definition, different streamlines at the same instant in a flow do not intersect, because a. In other words, an image of the flow characterized by streamlines is like a snapshot of the flow at one moment in time. These are streaklines extbf{streaklines} streaklines, because we are following the flow of smoke released from the smoke wire, through the air, from fixed points to the left of the picture. Mechanical Engineering 3. Want to see more mechanical engineering instructional videos? Visit the Cal Poly Pomona Mechanical Engineering Department's video library, ME Online: in time at which the observation is made. 3 mph Angle = Assuming the plant is located at (x,y)=(0,0), plot to scale: a) the streaklines at the end of each day. With regard to flow visualization, streaklines are defined as the traces of a colored material. r¢~v and @~v RESULTS AND DISCUSSION. t. Streaklines Reading: Anderson 2. It is the locus of particles that have passed sequentially through a prescribed path in the flow. The locus of fluid particles that have passed sequentially through a prescribed point in the flow. The speed of the flow is constant over a 10 s period, but the flow direction is not constant. AA200b - Applied Aerodynamics II Lecture 9 be tubulent and they are nearly impossible to compute analytically, except for some very simple cases. See also laminar flow, turbulent flow. Streaklines are a third type of line we can plot from unsteady velocity fields: these are lines that join particles that pass through the same point, at different times. SECTION 4. However, Tom Flannaghan's streamline plotting utility has been improved and merged into the codebase. We developed a method for extracting streaklines from remote-sensed SSC, and used the change in SSC along streaklines to reveal patterns of deposition and erosion in Wax Lake Delta, Louisiana. P7-41E). timelines c. The curves represent the streaklines for every tenth row and column. 2). Basically a differential pressure (d/p) flow meter, a pitot tube measures two pressures: the static and the total impact pressure. Key concepts are motivated by simple illustrations, leading to an introduction of conservation laws. The upper row is the side view of timelines, the middle row is the plane view of timelines, and the lower row is the plane view of the timeline surface, with contour lines. 7. The following animation illustrates the differences between a streakline and a pathline. Coordinates, reference frames, equations, functions,. 4. While material lines consist of any line-type arrangement of massless particles that moves with the flow, streaklines represent curves obtained by continuously releasing particles at a given location, called the seed. Find step-by-step Engineering solutions and your answer to the following textbook question: A flow is described by velocity field $vec{V}=a hat{i}+b x hat{j}$ where a = 2m/s and b =1s$^{−1}$. a. 3. In a separated flow the streamlines are separated from the surface. A streakline is a Pathline that moves more than a single point through the flow. Find step-by-step Engineering solutions and your answer to the following textbook question: What is the definition of a timeline? How can time ones be produced in a water. 4. In general, flow visualization is an experimental means of examining the flow pattern around a body or over its surface. Generally, fluid is defined as a substance which is capable of spreading and changing its shape, according to is surroundings, without offering internal resistance. =5 b. High-power lights or laser sheets are used to illuminate the smoke streaklines. 1. The trajectory of the particle as a function of time, $(x_p(t),y_p. A typical hydrogen bubble diameter is d=0. 2 Streamlines, particle trajectories, streaklines Suppose you freeze a velocity u(x,t) at a fixed time and look at the instantaneous vector field at that instant. I got the streamlines working, but when ever I am trying to plot the streaklines, and tried to set the integration time to the last time of simulation, the paraview (5. For a flow which does not change with time, the streamline, streakline, and pathline are the same line. For the following list of situations, classify each as a 1-dimensional, 2-dimensional or 3dimensional flow. In this application the user can type. Another technique would be to instantly inject a line of dye across streamlines and observe how this line moves as time increases. Codes to plot fluid pathlines and streaklines given an example. This tube is called a streamtube. Assuming the plant is located at (x,y)= (0,0), plot to scale: a) the streaklines at the end of each day. Under all flow conditions, these lines only grow in length, but never wiggle. Streaklines and timelines are effective visualization techniques for depicting vortex shedding, vortex breakdown, and shock waves in unsteady flows. In (b), integral curves of the guadalupe flow are shown (t0 = 15:55:20 UTC, τ = 06:06:40 UTC) with satellite images in. b) Consider the visualization of ground vortex flow in the figure. - Streaklines are time-dependent and represent the collection of particles that have passed through a particular location. The shear stress in a Newtonian fluid is i. Step 2/2. Some students want to visualize flow over a spinning baseball. Students are required to evaluate the visualization effects of streamlines, streaklines and pathlines based on following two-dimensional velocity field equation V = (uˉ,vˉ) = (0. Fluids – Lecture 15 Notes 1. 8x) +(1. Repeat steps 1-4 for any other printheads. Pathlines 3. To visualize Timelines, Pathlines, Streaklines and Streamlines provide a vivid visualization of a fluid flow. † Streakline: Instantaneous locus of all °uid particles that have passed a given point (snapshot of certain °uid particles). Are we seeing streamlines, streaklines, pathlines, or timelines?streaklines are a legitimate means of validating flow patterns in this location, where streaklines have been previously used [21,22]. Streaklines: Streaklines are the paths traced by particles that have passed through a specific point in the flow field at different times. Streaklines. . \%-50vector lines e. To understand streaklines, consider a fluid flow with an ink dye injected at a particular point. Pathlines show the path traced out by individual fluid particles over time. g. Each cell in the grid can have, at most, one traversing streamline. the flow is steady iv. 6+1. pathlines d. 3. 2. 7. Similarity requires that they match both the Reynolds number and the Strouhal number between their model test and the actual baseball that moves through the air at 80 mi / h and. The statement “ vorticity at x equals twice the angular velocity of the fluid at x” is often heard. A wind speed of approximately 2 m/s was used in this study. (2) and (3). This article is divided into two parts. streaklines d. Introduction. Simulations of streaklines in a cross-channel mixer and a perturbed Kirchhoff elliptic vortex are quantitatively compared to the theoretical results. a. The gasses typically include water vapor, but smoke differs from steam in that there are other gasses, such as carbon dioxide and sulfur oxides, plus there are small particles. A streakline is a curved line formed by a string of fluid particles which have passed through a certain point. The general background of different flow structures and the limitation of visualization techniques are reviewed first (Sec. Oakland Outer Harbor LB 3. Consider the visualization of flow over a 12° cone in Fig. Ta. , 2020; Shaw et al. 6+2. Communicate. 5sinωt-0. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. These animated gif images illustrate the differences between streamlines, streaklines, pathlines, and timelines. density c. 2. Chapter 4 • Differential Relations for a Fluid Particle. The direction. The time history of a marker particle may be found by solving the pathline. The lines created in this type of demonstration are streaklines. Euler's equation for steady flow expressed in streamline. Synoptic scale vorticity is analyzed and plotted on the 500-mb chart. These can be thought of as "recording" the path of a. \%-50vector lines What is the material derivative of mass? a. This is because when a particle on a streamline reaches a point, a 0, further on that streamline the equations governing the flow will send it in a certain direction x →. San Francisco Bar Waves. They differ only when the flow changes with time, that is, when the flow is not steady. Controls the closeness of streamlines. Figure 1: Laminar and Turbulent Boundary Layers 3How do streaklines differ from streamlines? 4–29C Consider the visualization of flow over a 15° delta wing in Fig. Good agreement in streakline patterns between potential flow theory and experiment is observed over the cone at $$alpha =. Consider the simple example with the flow shown in figure 4. Additionally, a methodology for quantifying the unsteady advective transport between the two fluids using streaklines is presented and verified numerically for the same two examples. Streakline definition: A locus of points of all the fluid particles that have passed continuously through a particular spatial point in the past. Euler's equation for steady flow expressed in streamline. Streaklines, Streamlines, and Particle Paths Duration 10:11. Mechanical Engineering. Examples of streaklines are a line of smoke from a chimney and a dye streak in a river where dye has been injected through a tube. Streak line changes with time. Streamlines, streaklines and pathlines are field lines in a fluid flow. Data are taken from two different streaklines (1 and 2) from different locations along the band length. Transcribed image text: QUESTION 9 Consider the visualization of flow over a 15° delta wing, as shown in the figure. y 0 = y ′ − t ′. A streakline involves the motion of all the fluid. This is a video that introcues basic concepts of fluid motion, using different visualizaton techniques extracted from a CFD simulation of particles flowing a. When density = 1, the domain is divided into a 30x30 grid. ) a. P4–32C. 流线，用来表征三维空间的速度场。在当流场随着时间改变的时候，即非稳定流动时，Streamlines, streaklines, and pathlines三个名词含义不同。. . In order to observe streaklines within a fluid you will first. precalculus. The term in the equation above could therefore also be written as g⋅sin (α). A visualization of three-dimensional steady flow around a sphere is created by taking an extended exposure photograph of the sphere submersed in flowing water with air bubbles. Besides various field-lines, we also compute and display the line integral convolution texture soPitot tubes were invented by Henri Pitot in 1732 to measure the flowing velocity of fluids. pΔA −(p + ∂p ∂sΔs) ΔA = −∂p ∂sΔsΔA (3. webm 1 min 46 s, 4,800 × 1,600; 115. The visualization is produced by colored fluid injected into water from ports in the body. At time t', the expression for pathlines is: x 0 = x ′ − 1 + \cost ′. 12 Uniform Flow Definition A uniform flow consists of a velocity field where V~ = uˆı+ v ˆ is a constant. Concepts for describing fluid flows: streamlines, particle paths, and streaklines. Examples can be seen in aerial photographs of smoke plumes emitted from smokestacks, or volcanic ash clouds. Section 7: Similarity and Dimensional Analysis. 3 1 Kinematics of Fluid Flow. specifies a set of points at which streaklines originate. Streamlines represent the instantaneous direction of flow at a given point, streaklines depict the path taken by a fluid particle over a certain period, and pathlines show the actual trajectory followed by an. As a means of overcoming this problem, a small number ofBoth the particle tracer and the particle pathlines filters are special in that they capture and modify geometry as they iterate over time. Understand the definitions for streamlines, streaklines, and pathlines. It is a lecture note for the course AA210A Fundamentals of. The wind velocity (km/h) is v=10i+5j for the first 5 hours and v=5i for the next 5 hours. They show the history of the flow at a particular point. A similar pattern can be seen at much larger scale in the air flow in the wake of an island. While streaklines are preferred in this case, they have the downside that the time and place of formation of the revealed structures is unclear. This circulation near. The plume lasts for three hours. The three water filled tanks shown in figure below are connected by pipes as indicated. These. vectorlines d. This type of flow results from uniform shear in the deformation. One can also record streaklines for an array or points by injecting 3. streaklines Under all flow conditions, as time proceeds, these lines wiggle/flop around while one end is anchored to a fixed point in the flow field. 4, no. Oil flowing in a straight horizontal. whereas pathlines are. This notes sheet looks at the foundations of fluid dynamics, including the difference between fluids & solids and liquids & gasses, the continuum viewpoint, field descriptions for movement of fluids, as well as streamlines, pathlines and streaklines. 1. 5sin(ωt)− 0. In this example, streaklines are simply horizontal lines. For a steady flow situation, the timelines and streamlines are the same. The patterns guide design modifications, aiming to reduce the drag. Intuitively, if we place multiple small balls into the water flow at the same position but at different time steps, the streakline is the path by connecting all the balls in the placement order. Let’s first go ahead and load a solution. However, often sequences of timelines (and streaklines) at different instants—being presented either in a single image. 2. Chemical Engineering questions and answers. Then find the equation (s) (within an arbitrary constant) that describe the streamlines, streaklines and pathlines for this flow. They allow tracking of particle trajectories and provide a time history of particle motion. give you hands on experience of the smoke flow visualization technique, and. related to the pressure field by the dynamic. To see how mass conservation places restrictions on the velocity field, consider the steady flow of fluid through a duct (that is, the inlet and outlet flows do not vary with time). Which of the following is correct? a) Pathlines of two particles in an one-dimensional flow can never intersect. A pathline is the. t. Vortex shedding within laminar separation bubbles forming over the suction side of a NACA 0018 airfoil is studied through a combination of high-speed flow visualization and boundary layer measurements. 2. The PIV-measured effective strain field (ε) and streaklines (white lines), superimposed on the raw images, are shown. Streamlines, Streaklines, and Pathlines Streamlines is a line that is everywhere tangent to the velocity field. Figure 3. Examples of streamlines around an airfoil (left) and a car (right) 2) A pathline is the actual path traveled by a given fluid particle. If any wet ink is left, blot it off with a dry swab or lint-free towel. Another technique would be to instantly inject a line of dye across streamlines and observe how this line moves as time increases. I got the streamlines working, but when ever I am trying to plot the streaklines, and tried to set the integration time to the last time of simulation, the paraview (5. Cases B and C distribute the energy in the spanwise direction and create additional low-speed streaks by doubling their spanwise. Label which is which on the diagram. Dye steadily injected into the fluid at a fixed point extends along a streak line. 11 Three types of fluid element trajectories are defined: Streamlines, Pathlines, and Streaklines. "the trajectories that individual fluid particles follow. Question: 2. (15pts, 5pts each) a) Consider the visualization of flow over a 12 cone in the. One should always be reminded that streaklines do not correspond to streamlines in an unsteady flow. These techniques are examples of time-dependent. 3. It is an instantaneous position of fluids that have passed through a fixed point of the flow field. pathlines Marked out of c. P4–32C. In such cases, the use of streamlines may not be appropriate as they assume that the fluid is. The wind tunnel is an open circuit suction style wind tunnel capable of wind speeds up to 9 m/s. these lines are basically imaginary lines which are tangent to a curve drawn in space. 這些最初應用在潛艇和飛艇. A stress on a fluid particle's. Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!) 8th Edition. Flow visualization is an approach focuses on methods to get information from the flow field datasets either in 2 or 3 dimensional. Are we seeing streamlines, streaklines, pathlines, or timelines? Explain. flow kinematics: streamlines, pathlines, and streaklines. a. Streaklines A streakline is the locus of points of all the fluid particles that have passed continuously through a particular spatial point in the past. The term ∂z/∂s ultimately corresponds to the sine of the angle between the vertical axis (z-axis) and the direction of the streamline (∂z/∂s=sin (α)). where V is the volume and t is the elapsed time. Transcribed image text: An experiment is conducted on Lake Oroville to determine the currents induced by wind speed and direction. Expert-verified. Smoke consists of gasses and soot. . Are we seeing streamlines, streaklines, pathlines, or timelines? Explain. Question. A typical hydrogen bubble diameter is d 0. Streamlines, streaklines and pathlines coincide when i. Mechanical Engineering questions and answers. Their fluids laboratory has a nice water tunnel into which they can inject multicolored dye streaklines, so they decide to test a spinning baseball in the water tunnel. The streaklines were captured by a high-speed camera (Photron FASTCAM Mini AX100 type 200K-M-32 GB), with a frame rate of 1000 frames per second. (a) A streakline is a time exposed lfow path of an individual particle over some period of time (b) A streamline represents an instantaneous flow pattern at a given time (c) Fluid within a streamtube must remain there and cannot cross the boundary of a streamtube (d) Just like streaklines, streamtubes are a time integrated quantityFor a steady flow situation, the curve representing the pathlines, streamlines, and streaklines are all the same. However, the performance of this method is limited by poor spatial resolution when it is conducted in a complex flow field. Considering a velocity vector field in threedimensional space in the framework of continuum mechanics, we have that Streamlines are a famiCivil Engineering questions and answers. related to rate of strain by the dynamic viscosity ii. 3) Consider the visualization of flow over a 12∘ cone in Fig. Streaklines: particles are continuously introduced at a certain point, the streakline shows the line formed due to the release of these particles from the specific point. Displays all PORTS stations for the specified region and the product types for each station. 1. Streaklines involve release particles at a defined interval. 2? The visualization is produced by time exposure of air bubbles in water. 2. 5 at y/δ* ≈ 0. Knowledge of the flow patterns within distributary systems is key for understanding deltaic hydro- and morpho-dynamics, yet synoptic measurements of flow fields remain virtually nonexistent. The purpose of this tutorial is to illustrate the difference between streamlines, streak lines and path lines for a time dependent velocity field using the java application called vector field manipulator. First, we extract streaklines from a map of remotely sensed SSC (Figure 1a, see Section 2. It has already been explained that in unsteady or turbulent flows, particles introduced one after the other in time (at the same place) follow different pathlines. 1. t. 6 respectively. 0 gal/min to mathrm {m}^3 / mathrm {s} m3/s. Students are required to evaluate the visualization effects of streamlines, streaklines and pathlines based on following two dimensional velocity field equation. Jan 1, 2017. 2) (3. 這些最初應用在潛艇. To obtain streakline, a dye is injected into liquid or smoke in gas at a fixed point in the flow field so as to trace the subsequent position of fluid passing through it. Find step-by-step Engineering solutions and your answer to the following textbook question: A flow is described by velocity field $vec {V}=a y^ {2} hat {i}+b hat {j}$ where a = 1 m$^ {−1} s^ {−1}$ and b = 2m/s. One this is accomplished you would than. Other required parameters should be assumed. The curve that is traced out as we follow the particle is called the pathline. They have almost equal magnitude above and below the fuselage due to the lift and gravitational forces’ balance to hold the quadcopter drone in the hover position. 4, 4. Determined by the surrounding velocity field from the moment of its injection into the flow until present time. 4 An idealized velocity field is given by the formula. 6 x i + 0. 79-94, 1975. Streamlines are a family of curves that are instantaneously tangent to the velocity vectors in a flow field. Two path lines for two particles may intersect each other. For the couple of weeks I am trying to plot the streaklines from my 3D simulations that I have performed using OpenFOAM. In simple terms, streamlines and streaklines are like a snapshot of the flowfield whereas pathlines are time-history of the flow. An enlarged view of the streakline, shown in (b), also illustrates the orientation of x- and y-axes with respect to the shear. Because of unsteady _____ shed in an alternating pattern from the cylinder, the smoke collects into a clearly defined periodic pattern called a Kármánvortexstreet. For example, we could mark a drop of water with fluorescent dye and illuminate it using a laser so that. , 2018; Cathcart et al. What does pathline looks like?What does streaklines look like?What does streamlines look like? We would like to show you a description here but the site won’t allow us. svg 1,025 × 469; 51 KB Simulation of von Karman street in flow around a disc - with streamlines. 0:00 Streamlines0:47 Eulerian Approach1:32 Pathlines and Lagra. 6+0. 3] Some students want to visualize flow over a spinning baseball. Chief Noter. Pathlines are the trajectories that individual fluid particles follow.