Streaklines and pathlines (particle paths) both use interpolation and will be supported. The video demonstrates some flow visualization techniques and illustrates streamlines, streaklines, pathlines, and time lines. Mechanical Engineering questions and answers. They differ only when the flow changes with time, that is, when the flow is not steady. streaklines are marked in a flow with smoke or dye ii. Figure 3. It is a strictly Eulerian concept. This is like ly due to the importance of the subaqueous. The particle tracking literature is primarily concerned with problems where thestreak翻譯：痕跡, 條紋;條痕, 特點, （常指不好的）特點，個性特徵, 短期, 一陣好運；一陣黴運, 一陣子，一連串，一系列, 快速移動, （通常指沿直線）飛奔，疾馳, 裸奔, （在公共場所）裸奔, 痕跡。了解更多。The images taken for Re = 131 and Re = 1004 contain vertical streaklines, consistent with laminar flow and the associated parabolic velocity profile. 3 Kinematics: Streamlines, Streaklines, Timelines, and Vorticity 18 3. Flow across the streak line is possible. Figure 1. 1. Streaklines eminating from a “source”, shown with two slice planes. We would like to show you a description here but the site won’t allow us. Show the streaklines of the plume at t=5h and t=10h. 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。. 91 m test section was used. The visualization is produced by colored fluid injected into water. Consider the simple example with the flow shown in figure 4. 1. 3. 10. Flow separates when the gradient dV/dz equals zero on the. Mechanical Engineering questions and answers. The wind field is modeled to be the following for the next 4 days and the steam is assumed to advect with the wind field. , 2016), which appears to validate the hypothesis that θ ≈ 0 particles behave similarly to. pathlines d. This segment discusses the differences between Streamline, Streakline, and Pathline for both steady and unsteady flow. Oakland Outer Harbor LB 3. One example of a pathline is the path defined by a balloon floating in the air. 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. Streaklines. flowvis_02 Page 3 of 3 A pathline is a line traced out by a particular fluid particle as it moves through space. 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. Solution. 1 Integral and Differential Approach 57 4. Streaklines: Streaklines are the loci of points of all the fluid particles that have passed continuously through a particular spatial point in the past. The relation between pathlines and streamlines is simple, as the latter are projections of the corresponding pathlines on physical space, as shown in Fig. The integration of (1) to obtain particle paths and/or travel times, is known as particle tracking, for which there exists a rich literature. The patterns guide design modifications, aiming to reduce the drag. =3 b. Civil Engineering questions and answers. In the present notes the column buckling was extensively studied in Chapter 8. 3. Study with Quizlet and memorize flashcards containing terms like A tiny, neutrally buoyant electronic pressure probe is released into the inlet pipe of a water pump and transmits 2000 pressure readings per second as it passes through the pump. (15pts, 5pts each) a) Consider the visualization of flow over a 12° cone in the figure. Particles may cross its path line. 3 Acceleration Field and Material Derivative The acceleration of a fluid particle is the rate of change of its velocity. e. Discuss how this dye line would appear at later. 3. + -. t. For a flow which does not change with time, the streamline, streakline, and pathline are the same line. An enlarged view of the streakline, shown in (b), also illustrates the orientation of x- and y-axes with respect to the shear. The SI unit for flow rate is m 3 /s, but several other units for Q are in common use, such as liters per minute (L/min). 6: Pathline. In the context of computer vision, streaklines may be used in a similar way to transport information about a scene, and they are obtained by repeatedly initializing a fixed grid of particles at. Then you can visualize curves x(s) that are tangent to the velocity at every point in space. a. – Timelines, pathlines, streaklines, and streamlines provide visual representation of a flow. In Figure 14. The streaklines are made up of two parts, involving the primary stream (indicated by the black solid lines) from the conventional nozzle inlet and the secondary stream (denoted by the red solid lines) from the slot injector. Contents 1 The challenge of fluid mechanics is mainly the kinematics of fluid flow. Pathlines are the trajectories that individual fluid particles follow. Section 7: Similarity and Dimensional Analysis. ISBN: 9781305387102. Streaklines are traced out by neutrally buoyant marker fluid injected into a flow field from a fixed point in space. 71 for K-regime transition. The pathline is the actual path in space followed by a particle which is moved by the flow of the vector field. The resulting transport problem is extremely challenging for traditional numerical simulation because the numerical domains need to be. Step 2/2. We assume that condition ν (t) < 1 / t of Proposition 1 below is satisfied [we have λ = 1 for solutions and ] that. III), including experimental and. expand_more. The following wind conditions are expected V = 10i cap - 5j cap mph for 0 < t < 3 hr V = 15i cap + 8j cap mph for 3 < t < 10 hr V = 5i mph for t > 10 hr Draw to scale the expected streakline of. 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. The room is heated by a heat pump so that the temperature. svg 1,050 × 900; 109 KB Pathlines streaklines. Streamline. Correct option with explanat. A streakline is a Lagrangian description. This Session for Practice Problems on Flow lines (Streamlines, Streaklines, and Pathlines) is a Part of the Problem Solving Series for the Introductory Fluid. Aerospace Engineering In aerospace engineering, both streaklines and streamlines are commonly used to describe the behavior of fluids around aircraft. They precompute a two-dimen-sional noise texture whose coordinates represent time and a boundary Lagrangian coordinate. Problem 4-31C: Consider the visualization of flow over a sphere in Fig. P4. For example, consider the initially straight dye line injected in front of the circular cylinder. The time history of a marker particle may be. Streamlines are a family of curves that are instantaneously tangent to the velocity vectors in a flow field. Normal smoke wire flow visualization uses a smoke wire to demonstrate the flow streaklines. . Concepts for describing fluid flows: streamlines, particle paths, and streaklines. Determine the motion of two-dimensional point vortices. Open ParaView. streamline, In fluid mechanics, the path of imaginary particles suspended in the fluid and carried along with it. Flow visualization can also be used to describe the advancement of the flow front into the cavity during the filling stage. Streakline definition: A locus of points of all the fluid particles that have passed continuously through a particular spatial point in the past. These can be thought of as "recording" the path of 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 →. It is an instantaneous position of fluids that have passed through a fixed point of the flow field. 4. It's a subtle but important difference. Streamlines, Streaklines, and Pathlines Streamlines is a line that is everywhere tangent to the velocity field. Are we seeing streamlines, streaklines, pathlines, or timelines? Explain. Volumetric measurement for the leading-edge vortex (LEV) breakdown of a delta wing has been conducted by three-dimensional (3D) flow visualization and tomographic particle image velocimetry (TPIV). Two path lines for two particles may intersect each other. Flow lines explained! Streamlines, Pathlines, Streaklines. 5: Streakline. At a Re = 1211, transitional flow was. streak: [noun] a line or mark of a different color or texture from the ground : stripe. . Are we seeing streamlines, streaklines, pathlines, or timelines? Explain. Leaflet | Esri. Jan 1, 2017. The general background of different flow structures and the limitation of visualization techniques are reviewed first (Sec. Location of The Tracer. Are we seeing streamlines, streaklines, pathlines,or timelines?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. Are we seeing streamlines, streaklines, pathlines, or timelines? Explain. 2. In the Lagrangian approach the velocity of a fluid particle Final answer. Researchers have presented many visualization techniques with similar goal, which is to enrich the information provided by the visualization. Oil flowing in a straight horizontal. 6 The Velocity Potential in Irrotational Flow 26a) In this we can clearly see that a Streakline flow is followed because as we can see in the flow fluid particle is away from the actual path of the flow. 79-94, 1975. 8xi+1. Figure 2: Visualization of flow over a sphere. A streamline ( ) is a line that is everywhere tangent to the velocity vector at a given instant. The shear stress in a Newtonian fluid is i. Mechanical Engineering. Analyze the graph of each function. For any steady flow the streamlines and streaklines are the same. 1. Mechanical Engineering questions and answers. e. The color expression in the streamline plot indicates fluid velocity (in m/s). Are we seeing streamlines, streaklines, pathlines, or timelines? Explain. Show the streaklines of the plume at t=5h and t=10h. The text defines the method for plotting the streaklines this way. A streakline is a curved line formed by a string of fluid particles which have passed through a certain point. 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. To evaluate the streaklines, we need to consider the time component of the velocity field equation. Streaktubes, with slice planes. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Streaklines are traced out by neutrally buoyant marker fluid injected into a flow field from a fixed point in space. 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. Our study demonstrates that the velocity field in deltas. These problems have already given me 3 days sleepless nights. 2) p Δ A − ( p + ∂ p ∂ s Δ s) Δ A = − ∂ p ∂ s Δ s Δ A. Unsteady Flow of Streaklines. Photo from. 1. 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. 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. t. 1. The rotation direction of the cone shapes the streaklines ingested into the boundary layers. a. Day 1 2 mph = 45 deg. 3) Consider the visualization of flow over a 12∘ cone in Fig. generates a stream plot of the vector field { v x, v y } as a function of x and y. Flow visualization is an approach focuses on methods to get information from the flow field datasets either in 2 or 3 dimensional. Figure 3. A pathline is a path which a fluid particle traces. If any wet ink is left, blot it off with a dry swab or lint-free towel. The lines created in this type of demonstration are streaklines. Section 7: Similarity and Dimensional Analysis. 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. pΔA −(p + ∂p ∂sΔs) ΔA = −∂p ∂sΔsΔA (3. Flow visualization can also be used to describe the advancement of the flow front into the cavity during the filling stage. 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. r¢~v and @~v RESULTS AND DISCUSSION. One should always be reminded that streaklines do not correspond to streamlines in an unsteady flow. You can also single-click to add individual. Obtain the equation for the streamline passing through point (2, 5). Draw the direction of flow on the streamlines, streaklines, and pathlines. 11 Three types of fluid element trajectories are defined: Streamlines, Pathlines, and 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. A streakline is a curved line formed by a string of fluid particles when passed through a cer. Colored fluid is injected through same (fixed) points, and the flow of these injected particles is thus transparent in water. Pathlines and streaklines provide ways to visualize flows. \%-50vector lines What is the material derivative of mass? a. We also go over how to obtain them experimentally. Similarity requires that they match both the Reynolds number and the Strouhal number between. Expert Answer. =1 . Synoptic scale vorticity is analyzed and plotted on the 500-mb chart. The wind tunnel is an open circuit suction style wind tunnel capable of wind speeds up to 9 m/s. From time t = 0 to t = 5 hr, radioactive steam is released from a nuclear power plant accident located at x = -1 mile and y = 3 miles. A pathline is the actual path traversed by a given (marked) fluid particle. T his text is an abbreviated version of standard thermodynamics, fluid mechanics , and heat transfer texts, covering topics that engineering students are most likely to need in their. For that we will need to solve the full Navier-Stokes equations within the me geometry of the wind tunnel and model, to obtain the flow. Data are taken from two different streaklines (1 and 2) from different locations along the band length. As soon as your flow is time dependent, trajectories, streaklines, and streamlines all look very different. 2. Basically a differential pressure (d/p) flow meter, a pitot tube measures two pressures: the static and the total impact pressure. 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. 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 are time-dependent and represent the collection of particles that have passed through a particular location. Consider the visualization of flow over a 12° cone in Fig. Question. give you hands on experience of the smoke flow visualization technique, and. 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. zero d. Dye steadily injected into the fluid at a fixed point extends along a streak line. It is the locus of particles that have passed sequentially through a prescribed path in the flow. 3 Acceleration Field and Material Derivative The acceleration of a fluid particle is the rate of change of its velocity. In order to observe streaklines within a fluid you will first have to mark the fluid in some way. , The velocity field of the form V=u(x,y,t)i+v(x,y,t)j is a two. In a steady flow the streamline, pathline and streakline all coincide. Question: 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. A streakline is a Pathline that moves more than a single point through the flow. webm 1 min 46 s, 4,800 × 1,600; 115. The bubbles tend to rise slowly in water because of buoyancy, eventually they reach terminal speed relative to the water. 5)The streaklines are aligned vertically close to the fuselage. svg 1,025 × 469; 51 KB Simulation of von Karman street in flow around a disc - with streamlines. The sheet is realised with a negative lens. •In experimental analysis, typically a tracer is released from a fixed point to visualize the motion of the fluid. specific mass b. 3. Similarity requires that they match both the. For different densities in each direction, use a tuple (density_x, density_y). Streamlines 2. . 0 gal/min to mathrm {m}^3 / mathrm {s} m3/s. Mechanical Engineering questions and answers. 3. Are we seeing streamlines, streaklines, pathlines, or timelines? Explain. timelines e. b) Pathlines of two particles in an one-dimensional flow can never intersect if the two particles move along the same direction. These are streaklines extbf{streaklines} streaklines. streamline翻译：形状, 把…设计成流线型，使成流线型, 改善, （常通过简化办事程序）使（机构）效率更高；简化。了解更多。Are we seeing streamlines, streaklines, path lines, or timelines? Explain. Streaklines are lines connecting all fluid particles that pass through the same point in space. 4, no. Photo from. This is because the structures have accumulated over the life time of the particles. With regard to flow visualization, streaklines are defined as the traces of a colored material in the flow. In all questions, assume steady flow, no electromagnetic forces, no chemical reactions, no shaft work, and a perfect gas. Pathlines are unique to each particle and do not cross, providing a clear trajectory for each. Learn more about streamlines, streaklines, pathlines, vortex core tracking MATLAB Can someone help me correct my code for tracking centre of vortex and for plotting streamlines, streaklines and pathlines by creating the code and not using Matlab 'streamline' function. Question. Streaklines are the loci of points of all the fluid particles that have passed continuously through a particular spatial point in the past. The following animation illustrates the differences between a streakline and a pathline. pathlines Under steady flow conditions, these two lines change over a fixed time interval in the same way. Streaklines are identical to streamlines for steady flow. Note that these notions are frame dependent. – All fluids satisfying the continuum assumption must have zero relative velocity at a solid surface (no-slip condition) and so most flows are inherently two or three dimensional. Courtesy ONERA. . Streaklines. Open your vector field,. Describe how streaklines and pathlines might be different from streamlines for each case. 1. We can see a fully developed turbulent flow profile at first; then, a separation zone and turbulent vortices appear after the bend. Initially, near X = 0, the streaklines are what we expect, i. Streamlines Streamline equations A streamline is defined as a line which is everywhere parallel to the local velocity vector Description. Martinez-AMORCO Pier Currents. This task is known as streamlining, and the resulting design is referred to as being streamlined. related to the pressure field by theFinal answer. Are we seeing streamlines, streaklines, pathlines, or timelines? The visualization is produced by colored fluid injected into water from ports in the body. and we could pick a point from the above example say p = ( 0. 1 / 4. 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. Calculating streamlines, particle paths and streaklines in Tecplot 360 EX 2014 R2. 6+2. For example, smoke particles. The velocity field of a flow is described by V › = (4x)i › + (5y + 3) j › + (3t 2 )k › . The visualization is produced by a time expo- sure of air bubbles in water. Streakline concentrates on fluid particles that have gone through a fixed station or point. • Streaklines: Streaklines are defined as the locus of the path from where all the particles havepassed through in the past. . 4: Definition sketch for derivation of the Bernoulli equation for incompressible inviscid flow. What is the line connecting all particles at t=4 s (see figure below)? There are 3 steps to solve this one. 016 Hydrodynamics Reading #3 Particle Pathlines: Trajectory of fluid particles (“more” lagrangian) flow kinematics: streamlines, pathlines, and streaklines. Repeat steps 1-4 for any other printheads. . \%-50gridlines e. The curves represent the streaklines for every tenth row and column. 7. 2. 4, 4. The main difference between a flow system and a uncoupled bunch of particles is pressure. Chemical Engineering questions and answers. Streaklines are used in a laboratory setting to observe fluid particle as they pass through a common point. Expert-verified. The time history of a marker particle may be found by solving the pathline. (Do not consider move or wiggle to mean growing longer. The smoke identifies the air that has flowed past the top of the chimney and the dye identifies the water particles that have flowed past the end of the dye injection tube. 1. Shown here is the visualization of flow over a 15 delta wing at a 20° angle of attack at a Reynolds number of 20,000. They are all. 4 3. 11 Three types of fluid element trajectories are defined: Streamlines, Pathlines, and Streaklines. Such imaginary curve in the flow field is known is stream line. V=u,v=0. These streamlines form a tube that is impermeable since the walls of the tube are made up of streamlines, and there can be no flow normal to a streamline (by definition). 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$^{−1}$. The governing equations are introduced in a simple manner, with an explanation of several useful and. these lines are basically imaginary lines which are tangent to a curve drawn in space. During the experiment dye is released continuously and floats are released every 30 minutes (called tracking drogues) to monitor the surface currents. Find expressions for and draw representative (i) pathlines, (ii) streamlines and (iii) streaklines. Introduction. Mechanical Engineering. timelines c. 0) crashes and gives the segmentation fault. 6 x i + 0. However, the spatial extension of the. 2. This link, however, has been the most helpful in understanding how to derive the necessary equations. We would like to show you a description here but the site won’t allow us. Dye steadily injected into the fluid at a fixed point extends along a streakline. Some students want to visualize flow over a spinning baseball. Streamlines Want to see more mechanical engineering instructional videos? Visit the Cal Poly Pomona Mechanical Engineering Department's video library, ME Online: Streaklines. , sinu-Fluid particles are m. Photo of the damaged Chernobyl reactor. Because of unsteady _____ shed in an alternating pattern from the cylinder, the smoke collects into a clearly defined periodic pattern called a Kármánvortexstreet. Streaklines. In this context, streaklines may be obtained by repeatedly initializing a grid of particles and moving all particles according to the optical flow, in the spirit of a Lagrangian fluid flow. In (b), integral curves of the guadalupe flow are shown (t0 = 15:55:20 UTC, τ = 06:06:40 UTC) with satellite images in. Where the angular velocity, w is equal to pi, 0 < x < 5 m, - 1 m < y < 5 m and 0 < t < 2 s. Mechanical Engineering. The first part focuses on the incompressible boundary layer. An illustration of streakline (left) and an example of streaklines, flow past a full-sized streamlined vehicle in the GM aerody-namics laboratory wind tunnel, and 18-ft by 34-ft test section facilility by a 4000-hp, 43-ft-diameter fan (right) 57:020 Mechanics of Fluids and Transport Processes Professor Fred Stern Fall 2013Streamlines and Streamtubes A streamline is a line that is tangential to the instantaneous velocity direction (velocity is a vector, and it has a magnitude and a direction). Stream functions are defined for two-dimensional flow and for three-dimensional axial symmetric flow. Euler's equation for steady flow expressed in streamline. 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. 3. i. Since then, laboratory flow visualization has become more and more exact. Question: low field predictions and setting the equations to solve le want to asses if and how we could evaluate the capsule performance numerically and compare the results those from the experiments. 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. We are not recording the flow of any single particle - we have the records of positions of many particles that started at the same point in sequential moments of time. The units of time correspond to the units of the vector field. (A pathline is an integrated pattern. A particle of the marker fluid that is at point (x, y) at time t must have passed through the injection point ( x_ {0}, y_ {0} x0,y0) at some earlier instant t=\tau t = τ. The differences between each technique cause misunderstanding to new. Nikolaos D. Red and yellow colors represent the different directions of motion. It discusses the conservation of mass, momentum and energy, the types of fluid flow, the properties of compressible and incompressible fluids, and some examples of fluid flow applications. The wind field is modeled to be the following for the next 4 days and the steam is assumed to advect with the wind field. Streamlines are defined as being lines that are everywhere tangent to the velocity field. The Stream Function. The flow is steady shear flow in the gap between two flat plates, with the top plate moving at velocity V to the right and the bottom plate stationary. CIRCULATION 31 velocity associated with second term is 1 2ω. Streaklines, Streamlines, and Particle Paths Duration 10:11. where (3) where t 0 is the time at which a fluid particle on the streamline passes through the point x 0 on the streakline. If you. 1. 1. 8. Tutorial - Illustration of Streamlines, Streaklines and Pathlines of a Velocity Field. They. 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. It is a little confusing, but think of a river which gets dammed. Cross-sectional areas of the streaklines are calculated at various points along flow to investigate morphological evolution. It is the locus of particles that have passed sequentially through a prescribed path in the flow. Streaklines are the loci of points of all the fluid particles that have passed continuously through a particular spatial point in the past. A. So, streamlines are a family of curves which, for every instant in time, are the velocity field envelops. Only one answer is correct. Consider the visualization of flow over a 12° cone in Fig. 在 連續介質力學 中， 物質導數 （英語： material derivative ） [1] [2] 描述 物質元 （英语：material element） 一些物理量（如 熱量 或 動量 ）的 變動率 ，而該物質元受制於由時間和空間決定的 宏觀向量場 。. Abstract. Flow visualization is the study of methods to display dynamic behavior in liquids and gases. For the toxic cloud release, one would be most interested in determining the streakline passing through the location of the damaged reactor. The time history of a marker particle may be found by solving the pathline. 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 topics which may be deduced about the nature of a flowing fluid without referring to the dynamics of continuum are explored in this chapter. 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. Such flow may actually flow upstream, against the direction of the free stream airflow. The resulting trajectories, streaklines, and streamlines are seen in figures 4. Displays all PORTS stations for the specified region and the product types for each station. These can be thought of as "recording" the path of a. Rendering the streaklines as tubes allows rendering with surface shading – which helps our eyes see thire orientations more accurately. Their fluids laboratory has a nice water tunnel into winch they can inject multicolored dye streaklines, so they decide to test a spinning baseball in the water tunnel (Fig. Another technique would be to instantly inject a line of dye across streamlines and observe how this line moves as time increases. \%-50gridlines b. P4–32C. Streaklines: instantaneous loci of all fluid particles that pass through a given point xo. One can release a stream of dye or a succession of small bubbles and then take a short exposure photograph in order to record the streakline, perhaps for a whole succession of moments in time. 、脉线和流线 迹线（Pathlines）：某一流体质点的运动轨迹。 脉线（Streaklines）：关注空间某一位置，在经历较短的时间后，可以标识出流动过程中经过该空间点的许多流体质点，所有这些流体质点都在一定的时间内，先后流经这个固定的空间位置，连接这些流体质点的线。Civil Engineering.