Dye steadily injected into the fluid at a fixed point extends along a streak line. Images are then recorded for further analysis. the flow is incompressible b. ME 363 - Fluid Mechanics Homework #11 Due Wednesday, April 16, 2008 Fall Semester 2008 1] A student team is to design a human-powered submarine for a design competition. 8. • Streaklines: Streaklines are defined as the locus of the path from where all the particles havepassed through in the past. Draw the direction of flow on the streamlines, streaklines, and pathlines. The plume lasts for three hours. What is the pathline of a particle at a location (1 m, 2 m, 4 m) at time t = 1 s?Expert Answer. See moreStreaklines. Communicate. 79-94, 1975. a. 5 1. 01106655, 0. The theory requires the firing angle to be less than about 40 degrees or so, which is fine in most instances. It's a subtle but important difference. These can be thought of as a "recording" of the path. Nikolaos D. The resulting trajectories, streaklines, and streamlines are seen in figures 4. Figure 1. Streaklines can cross and intersect, representing the simultaneous paths of different particles over time. 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. The video demonstrates some flow visualization techniques and illustrates streamlines, streaklines, pathlines, and time lines. Pathline and streaklines provide ways to visualize flows. Stream functions are defined for two-dimensional flow and for three-dimensional axial symmetric flow. 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). 2. Table 1. Courtesy ONERA. "the trajectories that individual fluid particles follow. C. Leaflet | Esri. Good agreement in streakline patterns between potential flow theory and experiment is observed over the cone at $$alpha =. Note that the higher temperature of the flow downstream of the shock causes the sodium to absorb more light in that region than upstream of the shock . Normal smoke wire flow visualization uses a smoke wire to demonstrate the flow streaklines. 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 Similarity requires that they match both the Reynolds number and the Strouhal number between their. Let's say the time interval is 0 to T. Question: 3 Problem Consider the velocity field u=U, v=V cos (27 (x – Ut)/k), (1) where U and V are constants and k a length. Streaklines are loci of points of all fluid particles that have passed continuously through a point in space in the past. related to rate of strain by the dynamic viscosity ii. As illustrated in Figure 1b , according to mass balance, the change in SSC of a depth-averaged fluid parcel as it travels downstream reflects exchange. 3. To visualize Timelines, Pathlines, Streaklines and Streamlines provide a vivid visualization of a fluid flow. Request a Free Trial. What is the line connecting all particles at t=4 s (see figure below)? There are 3 steps to solve this one. An explosion occurs at a nuclear power plant and radioactive steam is escaping from a broken pipe at time t=0. Examples of streamlines around an airfoil (left) and a car (right) 2) A pathline is the actual path traveled by a given fluid particle. 25. Photo of the damaged Chernobyl reactor. A) What is the difference between streamlines and streaklines? (Note; we did not have time to cover this difference in class, so you likely need to reference your book- see chapter 4) (2 pts) B) From which of Newton's fundamental laws of physics is the Bernoulli equation derived? (2 pts) C) What are the. Water flowing down a smooth, inclined roadway b. Transcribed image text: Some students want to visualize flow over a spinning baseball. Mechanical Engineering questions and answers. , 2018; Cathcart et al. The velocity field of a flow is described by V › = (4x)i › + (5y + 3) j › + (3t 2 )k › . Each cell in the grid can have, at most, one traversing streamline. For the couple of weeks I am trying to plot the streaklines from my 3D simulations that I have performed using OpenFOAM. Southampton Shoal Channel LB 6. Water tunnel test section Spinning baseball і 3. The path a fluid particle takes through a flow is actually called a pathline. \%-50timelines b. To visualize this in a flow, we could imagine the motion of a small marked element of fluid. That is, they satisfy that their tangent vector equals u(x,t) at the given time. Similarity requires that they match. Dye steadily injected into the fluid at a fixed point (as in dye tracing) extends along a streakline. This link, however, has been the most helpful in understanding how to derive the necessary equations. If any wet ink is left, blot it off with a dry swab or lint-free towel. 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. Fig. Are we seeing streamlines, streaklines, pathlines, or timelines? Explain. 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. streamline(___,options) plots streamlines using the specified options, defined as a one- or two-element vector with the form step or [step maxvert], where step is the step size in data units for interpolating the vector data and maxvert is the maximum number of vertices in a streamline. Flow lines explained! Streamlines, Pathlines, Streaklines. Dye steadily injected into the fluid at a fixed point extends along a streakline. Surrounding velocity field changes. Section 7: Similarity and Dimensional Analysis. Original and local streamlines for the Jet dataset. A streakline is a curved line formed by a string of fluid particles which have passed through a certain point. Module 4: Fluid KinematicsThis module i. e. t. Discussion Timelines differ from streamlines, streaklines, and pathlines even if the flow is steady. 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. Kinematics, Composition, and Thermodynamics. Jan 1, 2017. FIGURE P4–28CVisualization of flow over a 15° delta wing at a 20° angle of attack at a Reynolds number of 20,000. The net force on the stream tube in the flow direction is then. A scalar function. 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. Streaklines are lines deposited in the flow during a time interval by continuous emission of a tracer from a fixed point. the flow is steady iv. In other words, any material line that passes through a fixed. 3. The shape of the streamline does not change with time for all flow types. The governing equations are introduced in a simple manner, with an explanation of several useful and. 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。. This circulation near. Explanation: Fluid property based questions are given in which only one is correct. 1 Streamlines and Streaklines 18 3. 1 / 4. Where the angular velocity, w is equal to pi, 0 < x < 5 m, - 1 m < y < 5 m and 0 < t < 2 s. The statement “ vorticity at x equals twice the angular velocity of the fluid at x” is often heard. We will eventually allow streaklines and particle paths to. 7. streaklines are marked in a flow with smoke or dye ii. . For example, consider the initially straight dye line injected in front of the circular cylinder. these lines are basically imaginary lines which are tangent to a curve drawn in space. 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). Streaklines. Vorticity Basics. Flow lines explained! Streamlines, Pathlines, Streaklines. 1. 0:00 Streamlines0:47 Eulerian Approach1:32 Pathlines and Lagra. 100% (3 ratings) Transcribed image text: Some students want to visualize flow over a spinning baseball. Engineering. a. The visualization is produced by a time exposure of air bubbles in water. Photo from. FIGURE P4-31C Visualization of flow over a sphere at a Reynolds number of 15,000. for more FREE video tutorials covering Fluid Mechanics. The room is heated by a heat pump so that the temperature. It is easiest to visualize a streamline if we move along with the body (as opposed to moving with the flow). • Streamlines, streaklines, and pathlines Streamline: a line that is everywhere tangent to the velocity field. – 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. Generally, fluid is defined as a substance which is capable of spreading and changing its shape, according to is surroundings, without offering internal resistance. Tutorials are split in Self-directed Tutorials and Classroom Tutorials: Self-directed Tutorial ’s Section 1 to Section 5 provide an introduction to the ParaView software and its history, and exercises on how to use ParaView that cover basic usage, batch python scripting and visualizing large models. The inflow and outflow are one-dimensional, so that the velocity V and density ho. 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. Mechanical Engineering questions and answers. This type of flow results from uniform shear in the deformation. 3. The trajectory of the particle as a function of time, $(x_p(t),y_p. To evaluate the streaklines, we need to consider the time component of the velocity field equation. Oakland Inner Harbor LB4. Eulerian and Lagrangian Approaches. a. 2) p Δ A − ( p + ∂ p ∂ s Δ s) Δ A = − ∂ p ∂ s Δ s Δ A. The bubbles tend to rise slowly in water because of buoyancy, eventually they reach terminal speed relative to the water. 1 KINEMATICS OF FLUID FLOW. It is a strictly Eulerian concept. As soon as your flow is time dependent, trajectories, streaklines, and streamlines all look very different. A streakline is a Pathline that moves more than a single point through the flow. Streaklines are traced out by neutrally buoyant marker fluid injected into a flow field from a fixed point in space. 4 The Divergence of the Velocity and Green’s Theorem 23 3. Pathlines are useful for understanding the movement of water in rivers or the behavior of particles in chemical reactions or industrial processes. The time history of a marker particle may be found by solving the pathline. 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. 03922218). This is used to visualise the flow. It is the locus of particles that have passed sequentially through a prescribed path in the flow. 1. Slightly away from the fuselage and near the rotor blades, pockets of low-velocity flow circulation are observed. Question: Problem 2. precalculus. Figure 3. The high-speed. For the same particle starting locations, streaklines at T = 20 are shown in in Figure 4. 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. pathlines Under steady flow conditions, these two lines change over a fixed time interval in the same way. Streaklines and pathlines (particle paths) both use interpolation and will be supported. 8yj. 1–4. 1 Flow Patterns: Streamlines, Pathlines, Streaklines. The locus of fluid particles that have passed sequentially through a prescribed point in the flow. flow kinematics: 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. Chemical Engineering questions and answers. 0) crashes and gives the segmentation fault. 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. In other words, place a particle at point p, and move the particle one time step with the flow. The following animation illustrates the differences between a streakline and a pathline. Cases B and C distribute the energy in the spanwise direction and create additional low-speed streaks by doubling their spanwise. And they represent the velocity. Problem 4-31C: Consider the visualization of flow over a sphere in Fig. 98 MBFigure: Equation of motion of a fluid element on a streamline with taking into account the gravitation. vectorlines b. Smoke consists of gasses and soot. We would like to show you a description here but the site won’t allow us. Two path lines for two particles may intersect each other. The field dates back at least to the mid-1400's, where Leonardo Da Vinci sketched images of fine particles of sand and wood shavings which had been dropped into flowing liquids. 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. For illustration purposes, the streaklines are shown only on every 10th row and column. This Session for Practice Problems on Flow lines (Streamlines, Streaklines, and Pathlines) is a Part of the Problem Solving Series for the Introductory Fluid. Calculating streamlines, particle paths and streaklines in Tecplot 360 EX 2014 R2. Each cell in the grid can have, at most, one traversing streamline. (2) and (3). Concepts for describing fluid flows: streamlines, particle paths, and streaklines. Convert a volume flow rate of 3. 5: Streakline. Streamlines, Streaklines, and Pathlines Streamlines is a line that is everywhere tangent to the velocity field. , 2020; De Laurentiis et al. Nowadays flow visualization. In Figure 14. Expert-verified. 2 Flow visualization - Flow lines † Streamline: A line everywhere tangent to the °uid velocity ~v at a given instant (°ow snapshot). Streaklines show the path history of fluid particles that have passed through a particular location. CIRCULATION 31 velocity associated with second term is 1 2ω. Streaklines can show how individual particles move and disperse over time, which is important for understanding the spread of pollutants or the movement of marine organisms. , sinu-Fluid particles are m. Are we seeing streamlines, streaklines, pathlines, or timelines? Explain. The velocity field of a flow is described by V › = (4x)i › + (5y + 3) j › + (3t 2 )k › . 3 Kinematics: Streamlines, Streaklines, Timelines, and Vorticity 18 3. In steady flow, the fluid is in motion but the streamlines are fixed. Section 7: Similarity and Dimensional Analysis. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Name an application where timelines are more useful than streaklines. P4. Streaklines are identical to streamlines for steady flow. . e. Streaklines Another form of visualization is a streakline. (20) Sketch for Question 6. Streaklines can be seen as a special case of material lines. 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. 2 t j – 1. At some instant of time the position of all these particles are marked and a line is drawn. I am new to matlab. 4 3. 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). 4. and we could pick a point from the above example say p = ( 0. Determine the motion of two-dimensional point vortices. Engineering; Mechanical Engineering; Mechanical Engineering questions and answers; Some students want to visualize flow over a spinning baseball. Streaklines are well known in flow visualization [3,4] and fluid mechanics [5] as a tool for measurement and analysis of the flow. 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. 物質導數可作為 連續介質力學 對 形變 的 歐拉. (15pts, 5pts each) a) Consider the visualization of flow over a 12 cone in the. Show the streaklines of the plume at t=5h and t=10h. related to the pressure field by theFinal answer. In a steady flow the streamline, pathline and streakline all coincide. Discuss how this dye line would appear at later. 7. That is, they satisfy that their tangent vector equals u(x,t) at the given time. (A pathline is an integrated pattern. A region bounded by streamlines is called a streamtube. Continuity Equation When a fluid is in motion, it must move in such a way that mass is conserved. a. Researchers have presented many visualization techniques with similar goal, which is to enrich the information provided by the visualization. The equation for range (equation 7. 2. Are we seeing streamlines, streaklines, pathlines, or timelines? Explain. The streamed flow was illuminated by a laser sheet provided by a 532-nm 10 W CW laser. 1. In smoke wire flow visualization, smoke streaklines are generated from oil droplets on a heating wire or injected from the outer smoke generator/container during the experiments. In the Lagrangian approach the velocity of a fluid particleExpert-verified. Location of The Tracer. This Session for Practice Problems on Flow lines (Streamlines, Streaklines, and Pathlines) is a Part of the Problem Solving Series for the Introductory Fluid. 125 and μ = 0. 25. Another application is to visualize the velocity profile of a boundary layer or a channel flow. Flow development is. 0 mathrm {gal} / mathrm {min} 3. Streaklines and timelines are effective visualization techniques for depicting vortex shedding, vortex breakdown, and shock waves in unsteady flows. No flow across streamline. Controls the closeness of streamlines. A streakline is a curved line formed by a string of fluid particles when passed through a cer. 1. Another technique would be to instantly inject a line of dye across streamlines and observe how this line moves as time increases. This resource contains information related to overview of lagrangian and eulerian descriptions. streaklines are marked in a flow with smoke or dye ii. Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!) 8th Edition. Q = dV dt. We also go over how to obtain them experimentally. 物質導數. Observations of wind streaklines over the Red Sea from the ERTS-1 imagery. 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. a. Pathlines are the trajectories that individual fluid particles follow. The main difference between a flow system and a uncoupled bunch of particles is pressure. Label which is which on the diagram. What are streamlines, streaklines, and pathlines? Define each by drawing a sketch and providing an explanation. 3sin (ωt)−0. 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. Euler's equation for steady flow expressed in streamline. These animated gif images illustrate the differences between streamlines, streaklines, pathlines, and timelines. Are we seeing streamlines, streaklines, pathlines, or timelines?3. Because the streamlines are tangent to the flow velocity, fluid that is inside a stream tube must remain forever within that same stream tube. 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. This task is known as streamlining, and the resulting design is referred to as being streamlined. f (x)=2 x+\frac {9} {x^ {3}} f (x)= 2x+ x39. Describe a flow field for which this is true. Unsteady Flow of Streaklines. 11 Three types of fluid element trajectories are defined: Streamlines, Pathlines, and Streaklines. where V is the volume and t is the elapsed time. Give examples of an unsteady flow and a steady flow. Study with Quizlet and memorize flashcards containing terms like The continuum assumption for a fluid means that if the fluid was cut in half and in half again ad infinitum that the fluid's intensive properties, such as pressure and temperature, would be well defined in the limit at each point in space. These problems have already given me 3 days sleepless nights. Streaklines: - Streaklines are formed by visualizing the continuous lines formed by particles or fluid elements that have passed through a specific point in a flow field. Streamlines, streaklines and pathlines coincide when i. streaklines d. Determine the acceleration a (aceleration) for a flow with the velocity field , where t is time. Introduction. GIVEN say u=cos (t) and v=sin (t), How do I write a code to plot the pathlines and streaklines through the origin (0,0) for values of t=pi/2, pi, 3*pi/2 and 2*pi. Fluid flows are classified in terms of streamlines, streaklines, and pathlines. Engineering Mechanical Engineering Fluid Mechanics: Fundamentals and Applications Some students want to visualize flow over a spinning baseball. a. 1. These can be thought of as "recording" the path of a fluid element in the flow over a certain period. Streaklines and Their Applications 54 Streamline Coordinates 54 Questions 56 4 Basic Equations of Fluid Dynamics 57 4. 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. Similarity requires that they match both the Reynolds number and the Strouhal number between their. (10. 6+2. To understand streaklines, consider a fluid flow with an ink dye injected at a particular point. 6 x i + 0. It consists of the use of a high-speed camera capable of actually recording at high frame rates (in the order of 103 –10 4 frames per second) of the flow advancement inside the micro-cavity. Streaklines Another form of visualization is a streakline. Pathline: the line traced out by. 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. The stream function can be used to plot the streamlines of the flow and find the velocity. Dye steadily injected into the fluid at a fixed point extends along a streak line. The Stream Function. A region bounded by streamlines is called a. Streaklines. Ta. Tutorial - Illustration of Streamlines, Streaklines and Pathlines of a Velocity Field. 4. Determine how vorticity is produced by various mechanisms. 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. Uniform flow, Sources, Sinks, Doublets Reading: Anderson 3. 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. In simple terms, streamlines and streaklines are like a snapshot of the flowfield whereas pathlines are time-history of the flow. Author: Kreith, Frank; Manglik, Raj M. The static pressure is the operating pressure in the pipe, duct, or the environment, upstream to the pitot tube. 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 。. let me First define all these lines. Initially, near X = 0, the streaklines are what we expect, i. Streamlines, Streaklines, and Pathlines Streamlines is a line that is everywhere tangent to the velocity field. We extracted streaklines from remotely sensed SSC estimates, and quantified water fluxes and velocities based on the distance between them. A integral of a streamline gives the velocity field. y 0 = y ′ − t ′. 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. Expert Answer. , The velocity field of the form V=u(x,y,t)i+v(x,y,t)j is a two. 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. 6+0. 500-mb vorticity is also termed vertical vorticity (the spin is in relation to a vertical axis). AA200b - Applied Aerodynamics II Lecture 9 be tubulent and they are nearly impossible to compute analytically, except for some very simple cases. Streaklines: instantaneous loci of all fluid particles that pass through a given point xo. P4-31C. \%-50gridlines b. Pathlines, streaklines, streamlines berada pada satu garis yang sama Contoh Soal 2. Examples of streamlines around an airfoil (left) and a car (right) 2) A pathline is the actual path traveled by a given fluid particle. One this is accomplished you would than. 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. P4–29C. As a means of overcoming this problem, a small number of studies have used biogenic surface films as synoptic flow tracers, under the. Streaklines Reading: Anderson 2. Thus, the save state, which just captures the state at a particular time,. During the experiment dye is released continuously and floats are released every 30 minutes (called tracking drogues) to monitor the surface currents. At time t', the expression for pathlines is: x 0 = x ′ − 1 + \cost ′. density linearly scales this grid. If at a certain point in time all the particles introduced one after the other are joined together, a so-called streakline is formed. Currently, there is no functionality in matplotlib to plot streaklines. Similarly, the velocity vector is the projection of. Codes to plot fluid pathlines and streaklines given an example. . Streaklines are well known in flow visualization [3,4] and fluid mechanics [5] as a tool for measurement and analysis of the flow. Note that t 0 will be different for each fluid particle on a given streakline. ) a. generates a stream plot of the vector field { v x, v y } as a function of x and y. Open ParaView. 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. The net force on the stream tube in the flow direction is then. Mechanical Engineering. 1). It is a lecture note for the course AA210A Fundamentals of. streakline ( plural streaklines ) A locus of points of all the fluid particles that have passed continuously through a particular spatial point in the past. The streaklines show complex along-flow changes in cross-sectional shape that we interpret to be effects from temporal changes in grounding line dynamics and decay of ice topography due to flow. \%-50timelines b. In other words, place a particle at point p, and move the particle one time step with the flow. Step 2/2. 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. the local derivative of massWe 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. t. Oakland Outer Harbor LB 3. 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. streaklines allow students to easily understand the similarities and differences among these integral lines, which may be difficult to comprehend without visual explanation and interrogation. b) Consider the visualization of ground vortex flow in the figure. Streaklines show the path followed by a specific fluid particle as it moves through the fluid over a period of time. 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. timeline翻译：（事件发生的）先后顺序表, （显示做某事所需时间或某事何时发生的）时间表, （社交媒体上的）时间轴。了解. 4. 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. Similarity requires that they match both the Reynolds number and the Strouhal number between their model test. The three water filled tanks shown in figure below are connected by pipes as indicated. The plume lasts for four hours. Question: 2. Similarity requires that they match both the Reynolds number and the Strouhal number between their model. By studying streamlines, streaklines, and pathlines, engineers can gain insights.