 In this segment, what we're going to do is we're going to take a look at different ways of visualizing fluid flows that occur in fluid mechanics and we're going to look at a number of techniques here, but essentially we're looking at streamlines, streak lines, and path lines. And these techniques were developed for experimental fluid mechanics and what they did is they enabled researchers to gain insight into what was happening within a particular fluid flow. And in recent years, we replicate them using numerical methods, but we still do use them for experiments. So we'll begin with streamlines. So what a streamline is, it's a line that is everywhere tangent to the velocity vector at a given instance. So what I'm going to do, I'm going to use an airfoil to demonstrate this. So let's draw out an airfoil and it will place a streamline on here that comes up and over. And what we're talking about is a line everywhere tangent to the velocity vector. So that if that is actually a streamline, then what that means is that if we look at any point on here, the velocity vector needs to be tangential to that line. And so if you place a particle at t0 by t1 it would get there, t0, t1 it would get there, t0, t1. And by placing particles then you're able to visualize where the flow is going. So anyways, that is a streamline. The velocity vectors will always be tangential to the streamline itself. So here we have the condition where t1 is greater than t0. So streamline, the next one that we'll take a look at is a streak line. So the definition of a streak line is it's a locus of particles which all earlier passed through a common point and you may be thinking, well that's the same as a streamline, but it turns out that if you have non-steady flow, a streak line and a streamline will not necessarily be the same. Actually they won't. So what I'm going to do again, I'm going to draw an airfoil. So let's say we have our airfoil there and if this was an experiment in a wind tunnel, for example, quite often we use smoke visualization. So you may have a wand that you place into the wind tunnel. You have some smoke chamber here. It could be kerosene that you're burning and it's smoking. It could be titanium tetrachloride which reacts with the water vapor, makes titanium dioxide which you can then see many, many different ways, stage smoke, things like that. But from this one point, what will happen is the fluid will come along and it will go over the airfoil and that would be an example of a streak line because they are all originating from this one common point. Now if this airfoil was pitching, for example, that streak line is going to change dynamically. And so if the airfoil was to do a pitch up or a pitch down maneuver, the streak line would be a lot different. It might be something like that as the airfoil is going up into kind of a new configuration, something like that, depending upon where the pitching point would be. So that is a streak line. The next thing that we'll take a look at is a path line. So the definition of a path line, it is the path traversed by a given particle. So again, we'll use our airfoil example, draw out an airfoil and let's say we were to release a particle into the flow and I'm going to cheat here and draw my stream line because I won't be able to put the particles on it perfectly. But let's say, and I'll use reds that we can see it a little easier, t0, t1. So what we're doing is we're following this particle as time evolves, and each of these time points is later on than t8. So here we would have this scenario where t8 is greater than t7, which is greater than all the way down to t1 greater than t0. So that would show evolving time as the particle moves through the fluid flow that we're examining. Next thing that we'll look at is a timeline. So a timeline is a set of particles that form a line at a given instant, and for this particular case what we're going to be doing, we won't look at an airfoil, we'll look at pipe flow. So let's assume that we have a pipe, and we'll assume that it's laminar flow, so we have the parabolic profile, the poiseuille flow, and here we have a velocity profile u of y, and let's assume that y is the vertical and our other coordinate system x. So if we were to release particles, a set of particles that form a line at a given instant, so let's say this is t0, and quite often for pipe flow, fluid flow, if you have liquid, what we do is we use the hydrogen bubble technique where you put a wire through, you pass a current through it, and you get hydrogen bubbles, and then you can track them. But let's say this was t0, if we were then to look at those bubbles at a later point in time, we have this velocity profile here, so we know that the bubbles are going to be convecting to the right, and so if we look later in time, and I'll use a different color, so those bubbles will have moved, and the amount that they will have moved will depend upon their local velocity, which is related to the velocity field in the pipe. So there you can see the particles, in this case I'm saying they're bubbles, that would be a t1, and so t1 is greater than t0. So those are different methods by which we can visualize fluid flows, and it turns out that in steady flow, so if it is not changing with respect to time, so if you have steady flow, that would be a flow where d by dt of any term is equal to 0, if you have steady flow, streamline, streak line, and path line are all the same. So what we're going to do now, we're going to take a quick look at a video which helps demonstrate streamline on an aircraft, and what we're going to do, let me just start the clip here, so this is an Airbus 380, and it was on a flight between Singapore and Hong Kong, and there you can see the two engines, and what we're going to do, we're going to focus on the vortex generator of the engine itself, because that generates a beautiful vortex, depending where you're seated, that you're able to see coming over the wing, and so here you can see there's a visualization, it's basically moisture in the air that is condensing due to low pressure, so you can visualize, and there is landing, so what we were looking at was the vortex location during ascent, and then on landing, and here you can see the streamline during ascent coming over the wing, and there you can see the streamline during landing, and they're very very different, if you go back and look at the video and compare those two, but what it shows, and it makes sense, when you're ascending or climbing out away from the airport, the flaps and everything are in very very different configuration from when you're landing, and consequently you would expect the streamlines between those two to be different, but that engine to sail vortex generator generates beautiful flow visualization, that then enables you to see and visualize what the flow looks like over the wing of an Airbus 380, so that is an example of a streamline, and I guess it was steady flow, so it could be an example of a streak line and a path line as well, but those are techniques that we use quite often to visualize fluid flows, and then provide us with further insight into what is happening with a particular problem.