 In this segment what we'll be doing is we'll be taking a look at the velocity field which is a very important aspect of what we're usually trying to determine when we're solving fluid mechanic problems. So within a fluid we have the fluid moving at specific velocities which vary with space and time and we're trying to determine the velocity field when we're usually solving problems and when we're doing this there are two different points of view that are often used within fluid mechanics and so we say here in mechanics or it could also be in fluid mechanics but these two different points of view one is the Eulerian and the other is the Lagrangian. So first of all let's take a look at the Eulerian and this is typically concerned with fluid properties at a given point within the spatial domain so that is the Eulerian perspective and we contrast that with the Lagrangian which is more concerned with a particular particle as it moves through space and time. So if we're talking Eulerian, Eulerian would look something like this we would have a chunk in space or a location in space and the fluid will be moving through that point in space so it might have some vector v at that particular location but that particular location p is going to have spatial coordinates x, y, z and it will be at a particular point time t. Now if we contrast that, now this is fixed in space so it is not moving and when we look at the Lagrangian, the Lagrangian we have the same chunk of fluid however in this case it is free to move and consequently this would be a moving chunk of fluid not fixed in space and consequently if we were to look at any of the properties be it pressure, velocity, temperature they will only change with time as the fluid particle moves through space and we can draw a velocity vector like that and the velocity vector is going to change as you move through space. So in fluid mechanics we will typically tend to focus on the Eulerian more than the Lagrangian just because it's a little simpler but so in this course we will mainly look at Eulerian analysis. Okay so we're talking about the velocity field the velocity field is one of the most important things that we will be after when we're trying to solve fluid mechanic problems and it is a vector field that is going to be a function like we said of the three spatial coordinates x, y, z or x, y, z and time t. So the velocity field here we have it as capital V and a function of space and it will be a function of both space as well as time so let's take a look at the expression that we typically use so we will give it a vector x, y, z and t and we said that that is then a vector representation so we have the unit vector in the x direction multiplied by the velocity in that direction and usually we use little u so that will be x, y, z, t and then we have the unit vector in the y direction j and the symbol that we use for velocity in that direction is usually little v and then finally we have the velocity components in the z direction or k for the unit vector and there we use little w so that's typically the way that we express velocity for a fluid and from this what we can do is we can derive a number of kinematic properties and that's what we're going to spend the next few segments looking at but kinematic properties so what we're going to do now we're going to take the velocity field that we just talked about so that is this here and from the velocity field we're going to look at a number of different kinematic properties that are quite important within fluid mechanics and you'll be using these with throughout the course so we'll now take a step into looking at these different kinematic properties