 We're now going to look at a couple of other vector operators, the divergence of a vector field and the curl. So let's begin with divergence. And what divergence does, it will take us from a vector and it will result in a scalar. So let's imagine we have a velocity field and we will apply the divergence operator to that velocity field. The divergence operator we call that del dot, and in this case it would be del dot v. That's how you would say that, del dot v, and when we write it out mathematically this is what it is. So that is the divergence operator. We will see it in the continuity equation when we look at conservation of mass, but physically what it represents is the following. So it's the time rate of change of the volume of a moving fluid element per unit volume. And most often in fluid mechanics the place where we'll see it is if we're dealing with incompressible flow. And just from that definition it's the time rate of change of volume of a fluid moving element and if the fluid is incompressible the volume will not change. And consequently when we have incompressible flow we always write del dot v equals zero. And that is something that you should memorize because you'll be using it quite often in fluid mechanics. So that is divergence of a vector field discussed in terms of the velocity vector for the vector field. It could be other vector fields as well. The next one that we're going to look at is curl. The curl operator. We're going to see that quite often when we look at things like vorticity and circulation within a flow field. So the curl operator, we saw the cross product earlier. This is basically the cross product with velocity, you're operating on velocity. But here we go from a vector to a vector. So let's write out the curl. Then we're going to begin with some velocity field. So that is our velocity vector del cross v. That's how you will hear it. So I should say that del cross v. And that would be equal to, we use the determinant ijk partial partial x partial partial y partial partial z. And then we would have vx vy vz. And then you evaluate the determinant and we're going to get a vector coming out of this. Okay. Let me just double check, make sure to make any mistakes. Looks good. Okay. So that is the cross product. Another operator that we'll use. And like I said, we use that for circulation or vorticity in a flow. This operator you use a lot for the continuity equation. So those are two other operators that we'll be using.