 So we're now going to take a look at our second basic law, and that is the conservation of linear momentum. And if you recall the system equation, we had some of forces, and I think we had p for the momentum, but I'll expand it out, mv dt. And this is for a system. Now in terms of our extensive and intensive properties, so eta is then just the vector v, so with that we can rewrite using the relationship between the system and the control volume for the time derivative. So that's for a fixed mass on the left, and then on the right this is for a control volume. Now the forces that we have, so that's for the time rate of change, that would be the right hand side of f equals ma. Now for the forces, what we can say is that forces on the system equal the forces on the control volume. And those forces would consist of, we will have surface forces, and we will have body forces. So surface forces would be things such as pressure or shear, viscous shear, and body force would be, gravity would be one, you could have electromagnetics. So with that we put these two together, and what we get is the equation for conservation of linear momentum for a control volume. So this is conservation of linear momentum for a control volume. Now for students new to fluid mechanics, this term here quite often causes a little bit of grief. So what I'm going to do is I'm going to expand this equation, and remember this is a vector equation, so essentially there are three equations embedded here that we're looking at. I'll write out each of the different vector components. So that is the conservation of linear momentum expressed out as three different vector components, x, y, and z directions. And there are a couple of things that I want to make note of when you're doing analysis using this equation. And then this can be a place where students can sometimes be confused, and again it pertains to the last term that we saw in each of these different vector components. And it depends upon how you handle the signs, and so you have to be fairly careful about that. So let me just make a note. So the first thing is you'll want to determine the sign of the mass flow rate, so the rho v dot da. So let's look back at our equation. So that means that you'll want to figure out the sign of this, this, and this, and figure that out independently first. And the second thing to note. So the second thing to note is be careful about the signs of uvw as well. So essentially what I usually do when I solve these problems, first of all I look at the mass flow rate, which is crossing the boundary, and I determine the sign of this term. And then I also look at the velocity components. Remember this can have a sign as well, because it's a vector component, and depending upon your coordinate system it could be a plus or a minus. So you've got to be careful with those signs. This could be plus or minus, and this could be plus or minus, depending upon the orientation of the area, the vector, and the velocity itself. So those are a couple of the things you have to be careful about when you're applying the conservation of linear momentum to the control volume. The last thing I should say is that this has some restrictions to it, and I'll just make one last comment. The last disclaimer to make is that this equation is for control volume that is not accelerating. So you can have cases where the control volume is moving or even accelerating, and for those you have to be a little careful when this equation would not apply. We will be looking at an example of that in the next lecture, not in the next segment but in the next lecture we'll be treating a case for accelerating control volumes. Anyways, that provides the outline for how to apply the basic law of conservation of linear momentum to a control volume. What we'll be doing in the next segment is we'll be working a problem applying the conservation of linear momentum to a control volume analysis.