 When we simplify the Reynolds transport theorem for momentum, we are plugging in a beta value of velocity and a b value of momentum which yields the derivative of momentum with respect to time of the system, which remember is our definition of force. So I write it as force of the system as a vector, remember, is equal to the time rate of change of the integral of velocity times density with respect to volume plus the integral across the control surface of velocity times density times velocity with respect to area. Now we can start to simplify it. That term on the left, the sum of forces on the system, we break apart for convenience. So instead of writing it as one sum of forces, I will write it as the combination of the surface forces plus the body forces. That's the forces acting on the fluid as opposed to forces acting within the fluid. Our only body force for our purposes right now is going to be gravity. So or rather the weight of the fluid as a result of the acceleration of gravity. Our surface forces could include like a pressure being applied to the surface of the fluid or it could be maybe the fluid is inside of a nozzle or some sort of vessel that is exerting a weight on the fluid. Anyway, when I start to simplify it, it is easiest to keep track of the individual dimensions. I mean when you were in dynamics, how much easier is it to keep track of velocity in the x direction and y direction when you're trying to figure out say projectile motion? Same goes here. So if we had Cartesian coordinates, for example, we would keep track of our conservation momentum in the x, y, and z directions independently. Furthermore, note that our notational scheme here for velocity differentiates for velocity in the x direction, velocity in the y direction, and velocity in the z direction. The way that we note velocity in the x direction is with the letter u, the way that we note velocity in the y direction is with the letter v, and the way that we note velocity in the z direction is with the letter w. That's standard notational practice for fluid mechanics. Yes, v for y component of velocity can get confused with velocity by itself, which can get confused with a lot of other things that we abbreviate with v, but to try to help separate which v we're talking about, we write the y component of velocity as an italics v. Actually, we write u, v, and w and in italics generally just to try to keep track of them. So our conservation momentum in the x, y, and z directions look like this. Note that this velocity vector appears in all three dimensions. It is not simplified to the x component or the y component or the z component, it is just the velocity vector as a whole. Because this velocity vector times this area vector is how we are keeping track of our flow rate across the control surface.