 Even though we're through all three of our conservation terms, I want to introduce a fourth equation. I know, but you can be excited about this one because it's going to save you a bunch of time. It is for a simplification of the conservation of energy, and it's based on the work of this dude. This gentleman is named Daniel Bernoulli, and he observed that when you take the conservation of energy under very specific circumstances, it simplifies a whole bunch. Those circumstances are, when you have city flow without any friction along a streamline, where your flow is incompressible and you don't have any shaft work or heat transfer, then the quantity you get as a constant is the pressure over the density plus the velocity squared over two plus gravity times the height. That term is going to be constant when you have all six of these assumptions in place. This equation is not really a new equation, it's just a simplification of the conservation of energy equation, and it's named in Daniel Bernoulli's honor as the Bernoulli's equation or the Bernoulli principle, and this is about the handiest thing ever. All you have to remember is that there are a lot of assumptions in place before you can apply this. You should already be familiar with the concept of city flow, the concept of friction, incompressible flow, shaft work, and heat transfer. The only one that might be new to you here is the flow along a streamline. And a streamline is just the line that is parallel everywhere to velocity. So everywhere on that line, that line's profile is parallel to the velocity profile. So that would look like this on a vector field, or if you were looking at, say, a flow around a body, that would be the velocity profile, how the air or water is actually moving. That's a streamline. So you can only apply the Bernoulli principle along a streamline. So I could describe, say, the relative properties of this point and this point, or this point and this point, but I could not relate this point to this point with the Bernoulli principle. I would actually have to go back to our conservation of energy. Now, that was a lot of theory. Let's actually get into some examples.