 We're going to talk briefly now about the some of the basic equations that we use within fluid mechanics. And we'll be talking about these equations quite often and consequently it's useful to review them now. The first equation that we'll be looking at, and this is an important one, is conservation of mass. And within fluid mechanics we refer to that as being the continuity equation. Second equation is conservation of momentum. This will come out of Newton's second law, f equals ma, and we'll derive that for a control volume. Third one is conservation of energy, and that is the first law of thermodynamics. The place where you would see that in this course would be if you have a non-isothermal flow, gas dynamics, high speed flows would be involved with that, but we really won't be looking at that in an introductory course, the fluid mechanics. Next equation, which couples and follows on from the energy equation, is the equation of state. And that's something that you would see in a thermodynamics course. Ideal gas law, ideal gas equation, p equals rho rt, and we will use that from time to time when we're dealing with variable pressure or temperature flows. And finally what we have here is we have to apply boundary conditions. We already talked about the no slip or no temperature jump, but boundary conditions are also important. And the boundary conditions apply at any of the surfaces or interfaces for the domains that we're studying, so it could be solid surfaces, as we saw with the no slip, could be an interface between fluids, it could be an inlet or accept. So we have a lot of different types of boundary conditions, and we need to know the conditions of those boundary conditions. So within this course, for the most part, what we will be doing is we will definitely be looking at the continuity equation in conservation of mass. Conservation of momentum, that's another one that we'll be spending a lot of time on. We'll spend a little bit of time looking at conservation of energy as well for non-isothermal flows. And finally we won't really spend a lot of time with the equation of state, a little bit with fluid statics, but not much. And we will look a little bit at the boundary conditions, and consequently in this course, the main areas where we'll be focusing our efforts, boundary conditions will come in. We mainly look at continuity, conservation of momentum, and conservation of energy. So those are the basic equations that we will be using within fluid mechanics. Now, sometimes it can be confusing for a student starting in fluid mechanics, because there are a lot of different definitions and terms and different types of flows that you'll hear people talk about. So what I want to do now is I want to sketch out something that was sketched to me when I was a student taking fluid mechanics, and I found this very helpful. And it's referred to as being the big picture. So how does this all kind of fit together? And so in a way, it's kind of a mind map or knowledge map of how the different areas of fluid mechanics stick together or couple together. So if you recall, we talked about continuum fluid mechanics. So that's what we're looking at. And that's where we assume that the spatial dimensions that we're looking at were not on the order of the mean free path of the molecules. So it's not a rarefied gas or flow that we're looking at. We can assume the density is constant for the size of the units that we're looking at usually. And then within continuum fluid mechanics, we have two divisions. One is inviscid flow. You'll sometimes hear about ideal aerodynamics or inviscid. This is a branch of fluid mechanics that was developed. It's kind of a mathematical construct, but it was developed long ago by the mathematicians that were studying fluid mechanics. What they did is they decided to neglect viscosity in order to simplify the equations. On the other side would be the branch where viscosity is important, and that would be viscous flows. And so those are two separate areas. And these both fall under continuum mechanics or continuum fluid mechanics, I should say. And then within viscous, viscous flows can have two different states. You can, depending upon the velocity or the conditions of the flow, and one state is laminar and the other one is turbulent. And we'll look at a number, the Reynolds number, which basically determines where we are within the flow domain if we're either in the laminar state or the turbulent state. And you can also be in transitional, but we really won't get into the transitional flows in this course, but transitional would be between the two of them. Consequently, viscous flow can be laminar or turbulent for the same boundary conditions. So it's non-unique in a way. You can have two solutions to the Navier-Stokes equations. And then under that, as we go down, what we can have, and this is where basically our inviscid flow and viscous kind of come together. And so they can merge up again under here. And down under here we can then have further subsets. And so one of these is if the flow is compressible or you can have incompressible. And we use the Mach number in order to determine whether or not we have compressible or incompressible flow. Mach number is ratio of the speed of the fluid to the speed of sound in that fluid. And typically the rule of thumb is if the Mach number is greater than 0.3, you would say it's compressible. If Mach number is less than 0.3, then it is incompressible. And if we recall from an earlier lecture, we said del dot v is equal to zero would be the thing that would tell you whether or not it's incompressible or not. And then on the other side here, what we can have is we can have internal. So internal flows would be, for example, flow within a pipe, within a channel, or we can have external flows. So external flow would be the flow around a baseball or around an aircraft, for example. So we have internal and external flows. And then these again kind of fall under here. So those are all of the different types of flows that we can have and situations that we can investigate. And on top of all of that, this could either be steady. So remember for steady, we said partial with respect to t would be equal to zero for the terms. It could be unsteady and unsteady gets a little more interesting, a little more complex. So you could have an unsteady flow and this could be for a gas like air, nitrogen, helium, or it could be for a liquid. And with that, we'd be looking at water, oil, anything like that. Typically, however, what we're going to do, we're only going to look at Newtonian fluids, which we talked about earlier with the relationship. We won't be looking at non-Newtonian fluids in this course. So that's kind of the big picture, how everything fits together. And hopefully that helps. You can also refer back to this as we go on and talk about different types of fluid flows and how we would approach analyzing them. Inviscerate flow, that would be ideal potential flow. And we'll touch on that a little bit in the course, not a whole lot. Sometimes that's also ideal aerodynamics. Those are different ways of referring to the same thing. So that's the big picture of fluid mechanics. We'll continue on now.