 As we start quantifying the behavior of internal and external fluid flows, we are going to be using empirical equations, that is, equations which are generalizations drawn from experiments. To be able to generalize a fluid flow as much as possible, we describe its properties, characteristics, and conditions with non-dimensional numbers. One of the most useful non-dimensional numbers for this purpose is the Reynolds number, which is a ratio of inertial forces to viscous forces, within a fluid which is subjected to relative internal movement due to different fluid velocities. This proportion can be simplified to the density times the velocity times a size parameter divided by the dynamic viscosity of the fluid. Or, for convenience, we can introduce a normalized viscosity called kinematic viscosity, which represents the proportion of a fluid's dynamic viscosity to its density. Writing it this way allows us to use a single lookup to characterize the fluid's properties. The size parameter, shown as x here, is also referred to as characteristic length. It is a parameter which indicates how big or small that flow condition is, or the characteristics are. It can be different things in different circumstances. For internal flow, it's usually a diameter. For flow across an airfoil, it might be the chord length of the airfoil. The thing that matters is that the length parameter is used the same way when we're generalizing and when we're trying to apply those generalizations. You can think of inertial forces as how much energy there is in the motion of the fluid, and viscous forces as how resistant to motion the fluid is. When the inertial forces are large relative to the viscous forces, i.e. a high Reynolds number, any molecule's energy is going to have a lot of effect on any other molecule it interacts with. This can introduce turbulence to the flow. When the viscous forces are large relative to the inertial forces, i.e. a low Reynolds number, a molecule doesn't affect the molecules around it much. This generally leads to smooth sheets of fluid flow which we call laminar, which is a fancy way of saying not turbulent. When we are applying our generalizations based on empirical evidence, we do so by characterizing fluid flows into categories and generalizing that category. The two categories we are going to be using are turbulent and not turbulent, which we're calling laminar. We are treating the distinction between the two as occurring at a specific Reynolds number called a critical Reynolds number. For our purposes, the critical Reynolds number is a firm line in the sand. Any flow with a Reynolds number less than the critical Reynolds number is considered laminar, and any flow with a Reynolds number greater than the critical Reynolds number is considered turbulent. This is a model of reality and therefore flawed, but it is a useful way to reach accurate enough predictions of how a fluid will behave. For example, for flow in pipes, we use diameter as the characteristic length for our Reynolds number, and we use a critical Reynolds number of 2300. That means anything less than 2300, even 2299, is considered laminar flow, anything greater than 2300, even 2301, is considered turbulent.