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Turbulence at high velocities and Reynold's number

Video transcript

- [Voiceover] Okay so we saw that if you have nice laminar streamline flow, Poiseuille's Law told you how much volume per time would flow through a pipe. But how do you know when you're going to have a nice laminar flow? What determines when this thing becomes chaotic? What determines when these start to cross, these layers of flowing water, or fluid? How you know when they're going to start to cross, which is going to cause these vortices and eddy currents. When will this happen? Turns out, there's a way to predict it. It's hard. This is very hard. In fact, not only is it hard to predict it, once you know that it's going to happen, once you know things are going to become turbulent, it's even harder to try to describe the behavior. Typically you have to resort to a computer simulation rather than an analytical calculation. But there is a number, it's called the Reynold's Number. What this number does is it gives you a way to predict what's the first speed, what's the critical speed... Where if you went over this speed, if the fluid were to flow faster than this speed it would become turbulent. The flow would become chaotic. The way you find it is you take this Reynold's Number-- I'm going to call that R-- you multiply that by the viscosity. Remember eta, this Greek letter we were using for the viscosity. You divide by two times the density of the fluid, multiplied by the radius of the tube. This gives you the first speed where you would expect turbulence. Now, if you measure the Reynold's Number to give you an idea for blood, because this comes up a lot when you're talking about blood flow and the aorta you might worry that there might be turbulence. For blood, the Reynold's Number is around two thousand. It's unitless, it has no dimensions. There's no units here, all the units cancel out. The Reynold's Number is a unitless, dimensionless quantity. Knowing the Reynold's Number gives you a way to predict what's the first speed where you might expect turbulence, and therefore the first speed where you might expect Poiseuille's Law to not give you an accurate description of the flow of the fluid.