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Turbulence at high velocities and Reynold's number

Video transcript

okay so we saw that if you had nice laminar streamlined flow plazas law told you how much volume per time would flow through a pipe but how do you know when you're gonna have a nice laminar flow what determines when this thing becomes chaotic what determines when they start to cross these layers of flowing water or fluid how do you know when there's 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 reynolds number and 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 Reynolds number I'm going to call that are you multiply that by the viscosity and remember ADA 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 and this gives you the first speed where you would expect turbulence now if you measure the Reynolds number to give you an idea for blood because this comes up a lot when you're talking about blood flow in the aorta you might worry that there might be turbulence for blood the Reynolds number is around 2,000 and it's unit has no dimensions there's no units here all the units cancel out and the Reynolds number is a unitless dimensionless quantity so knowing the Reynolds 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 kwazii's law to not give you an accurate description of the flow of the fluid