1 00:00:01,278 --> 00:00:02,255 - [Voiceover] Okay so we saw that 2 00:00:02,255 --> 00:00:06,147 if you have nice laminar streamline flow, 3 00:00:06,147 --> 00:00:07,915 Poiseuille's Law told you how much 4 00:00:07,915 --> 00:00:10,641 volume per time would flow through a pipe. 5 00:00:10,641 --> 00:00:12,298 But how do you know when you're going 6 00:00:12,298 --> 00:00:15,109 to have a nice laminar flow? 7 00:00:15,109 --> 00:00:18,400 What determines when this thing becomes chaotic? 8 00:00:18,400 --> 00:00:20,400 What determines when these start to cross, 9 00:00:20,400 --> 00:00:23,136 these layers of flowing water, or fluid? 10 00:00:23,136 --> 00:00:25,072 How you know when they're going to start to cross, 11 00:00:25,072 --> 00:00:28,816 which is going to cause these vortices and eddy currents. 12 00:00:28,816 --> 00:00:30,409 When will this happen? 13 00:00:30,409 --> 00:00:32,159 Turns out, there's a way to predict it. 14 00:00:32,159 --> 00:00:33,408 It's hard. 15 00:00:33,408 --> 00:00:35,207 This is very hard. 16 00:00:35,207 --> 00:00:37,328 In fact, not only is it hard to predict it, 17 00:00:37,328 --> 00:00:39,295 once you know that it's going to happen, 18 00:00:39,295 --> 00:00:41,305 once you know things are going to become turbulent, 19 00:00:41,305 --> 00:00:45,341 it's even harder to try to describe the behavior. 20 00:00:45,341 --> 00:00:48,284 Typically you have to resort to a computer simulation 21 00:00:48,284 --> 00:00:51,578 rather than an analytical calculation. 22 00:00:51,578 --> 00:00:53,114 But there is a number, 23 00:00:53,114 --> 00:00:55,378 it's called the Reynold's Number. 24 00:00:55,378 --> 00:00:57,994 What this number does is it gives you a way to predict 25 00:00:57,994 --> 00:01:00,554 what's the first speed, 26 00:01:00,554 --> 00:01:02,714 what's the critical speed... 27 00:01:02,714 --> 00:01:04,946 Where if you went over this speed, 28 00:01:04,946 --> 00:01:07,642 if the fluid were to flow faster than this speed 29 00:01:07,642 --> 00:01:09,217 it would become turbulent. 30 00:01:09,217 --> 00:01:10,753 The flow would become chaotic. 31 00:01:10,753 --> 00:01:13,553 The way you find it is you take this Reynold's Number-- 32 00:01:13,553 --> 00:01:15,465 I'm going to call that R-- 33 00:01:15,465 --> 00:01:18,121 you multiply that by the viscosity. 34 00:01:18,121 --> 00:01:19,513 Remember eta, 35 00:01:19,513 --> 00:01:22,129 this Greek letter we were using for the viscosity. 36 00:01:22,129 --> 00:01:25,728 You divide by two times the density of the fluid, 37 00:01:25,728 --> 00:01:29,545 multiplied by the radius of the tube. 38 00:01:29,545 --> 00:01:30,817 This gives you the first speed 39 00:01:30,817 --> 00:01:32,736 where you would expect turbulence. 40 00:01:32,736 --> 00:01:35,000 Now, if you measure the Reynold's Number 41 00:01:35,000 --> 00:01:36,881 to give you an idea for blood, 42 00:01:36,881 --> 00:01:38,792 because this comes up a lot when you're talking 43 00:01:38,792 --> 00:01:40,960 about blood flow and the aorta 44 00:01:40,960 --> 00:01:42,832 you might worry that there might be turbulence. 45 00:01:42,832 --> 00:01:47,009 For blood, the Reynold's Number is around two thousand. 46 00:01:47,009 --> 00:01:49,572 It's unitless, it has no dimensions. 47 00:01:49,572 --> 00:01:51,841 There's no units here, all the units cancel out. 48 00:01:51,841 --> 00:01:56,188 The Reynold's Number is a unitless, dimensionless quantity. 49 00:01:56,188 --> 00:01:57,444 Knowing the Reynold's Number gives you 50 00:01:57,444 --> 00:02:00,110 a way to predict what's the first speed where 51 00:02:00,110 --> 00:02:01,625 you might expect turbulence, 52 00:02:01,625 --> 00:02:03,772 and therefore the first speed where you might expect 53 00:02:03,772 --> 00:02:06,436 Poiseuille's Law to not give you an accurate 54 00:02:06,436 --> 00:00:00,000 description of the flow of the fluid.