Turbulence at high velocities and Reynold's number
About this video
The narrator asks when smooth, laminar fluid flow breaks down into turbulent, chaotic flow. He introduces the Reynolds number, a unitless value that predicts the critical speed where turbulence starts. Once turbulence begins, Poiseuille's Law no longer describes the flow accurately, which matters for blood flow in the aorta, where the Reynolds number is around 2000.
You'll be able to
- explain what turns laminar flow into turbulent flow
- describe how the Reynolds number predicts the critical speed for turbulence
- explain why Poiseuille's Law fails once flow becomes turbulent
Key words
- Laminar flow
- Smooth fluid flow in layers that do not cross each other.
- Turbulence
- Chaotic fluid flow with vortices and eddy currents, caused by layers crossing each other.
- Reynolds number
- A unitless number that predicts the speed at which flow in a tube becomes turbulent.
- Viscosity
- A measure of how resistant a fluid is to flow, written as eta in the video.
- Poiseuille's Law
- A formula for the volume of laminar flow through a pipe per unit time, which only holds while the flow stays smooth.
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.
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