- [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.