Let's talk about the Reynolds number.
The Reynolds number is typically seen as "Re".
What this is, is a dimensionless group that is defined for
fluid flowing in a pipe. We write that as the
density of that fluid times the velocity of the fluid
times the diameter of the pipe over the viscosity of the fluid.
And the nice thing about the Reynolds number is that it follows a pattern:
if it is less than 2100, we say that the flow is "laminar":
it follows nice streamlines, "nice" being fairly straight.
Whereas if the Reynolds number is greater than 2100,
we consider it to be "turbulent".
"Turbulent" is defined as a flow that is heavily agitated,
so we might just see it all over the place, maybe get some eddies,
or what you might see in a very fast stream of water.
So, just to do an exercise in unit conversion and to see what a dimensionless group is,
let's go ahead make up some values and figure out what the fluid flow for water
would be given certain properties.
So I'm totally making these up, but the density of water is going to be
in this case one gram per centimeter cubed.
Let's say that the velocity is
a hundred centimeters per second, so moving fairly fast.
The diameter of the pipe that we're going to look at,
let's say that it is a meter wide, so fairly large.
And then the viscosity of the water is about a centipoise (cP)
and a centipoise is equivalent to one times ten to the minus three kilogram per meter-second.
Alright, so given these values, go ahead and try to calculate what the reynolds number would be for this fluid.
Okay, there are two ways to approach this: one is we can make sure that all the units
we're using up front match and then we could just plug in numbers,
or we could set up one single dimensionless equation for the Reynolds number and go from there.
I prefer going the first route: it makes it easier
since we know that these are the only variables that we're going to use.
So if we start with grams per centimeters cubed,
we have to make sure everything else is in those terms.
We have centimeters per second here, and we have meters here,
so we need to convert this to a hundred centimeters.
Then last is the centipoise.
If we have 1 x 10^(-3) kilograms per meter-second,
we can convert to grams using that conversion factor.
And we can convert to centimeters using that conversion factor.
So this is going to give us 1 x 10^(-2) grams per centimeter-second.
So now all these units are the same, and we can go ahead and start to estimate our Reynolds number.
Okay, so if we plugin these values, again, the Reynolds number is equal to the
density times the velocity times the diameter over the viscosity,
then we'll see that 1 g/cm^3 times
our velocity of 100 cm/s,
times our diameter of 100 cm, this is going to be
divided by 1 x 10^(-2) grams, and then centimeter-second goes on top.
So if we were to see what the units of the remaining value is going to have,
grams on top cancels with grams on bottom,
the centimeters times centimeters times centimeters gets cancelled by the centimeters cubed,
and the seconds get cancelled.
So we're left with a unitless number, which in this case is going to be
100 times 100 times 100 or: 1 x 10^(6).
So in this case, we're going to say that
Reynolds number is greater than 2100, it is actually
1 million in this case, so
it's highly turbulent, which is what we'd expect with a velocity of
100 cm/s in a very large tube for water.
Hopefully this gave you some practice at unit conversions and you will see the Reynolds number in the future,
and a lot of other dimensionless groups.