Name: Navier-Stokes Equations - Numberphile
Uploaded: 2020-03-27T18:39:32.000Z
Duration: 21 min 3 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

Dude, I think this is the first for number five on the ribs as well.

I'm going to say this is complete commitment, Thio.

The 1st 1 grand dot U equals, not on the 2nd 1 row.

Do you buy the T equals minor scratch P plus mu Grand Square.

You rode like roast mathematical equations.

Perhaps they look quite scary, but they're actually universal laws of physics.

So this is why these guys model every single fluid we have on Earth.

And I mean every fluid, the fluid in your head.

These guys tell you how it moves, how it behaves.

What's going on with that fluid so fluid?

I tend to think of it as something which changes shape to match the container.

Do you think about a glacier flowing down a mountain?

You watch those time lapse videos kind of looks like a river.

So ice in that sense behaves like a fluid.

It is changing its shape to fit the valley, the glacial valley, which is blowing it.

So this is just saying I have some blob of fluid.

It moves around, you know, with some velocity and maybe changes shape.

I would want the same massive fluid to still be there.

So this is just having goes that mass times Acceleration is force.

The top one tends to be the mass equation.

Conservation of mass or the in compress ability equation on the 2nd 1 is the momentum equation or the small one in the big one.

So we've got a component in the ex direction, a component in the UAE direction, a component in the set direction.

How fast the water in the river is flowing.

How fast The air around a Formula One car is going thinking about aerodynamics, how fast the custody is blowing off your spoon, any sort of movement of the fluid that the speed and that motion is going to be encapsulated by the velocity.

Now, Abla, we do love our Greek letters in maths so that the symbol NAMBLA is telling us what to do to our were lost to you.

It's a derivative telling us to differentiate our vector.

You in a particular way on the way it tells us to do that is we have our three components.

U V w What we're gonna do is we're just gonna do, do you buy the ex?

So differentiate the first bit of respect to its coordinate, which is exits the first corner of the X coordinate different shape, respect to act.

Then we're gonna add derivative of the 2nd 1 with respect to our second coordinate, do I?

And hopefully you've figured out the pattern we're then gonna add on DW by the set.

So this is the divergence off our velocity.

So it's saying, How does the X component of my velocity you?

How does that change as I move in the ex direction that how does V my y component change in the wind direction on?

How does the third component W in the said direction?

How does that change in the set direction?

So this is equal to zero equation number one.

So we're expecting force equals mass times acceleration.

And when we take a time derivative of velocity, that's exactly what acceleration is.

You increase your speed, you accelerated.

With respect to time or you decrease your speed, you decelerated.

So that's what the first term is going to describe.

You think of mass in this situation to be a density.

So it's how you know fresh water has a smaller density than salt water, so salt water is heavier in that sense.

But it's sort of mass and density are the same thing when it comes to fluids.

That's how you you sort of work with those things.

So row this Greek letter here, that is going to be our density.

That's our new to second law of the left hand side.

And then all of this sort of stuff going on over here.

So what we've got, we have the 1st 2 terms.

These guys are what we call the internal forces.

So this is the force between all of those fluid particles hitting into each other.

Crashing slide in grinding past one another.

There's internal force there, and then the 3rd 1 this just capital F.

This is a bit of a cheat because we just say this is our external force F So this could be gravity is the standard.

Then you would nor normally you just replace F g.

In most situations, if you want to go really fancy, you can put in electromagnetism, and we can sort of combine Naevia Stokes Maxwell's equations and get my Neto hydrodynamics, and that is how stars form and Galaxies form on that is just next level.

Italian Stokes was hard, like Neto, hydrodynamics like Try to model the growth of the sun.

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