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/sci/ - Science & Math

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15509032 No.15509032 [Reply] [Original]

Can someone explain navier stokes equations to me?
What do they say, why are they important and why are they hard to solve?

>> No.15509058

>>15509032
Ask chatgpt

>> No.15509169

>>15509032
Why do niggas want to know about end-game math, without mastering all the previous levels?

>> No.15509180

>>15509169
A crash course for fundamentals would be nice
MIT OCW is like 100+ hours of what could be covered in 10

>> No.15509183
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15509183

>>15509032
I believe you cannot solve them because there aren't enough equations for you to solve for the variables. You can however use PDEs to approximate (discretisation using numerical methods to solve PDEs) to come up with approximations (similar to how ANSYS and OPENFOAM works).

>t. Aerospace Engineer

>> No.15509321

>>15509032
>What do they say
its F=ma, but for fluids specifically
>why are they important
engineers need to model fluid flows for technical applications. they use numerical procedures to get an approximate solution (e.g. finite volume method).
mathematicians are interested in exact solutions (they probably have a reason although it might just be autism)
>and why are they hard to solve?
the solution requires solving a system of coupled, nonlinear partial differential equations. this is non-trivial in the general case

>> No.15510340

>>15509321
Got it, simpler than i thought. The numberphile video gave me jackshit

>> No.15510540 [DELETED] 

>>15509183
They are parabolic PDEs, there are analytical solutions in few special cases, i.e. Stokes flow, Poiseuille flow.

>> No.15510556

>>15510540
That's true, but usually "NS" refers to the NS equation with arbitrary coefficients, for which there is no known solution.

>> No.15510560

>>15509032
Think about how water moves when you're taking a bath. Sometimes it's calm, sometimes it moves quickly, and sometimes it swirls around in little circles. The Navier-Stokes equations are like a special set of rules that can help us understand and predict exactly how this water is going to move.

These rules are very important because they don't just apply to your bathwater, they can help us understand how fluids move in many different situations: like air flowing around an airplane, blood flowing in our bodies, or even how weather patterns move around the Earth!

However, these equations are quite tricky to solve. This is because fluids can move in really complex ways - they can twist and turn, speed up or slow down, and sometimes do all these things at the same time! Just like it might be hard to guess exactly how a group of ants might move around, it's also hard to guess exactly how a fluid like water or air might move. The Navier-Stokes equations help us make these guesses more accurate, but solving them can be like trying to solve a super challenging puzzle.

So, in a nutshell, the Navier-Stokes equations are important rules that help us understand and predict how fluids like water or air move, but they can be very challenging to solve because of the many complex ways that fluids can behave.

>> No.15510579

>>15509183
>cannot solve them because there aren't enough equations for you to solve for the variables
>But numerical approximation will magically change that.
>t. Aerospace Engineer
How the fuck did you get your job?

>> No.15510593

>>15509183
If they have multiple solutions, does that mean that they don't fully describe fluid motion, since theoretically we should be able to model it 100% accurately, discounting quantum effects which I assume don't matter at this scale?

>> No.15510594

>>15510560
underrated reply

>> No.15510595

>>15510594
This >>15510560 is literally a chatGPT post.

>> No.15510596

>>15510595
oh
lol

>> No.15510597

>>15510596
It wasn’t from me btw, I can just tell because when you ask for an explanation chatGPT always sounds like a r*dditor

>> No.15510662

>>15510595
exactly why its underrated

>> No.15510731

>>15509032
navier stokes will never accurately predict fluids when either a significant amount of time, or extremely detailed structures are involved.
Because real fluids are made of quanta (the particles making the fluid). A continuous model neglects this and the minute interactions between the quantia, so it will always diverge from reality. Fore fluids are chaotic systems. Seemingly insignificantly small deviations will lead to massive changes over time.

>> No.15510890

>>15510731
Lol quantum retard

>> No.15510949

I have a question about fluid dynamics

If you have a (constant area) pipe with a fluid that is moved by a pump
1) We have continuity equation that states the flow rate must be constant in every section in this pipe. Since the area of every pipe section is the same, that means the speed must be the same in every part of the pipe
Then there is friction, which my intuition would say slows down the fluid. But this wouldnt make sense, so it means all the extra energy would have to go to heat. Is that a correct understanding of the situation?

>> No.15511014

>>15510579
It's been literally years since I learnt about them, and the second you leave university and get a job you never need to do this. ANSYS already does all of this for you, as long as you know how turbulence models, boundary layers and the properties of the atmosphere work

>> No.15512122

>>15510949
Yes but most just ignore the heat and friction effects because I need to pass Fluid Dynamics somehow.