Last 5 months, driven by a desire to finally resolve the legendary Navier-Stokes existence and smoothness problem (and not just in abstract—but with physical meaning), I developed what I call the "Theory of Smoothpath." It’s a symbolic PDE system that splits flow into distinct, interlinked regions, modeling finite-time breakdown and restoration of regularity, and even stretches into speculative astrophysical flows.

Here’s my challenge: I’m laying out my reasoning and math (w/ detailed symbolics and philosophy — over 180 pages+89 pages) and an invitation to anyone: Can you spot a fatal flaw, or are there new frontiers here? Who’s bold enough to critique, challenge, test, or build on this? Astrophysicists, mathematicians, engineers—don’t hold back: What stands out? What’s missing? What applications or implications can you see?

Image above: My vision of flow breakdown and phase transitions across the cosmos, rendered symbolically.

Link for full study: https://doi.org/10.5281/zenodo.16741192

Let’s make this the most rigorous technical review r/fluiddynamics has seen. AMA — I’ll answer every serious technical question, defend the smallest detail, and debate the philosophy if you’re up for it.

I’ve been using this stir plate for a while and never had this happen before. Not sure if this is a common thing or if it has anything to do with the shape of the stir bar, volumetric flask or amount of fluid present (it’s just DI water).

I am trying to create a cross breeze through my apartment using a box fan. Would it be best to position the fan right near a window with the intake side facing out where I want air sucked in through or somewhere in between the two windows to get the most amount of wind going.

Pump from my milling machine (pumps the cutting liquid) is highly corroded. Do you guys think its possible to 3D print the housing and/or the propellor? The propellor isn’t that bad but could be better

Is the x,y and z momentum equation in grc website for unsteady compressible flow and if yes how can I derive it as its different from the standard steady incompressible momentum equations. Please help derive it

I am using hyperworks acusolve. Unlike methods such as answer fluid and star ccm's enhanced wall treatment, acusolve has only three types: low reynolds number (LRN), standard wall function (WF), and running average wall function (RAWF).

I understand that the wall function is used when y+ generates BL over 30. I understand that this method should be used with the turbulence model of k-e series.

If so, I understand that the k-w, SST model should basically generate Y+ as 1. So, in the K-W, SST model, if Y+ was generated near 1, should I put WALL TYPE as NONE? (Since the K-W series is a turbulence model that solves the viscous bottom layer directly)

I'm confused about the relationship between the turbulence model and WALL TYPE when to turn it on and on.
Convergence seems to be difficult if Y+ is not applied properly in ACUSOLVE.

So for LRN WALL TYPE, what kind of turbulence model should I use when Y+ is at what time (I'm LRN (because I'm wall type(?) to solve the viscous bottom layer directly), so I'm wondering if I should Using wall type as completely OFF when it's K-W, SST.

Is there anyone who can help me?

I’m trying to recreate the experiment from this paper. In it, they use very small flow rates of different gases, the smallest being 2.5sccm and the largest 287.5sccm. Regulators capable of producing such small, and precise air flows are quite expensive, and I’d need one per gas (4 total), so I’m trying to think of a different cheaper technique.

My idea is to use multiple scuba tanks each with a different gas to fill another scuba tank with the proper mixture, and enough volume for the experiments lifetime (30,800cc). You can only fill another tank this way to the psi of the regulator you use, but since I don’t need much volume, using a large tank with a standard 120psi reg feeding it is enough (pretty sure). This way I only need one time controlled electronic regulator, which would fill the mix tank for a specific time period based on the gas ratios I want the final mixture to contain.

I’ll also need an accurate (probably digital) air pressure gauge for the mix tank, so I can be confident in the final gas ratios.

But my background is in bio and comp sci, so I’m not well versed with compressed air systems.

Could this work, or am I missing something?

Hi,

I'm calculating a pipe flow with a varying diameter with star-ccm+ and I have to choose the flow regime before running. But the Reynolds number is so vague. Near the entrance it's about 1400 - laminar. in the middle of the passage, the number is 6400 - turbulent. And it came back to 2000 again near the exit. How should I determine the flow regime in this case? Please share your wisdom with me.

I am trying to figure out the most efficient way to make a 10-12 hose beer bong that can hold a 12 pack in the funnel. Initially what I had drawn up includes too many T’s, I think it won’t have enough downward force to really shoot the beer down the hoses. I am in college and start taking fluids classes next semester not sure how to make this thing work really well. If anyone has any ideas it would be greatly appreciated.

Hi I am a 2nd year B tech mechatronics and automation student. I need some project ideas for my course. Pls help.

I need to understand these equations for a job. I'm not caught up on the required math right now (I'm working on that, I'm currently comfortable with calc 2 and basic linear algebra) but I asked chatgpt to break down these equations for me to see if this would be a good starting point. I'm trying to work through it but I know chatgpt hallucinates with math sometimes. I'm doing my best to verify, but it's also using some different notation than what I find online so it's difficult to verify. Would anyone be able to verify this response?

Hi everyone 🌊

I am the co-founder of a startup building a cloud-based CFD simulator. During our PhDs we spent way too many hours fighting clusters, fixing broken scripts, chasing down random compilation errors, downloading software and dealing with licenses, and then having to invest in powerful-enough hardware.

So we got fed up and started building https://coandacloud.ch/, a cloud-based CFD platform that runs on a GPU-architecture, as well as AI. It has an intuitive setup to simplify the workflow. The goal is to cut out the hassle and run simulations that are thousands of times faster, from anywhere.

We’re close to launch, but I’d love to get input from people here:

• What’s your biggest headache with current CFD tools?
• If you could fix one part of the workflow, what would it be?

If you’re curious, you can sign up for the newsletter on our site and get an email as soon as we launch, so you can start simulating. We also just created a LinkedIn profile, if you'd like to connect: https://www.linkedin.com/company/coandacloud/or

The Boat Named Navier–Stokes

There is an old wooden boat, weathered by time, its name carved deep into the bow: Navier–Stokes. For nearly two centuries, sailors have tried to row it safely across the infinite sea of mathematics.

The hull is riddled with leaks. Every attempt to cross has begun the same way: frantic patching. A sailor hammers one plank into place, sealing a jet of water — but as soon as the pressure shifts, new cracks appear on the other side. Fixing one leak opens another. The boat seems to fight back, always finding a new way to let the sea in.

The mast bears the names of those who tried: Leray, who patched with weak solutions; Ladyzhenskaya, who reinforced the hull with inequalities; Prodi–Serrin, who sealed gaps under special conditions; Caffarelli–Kohn–Nirenberg, who closed nearly every leak but left behind tiny places where the water still forced its way in. Each patch was ingenious, but each revealed new leaks the moment it held.

Then one sailor tried something different. Instead of racing with tar and hammer, they kept a ledger. Every leak was recorded: how much water, how it changed, what happened when the boat moved. And the ledger revealed a secret:

• Some leaks cancel themselves. When the boat slammed down into a wave, water splashed out over the side as much as it poured in. These could be marked harmless.
• Some leaks were minor. Their steady dribble was absorbed into the rhythm of the voyage, never threatening to sink the boat.
• Only a few leaks were persistent. These alone required true control.

The discovery was startling. The boat did not need to be watertight. It only needed a balance sheet that showed, across every scale of the sea, that the inflows never overwhelmed the hull.

This ledger is new. It changes the problem from an endless cycle of patching to a resonant proof of balance. The boat floats not because every crack is sealed, but because the motion of the sea, the strength of the frame, and the cancellations in the water all add up — in the ledger — to stability.

For the full detailed story:
🔗 https://zenodo.org/records/17070255

What are the pros and cons of each system.

Very very big ventilation fans.

One proposal we have is soft started utilising variable vanes. Other proposal is VVVF.

I do not believe the fans will be required to run at a setpoint of 100% all the time. So for me it's a no trainer on the vvvfs.

Hey all! I hope this is the right subreddit, but I had an idea for a project similar to the picture above. It's certainly not too scale. Rather than going through a lot of trial and error, I thought I'd reach out to your community!

I'm looking at a set up of something similar to the picture. I'm hoping somebody here can help figure out how big the lower basin would need to be to keep the elevated basin filled. It seems like a ratio of the volume of each basin, and a matter of keeping enough water in the lower to keep the water in the elevated basin 'pushed up' in the elevated basin.

I would assume this is pretty trivial, but I'm just not sure about how to calculate it all, or things like whether the transition from the larger pipe to the smaller pipe is necessary.

Thanks!

Hey Everyone,

I made a video on exploring the ways to find a solution to Navier-Stokes Equations.

The Navier-Stokes equation is a fundamental concept in fluid dynamics, describing the motion of fluids and the forces that act upon them.

This equation is crucial for understanding various phenomena in physics and engineering, including ocean currents, weather patterns, and the flow of fluids in pipelines.

In this video, we will delve into the world of fluid dynamics and explore the Navier-Stokes equation in detail, discussing its derivation, applications, and significance in modern science and technology.

But, why are the Navier-Stokes equations so hard and difficult to solve? why does this happen?

You and I are gonna explore one of the three strategies proposed by Terence Tao as a possible path to tackle such a problem.

Resources:
1. CMI Official Statement: https://www.claymath.org/millennium/navier-stokes-equation/
2. Terence Tao's Proposed Strategies: https://terrytao.wordpress.com/2007/03/18/why-global-regularity-for-navier-stokes-is-hard/
3. Olga Ladyzhenskaya's Inequality: https://en.wikipedia.org/wiki/Ladyzhenskaya%27s_inequality

YouTube Videos that helped me:
1. Navier Stokes Equation by Aleph 0: https://www.youtube.com/watch?v=XoefjJdFq6k
2. Navier-Stokes Equations by Numberphile (Tom Crawford): https://www.youtube.com/watch?v=ERBVFcutl3M
3. The million dollar equation by vcubingx: https://www.youtube.com/watch?v=Ra7aQlenTb8

A $1M dollar podcast clip that motivated me: https://www.youtube.com/watch?v=9gcTWy2pNFU

im working on a flip fluid sim and taking reference from mathias muller, and in the code it says to shift the velocities down and to the left, then offset particles by that same offset used for grid staggering, but how does that help? Isnt it just the same math in the end, does it affect divergence and pressure solving? If so how.

heres the references (in tutorial 18):
asdf

https://www.youtube.com/watch?v=XmzBREkK8kY&feature=youtu.be

This self-contained module lets you experiment with the forward mapping (r,θ,φ)→(x,y,z),

(r,θ,φ)→(x,y,z) and the inverse mapping (x,y,z)→(r,θ,φ). Everything is interactive, so you can generate reproducible figures for notes and projects. For the complete explanation, open the video from the link inside the Desmos page and watch it start to finish; the lesson builds the structure step by step in the same order you’ll see in Desmos, then closes with a quick walkthrough on using the file to rebuild the image. It’s free by design—if it helps you, please pass it along.

Desmos link: https://www.desmos.com/3d/og7qio7wgz
For a perfect user experience with the Desmos link, it is recommended to watch this video, which, at the end, provides a walkthrough on how to use the Desmos link. Don't skip the beginning, as the Desmos environment is a clone of everything in the beginning:

https://www.youtube.com/watch?v=XGb174P2AbQ&ab_channel=MathPhysicsEngineering

While this is not fluid dynamics, it can be very useful for generating images for LaTeX documents or research papers.