Stumbled upon this inground pool installed by the homeowner and the plumbing looks like a nightmare to me but I could be wrong .what do you think? It's a pool/spa combo

I tested a few local llms to see if they could be useful for my work with hydraulics/hydrodynamics.

The background was a question which I believe have no exact analytical solution, but that a fair approximation may exist. The motivation was that ChatGPTs chatinterface in pro-mode gave an answer that was clearly unsatisfying, so I wondered if some local llms could work better. Also I was not sure if my own solution was good, so wanted help/inspiration.

Prompt: Two large seas are connected through a narrow passage with width b. The first sea has a higher water level than the other. The sea floor has constant height. Water flows through the narrow passage from heigh to low water level. We assume that the first sea is so large and the width so small that the water level in the first and upstream sea is constant. The second and downstream sea is also large, but of finite size. The water level changes slowly. The flow is inviscid. What is the flow rate through the passage? How does the water level in the second sea change through time. The flow is subcritical.

Most of the tested llms ended on this approach:

1. Use Bernoullis equation to find the velocity in the passage
2. Say something on the cros section in the passage (many said something odd)
3. Calculate flux as velocity times cross section
4. Use flux to set up ODE and separate it.

The problem was usually (2). They knew that the cross section should be the passage width times something, but only few decided that the water level in the second sea was a good approximation.

Even with an odd answer in (2), most models did (3) and (4) well, but with a wrong cross section.

ChatGPT: Failed on step (2). Used some reference water level to find cross section, but this is an abitrary level so does not work.

Gemma 4 26b a4b: Got it right very fast. Winner

Qwen 3.6 35b a3b: Got it right, but slower

Qwen 3.8 27b: Got it right, but very slow

Ministral 3 3b: magically got it right extremely fast. Winner

Ministral 3 12b: Did not specify water level for cross section in (2), but got it right when asked to do so

LFM2.5-8B-A1B: Had problem already on (1)

ZAYA1-8B: Got lost

LFM2.5-20B-A2B: Had problems on (2). Also after some help

Gemma 4 e2b: Had problems on (2).

Conclusion: Small llms can be good for this kind of tasks, but we are still not at a point where the smallest MoEs can do it.

Question: do any of you have success applying small llms for this kind of applied physics problems?

La Relatividad y la cuántica no se la llevan , en la cuántica para que las ecuaciones no exploten crean parches los cuales sus fundamentos no estan comprobados , las matemáticas tienen un problema , el mismo problema que no une lo macro y lo micro , la TCC y Navier-Stokes PADECEN DEL MISMO SINTOMA , LO QUE ANTES ERA MISTISISMO HOY SE LE LLAMA POR OTRO NOMBRE Y AUN ASI NO SABEN QUE ES , el OBSERVADOR ALTERA LO OBSERVADO ??? JAJAJS LA VELOCIDAD DE LA LUZ NO ES EDTANDAR , AGUJEROS NEGROS Y TERMODINAMICA PURA ,

SI LOS SIMIENTOS SOBRE LOS QUE CONSTRUYERON EL EDIFICIO ESTAN INCOMPLETOS ,LAS PROBABILIDADES DE QUE SE CAIGA SON INFINITAS

I'm very sorry if this goes against the rules. There's a fine line between reverse-engineered software and piracy, especially since the code is brand new and it's not a copy as I understand. However, I've wanted to try this software for years, and it's unbelievably expensive in my local currency, so maybe I'll finally have the chance.

I am in college and my professor makes this subject seem easy. He is really good at explaining topics and derivations. How can I get to that level?

The problem is whenever I try a homework problem I get stuck. I try really hard to not look up answers to the point where my head starts to hurt. I love this subject but dammit it's really hard for me.

Here is what I have been doing:

I Read the textbook and things make sense as I read it. This helps me grasp the basics.

But whenever I try and jump into a problem my brain freezes. I get the answers wrong because I forgot to use an assumption of the many assumptions that exist. This is so frustrating. Or I forgot to apply one of the conservation laws.

I might just be too dumb for this but any advice is appreciated.

I came across this question while doing a fluid mechanics past paper. Do you think drawing the three graphs correctly would be enough to get full marks? or would you also include calculations since each question is worth 3 marks. I've already emailed my professor about this, but since it's the weekend, I probably won't get a response for a while so I thought I'd ask for some advice here.

A few weeks ago, I shared a post here looking at the physical telemetry behind OpenAI’s Lean 4 Navier-Stokes proof (showing that their forced blowup construction would vaporize liquid water at 0.7 nm and punch through Mach 0.3 before reaching the singularity).

The discussion in the comments was really eye-opening for me. Coming from computational modeling rather than fluid dynamics, several researchers here (special thanks to u/cowgod42, u/Cute_Presence_2861, and u/FreeAsABird491) pointed out the real question:

Navier-Stokes is already known to be an approximation that breaks at molecular scales. The real question is: can this massive AI formalization machinery (millions of lines of computer-checked Lean 4 math) actually be directed toward real fluid dynamics, or is it doomed to produce measure-zero mathematical curiosities?

Over the past weeks, we took that critique to heart and drafted a 4-stage roadmap to connect formal computer-checked mathematics with real continuum mechanics and quantum fluids:

1. Automated "Reality Gates" on formal proofs

Right now, proof assistants only check if the mathematical syntax is valid under pure axioms. They have no concept of physical units. We propose formalizing non-negotiable admissibility constraints:

- Knudsen Gate (Kn < 0.01): if enstrophy concentration forces length scales below the molecular mean free path (~0.3 nm in water), the proof assistant flags that the continuum assumption has broken down.

- Mach Gate (M < 0.3): if localized core velocity exceeds 0.3 c_s, incompressibility is marked invalid and acoustic shock coupling is required.

- Thermal Dissipation Gate: viscous shear heating cannot exceed the latent heat of vaporization without modeling a phase change into vapor or plasma.

1. Physical Regularization vs. Measure-Zero Forcing

The OpenAI construction relies on an exquisitely engineered external force with a Jacobian condition number of 10^28. At 300 K, ambient thermal noise (k_B T) destroys that state immediately.

Instead of looking for unconstrained point singularities, formal verification should focus on physically regularized families:

- Navier-Stokes-Voigt and Leray-alpha models that introduce a finite viscous cutoff length.

- Gross-Pitaevskii models in quantum fluids, where vorticity naturally regularizes into discrete vortex cores with healing length ξ = ħ / √(2mμ).

1. Pre-Singularity Trajectories & Turbulence Boundaries

As pointed out by CFD specialists in the last thread, knowing exactly where the continuum approximation terminates is what subgrid-scale turbulence models need. Formal proofs can be used to rigorously bound energy cascade rates right up to the cavitation boundary.

1. Direct Connection to Laboratory Quantum Fluids (Vortex Lattices)

In 2D quantum vortex dynamics, formal Lean 4 theorems (such as universal optimality of triangular lattices under completely monotone repulsions) directly describe real phenomena:

- Abrikosov vortex crystal ground states in rotating superfluid He-4 and BECs.

- Tkachenko wave propagation modes.

- Wigner crystallization of electrons on liquid helium.

We have compiled these derivations, along with reproducible Python scripts and a Rust/CVODE integrator, into an open draft for students on Zenodo.

I’m an independent citizen scientist (but with solid background from my initial academic study) and more an AI guy at work and still learning from folks in the field mostly udirng wekk-end...it was in FORTRAN at that time and on CRAY-1 ;-), so I’d love to ask:

If you could task an automated formal theorem prover with one real challenge in fluid dynamics (regularization bounds, turbulence scaling, or vortex stability), what would give you the most practical value?

(All source files, Lean definitions, and Zenodo DOI links are in the first comment below to keep the discussion clean. but I will repost if interested)

A textbook on the physics of quantum fluids taught through three instruments used together, written as a tribute to the experimental work of nstitut Néel, Grenoble.

(i) their inelastic neutron-scattering measurements — the roton-like collective mode of a monolayer of liquid helium-3 (Nature 483, 576 (2012)) and the dispersion relation of superfluid helium-4 with its thermodynamic consequences (Phys. Rev. B 103, 104516 (2021));

(ii) the Lean 4 library QuantumFluids, whose 37 modules and 310 theorems are catalogued in full in Appendix A and were audited for the book (every module compiles with no sorry and depends only on the axioms propext, Classical.choice and Quot.sound);

(iii) the rusty-SUNDIALS solver: CVODE and the projected Gross–Pitaevskii engine qf-pgpe.

If interested : https://zenodo.org/records/23272154 and for the github : https://github.com/xaviercallens/SocrateAI-Scientific-QuantumFluids and for the book https://github.com/xaviercallens/SocrateAI-Scientific-QuantumFluids/blob/master/book/quantum_fluids_book.pdf

En ese DOI Conseguirán La Respuesta , y La Prueba irrefutable es MEDIR EL TIEMPO DE TRANSITO DE LA PARTICULA

QUEDO ATENTO A DEBATIR

SI QUIEREN LA MECANICA DE LA INTERACCION , TAMBIEN ES PRECISA

SOLO TIENES QUE SABER LO QUE LA MISMA CIENCIA COMPROBO

EL VACIO NO ESTA VACIO 🕯💀

I’m an independent researcher (high school student) working on swim-cap hydrodynamics and the sphere drag crisis. I’ve put together a controlled computational comparison of a smooth sphere and a textured swim cap at competitive swimming speeds, using unsteady RANS simulations with the Langtry–Menter transition model in OpenFOAM. The method combines transition-model diagnostics with wake analysis, and the setup is checked through grid, time-step, and free-stream turbulence studies.

I’m looking to submit the preprint to arXiv ideally under the physics.flu-dyn category or physics.comp-ph or physics.class-ph, but since this is my first submission, I need an endorsement.

If you’re an arXiv endorser in physics.flu-dyn, physics.comp-ph, or physics.class-ph and would be willing to take a look (or point me to someone who might), I’d be super grateful. Happy to share the PDF privately.

Thanks for reading, and cheers to everyone who helps support solo researchers out there.

Feel free to DM me or reply here.

These actually seem like targets that are more likely to splash than some targets just inside the edge of the water. Personally, I’m always at 11:45, 1 inch in from the water's edge.

I have a question on an upcoming exam where I am asked to calculate the time required to empty a tank with a pump. I am given the dimensions of the tank, the capacity it is filled to and the pump rate. The question is posed to be answered simply using (Volume/Pump Rate) but I want to go above and beyond and use calculus to answer it. How would I go about this?