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?