# rect_duct

Family 16: laminar flow in a straight rectangular duct (OpenFOAM, the whole duct: flow cases have no symmetry role).

The pressure-drop coefficient f Re (Fanning), read from the drop between the two ends. Exact anchor at every point: the
series solution, fitted by Shah and London to 0.05 %: f Re = 24 (1 - 1.3553 a + 1.9467 a^2 - 1.7012 a^3 + 0.9564 a^4 -
0.2537 a^5) with a = short side / long side. The uniform inlet adds an entry drop of about 1.4 q; it is small in a duct
30 hydraulic diameters long at these Reynolds numbers, and it is left in (so the answer rises slightly with Re).

## Parameters (nondimensional)

| parameter | range |
|---|---|
| `aspect` | 1.0 - 5.0 |
| `Re` | 1.0 - 20.0 |

## Answers and their error bands

| answer | error band (median / 95 % / max) | similarity x2 / x4 | CalculiX (same mesh) |
|---|---|---|---|
| `fRe` | 11 % / 17 % / 17 % | max 0.034 % | max - |

## Checks

- points: 80 solved, 0 failed
- three-mesh studies: 16 (every 5th point); the band of each point is 1.25 x the largest standard-mesh error among its 3 nearest studies
- symmetry check (max): 0 %
- neighbour check: flagged 0, re-solved on a finer mesh 0, unresolved 0
- direction checks: fRe vs aspect ok (rho 0.985)

## Against hand theory

| ratio | median | 95 % | max |
|---|---|---|---|
| `fRe_over_exact` | 0.9623 | 0.9852 | 0.9931 |

## Columns of points.csv

parameters, the answers, `<answer>_band` (relative), the hand-theory ratios, `mirror_err`, `equilibrium_err` (where a single reaction exists), `<answer>_loo_err` / `_neighbour_flag` (leave-one-out prediction from all other points), `<answer>_recheck_diff` / `_flag_resolved` (finer re-solve of a flagged point), `has_gci` / `has_similarity` / `has_calculix`, `nodes`, `solve_s`, `studio` (version).

Solved with NovaSolver Studio through the same commands an AI client uses over MCP; the first section says which solver and mesh. The claim is verification (the equations are solved within the band), not validation against tests.

## License

This data is licensed under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/
Credit: NovaSolver, https://novasolver.jp/studio/verified/
Provided as is, without warranty. Design decisions remain the user's responsibility.