Fresh OpenFOAM execution: 9 solves in 16.1 seconds. Numerical checks: passed.
Steady, incompressible, fully developed laminar flow between parallel plates. 2D flow; 100 mm reference width converts flow per width to total flow.
Fixed water properties: density 998.2 kg/m³; dynamic viscosity 0.001003 Pa·s.
For this fully developed parallel-plate model, Q = W h Ū and Δp = 12 μ L Q / (W h³). The Reynolds number uses hydraulic diameter 2h. The model omits sidewall and entrance losses.
Reference: Richard Fitzpatrick, Flow Between Parallel Plates, University of Texas at Austin. This is an analytical solution comparison, not comparison to a measured device.
| Gap mm | Analytical Pa | OpenFOAM Pa | Allowance Pa | Budget margin Pa | Decision |
|---|---|---|---|---|---|
| 1.5 | 178.3 | 178 | 0.348 | -138.3 | Review / exceeds |
| 2 | 75.22 | 75.08 | 0.147 | -35.22 | Review / exceeds |
| 2.5 | 38.52 | 38.44 | 0.0751 | 1.485 | Meets |
Recommend the smallest tested gap only if all numerical checks pass and its pressure drop plus the larger of analytical discrepancy or medium/fine difference stays below budget. This is a numerical allowance, not a total physical uncertainty bound.
The analytical comparison verifies this idealized flow calculation. Sidewalls, entrance effects, fittings, temperature variation and manufacturing tolerance require separate assessment for a physical channel.
| Gap mm | Grid | Cells | Iterations | Δp Pa | Reference error | Mass imbalance | Checks |
|---|---|---|---|---|---|---|---|
| 1.5 | coarse | 512 | 125 | 176.93 | 0.775% | 4.4e-11% | All passed |
| 1.5 | medium | 1152 | 182 | 177.69 | 0.346% | 1.04e-10% | All passed |
| 1.5 | fine | 2048 | 284 | 177.96 | 0.195% | 7.68e-11% | All passed |
| 2 | coarse | 512 | 112 | 74.642 | 0.775% | 1.3e-09% | All passed |
| 2 | medium | 1152 | 186 | 74.965 | 0.346% | 3.24e-10% | All passed |
| 2 | fine | 2048 | 289 | 75.078 | 0.195% | 7.28e-11% | All passed |
| 2.5 | coarse | 512 | 117 | 38.217 | 0.775% | 8e-11% | All passed |
| 2.5 | medium | 1152 | 188 | 38.382 | 0.346% | 1.48e-10% | All passed |
| 2.5 | fine | 2048 | 293 | 38.44 | 0.195% | 2.4e-11% | All passed |
Pass thresholds: reference error <2%; medium/fine pressure change <1%; flux imbalance <0.1%; velocity-profile L2 error <2%; final initial residuals ≤10⁻⁷; solver reports convergence; mesh passes checkMesh.
Pressure is fitted over the middle half of the channel and extrapolated to its length. Incompressible OpenFOAM pressure is multiplied by density to obtain Pa. Values are extracted from final p, U and phi fields. Residual histories, exact dictionaries, generated meshes and final fields are in the evidence ZIP.
Solver: OpenFOAM Foundation 10 / simpleFoam. Study ID: c285c4d248f1f2f8dc00ae43e01fae051e29f2c0f136250a.
Worker SHA-256: 964ea1a73bb0d6154c1af169e6b13ac81b3c9e6172e5e1740d6593c47d16cf51
Case generator SHA-256: 1d8649688ab223edfeda2aa880b3613f3108d9b6bc4b30bd18830ef0f6c38774.
The ZIP contains this report, result.json and sha256.json covering its case files. Download the report and evidence within 48 hours; use your browser's Print / Save as PDF for a PDF copy.