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← Calculator · Formula review historyAudit date 2026-11-12 · audited solver version
Fanno is an adiabatic flow model, not an alternative friction-factor correlation. Both connected modes use Darcy friction. Crane 2010 mentions Fanno on p. 1-11, but its practical discharge method uses modified Darcy and net expansion factor Y. The app currently implements complete isothermal pipes and a separate Fanno pipe path; it does not implement Crane’s Y-chart discharge procedure.
No arithmetic defect was found in the checked pipe cases. Agreement with each model’s own equations is separate from agreement between models. The Y-method comparison below remains an open same-system validation item.
| App/reference | Thermal assumption | Current status |
|---|---|---|
| Legacy gas approximation | Constant T; mean density; neglects distributed acceleration | Matches simplified isothermal pipe algebra in checked scope |
| Complete isothermal | Constant T; distributed acceleration | Crane Eq. 1-27 algebra and independent reference check |
| Adiabatic / Fanno | No heat transfer; constant stagnation enthalpy | Own analytical and momentum/energy checks |
| Crane modified Darcy + Y | Specified discharge convention | Audit-only published-example arithmetic; no production Y solver |
Same inlet static pressure/temperature, mass flow, Darcy factor, length and bore. These are thermal-model comparisons, not interchangeable answers or pass/fail tests against one another. Pressure is absolute.
| Case | Inlet M | fD L/D | Isothermal outlet kPa | Fanno outlet kPa | Fanno outlet K |
|---|---|---|---|---|---|
| Low Mach | 0.02 | 20.0000 | 497.191 | 497.191 | 300.000 |
| Moderate Mach | 0.20 | 1.0000 | 484.915 | 484.934 | 299.851 |
| High Mach | 0.60 | 0.1500 | 455.863 | 463.277 | 296.949 |
| Near isothermal limit | 0.30 | 4.6218 | 242.590 | 262.528 | 287.421 |
| Different model limits | 0.30 | 5.0821 | Limit exceeded | 207.805 | 278.465 |
| Gamma 1.3 | 0.35 | 0.5000 | 475.491 | 475.706 | 299.445 |
| Gamma 1.67 | 0.35 | 0.5000 | 466.097 | 467.003 | 298.353 |
The built-in 60,000 lb/hr, 90 ft example ends at 55.2431 psig / 80°F isothermally and 56.7268 psig / 66.9196°F with Fanno. The operating Darcy factors match.
Published rounded arithmetic gives 3,761.904 SCFH versus the printed 3,762 SCFH. Treating the given inlet state as pipe-static and matching the unchoked pipe outlet to ambient gives about 4,062.4 SCFH by Fanno, on the book’s rounded 520°R standard basis.
The common-SI mass-flow difference is 8.022%. Crane includes exit K = 1; the pipe-only Fanno model contains distributed fD L/D. Source static-versus-stagnation energy conventions also affect the result. Lumping the exit into duct friction or reinterpreting the source changes the answer, but neither diagnostic establishes the correct same-system mapping. The difference is recorded as unresolved, not accepted as chart accuracy or fixed by tuning coefficients.
Standard volume also needs care: Crane uses nominal 60°F, whereas this app uses 68°F. At the same standard pressure, that exact temperature-basis difference is 1.5394%. Mass flow is the primary comparison.
Darcy convention checked; no factor-of-four error found. Serghides was checked against iterated Colebrook at 25 turbulent operating points; maximum relative discrepancy was 0.003090%. Independent analytical and direct momentum/energy checks cover the controlled cases. Existing conservation, boundary, material and scope tests remain active.
The source for Crane example/page details is a public transcription of the 2010 printing, with its scope language also checked against the user-linked Scribd preview. Original page images and the Y-chart reading have not been visually confirmed in this audit. A production Crane-Y implementation, experimental validation, and browser interaction verification remain outside this completed audit scope. No production solver coefficients, pipe data or application limits were changed.
User-linked Crane 2010 preview · 2010 transcription · Publisher errata · Niemeyer Fanno derivation · MathWorks analytical benchmark