Checked 23 October 2026 (UTC). The laboratory contains original code and original canvas/SVG/MathML teaching visuals. No external artwork, textbook figure, source-code block or proprietary flow package is redistributed. References below support the model formulation and its limits; they are not empirical validation of this implementation.
| Source | URL | Used for / boundary |
|---|---|---|
| Kyle Niemeyer, Oregon State University, Gas Dynamics Notes: Flows with friction (Fanno flows) | https://kyleniemeyer.github.io/gas-dynamics-notes/compressible-flows/friction/ | University-author derivation of constant-area adiabatic flow, Darcy wall-shear convention, integrated friction exposure and sonic reference state. Equations were independently re-derived and coded. |
| Kyle Niemeyer, Oregon State University, Gas Dynamics Notes: Flows with heat transfer (Rayleigh flows) | https://kyleniemeyer.github.io/gas-dynamics-notes/compressible-flows/heat-transfer/ | Heat addition, momentum-flux conservation and sonic-reference ratios. Used as an equation cross-check, not a copied implementation. |
| NPTEL, Compressible Flow, Lecture 41: Fanno Line Flows | https://archive.nptel.ac.in/content/storage2/courses/112104118/lecture-41/41_2_fanno_line_flows.htm | The sonic endpoint and the need to revise the inlet when a requested length exceeds a fixed-inlet branch. |
| NPTEL, One Dimensional Compressible Flow, Lecture 11: Flow With Heat Addition: Rayleigh Flow | https://archive.nptel.ac.in/content/storage2/courses/112103021/module2/lec11/1.html | Control-volume interpretation, specific heat input and total-temperature change. |
| Alak Bandyopadhyay and Alok Majumdar, Alabama A&M University / NASA Marshall Space Flight Center, Modeling of Compressible Flow with Friction and Heat Transfer using GFSSP, TFAWS 2007, NASA document 20070036728 | https://ntrs.nasa.gov/citations/20070036728 | Context: analytical Fanno and Rayleigh solutions are useful code-verification cases. This lab does not run GFSSP and has not reproduced the paper's finite-volume or experimental comparisons. |
Equation cross-check cautions
The university Rayleigh webpage contains isolated displayed-equation and explanatory typographical inconsistencies. The present implementation was derived from rho u = constant, p + rho u^2 = constant, and q = cp delta T0, then checked with an independent velocity quadratic. Density is calculated from p/(RT), and cooling/heating is decided by total temperature, not total pressure. The source's heat-addition example separately rounds cp to 1000 J/(kg K); it was not imported as an exact numerical reference because this lab closes cp = gamma R/(gamma - 1).
Parameter provenance and scientific claims
The nominal inlet (200 kPa absolute, 300 K), duct diameter (0.15 m), length ratio and Darcy factor are explicitly illustrative teaching inputs. They are not measurements from an aircraft. Constant-air-property parameters are conventional ideal-gas teaching values; high-temperature warnings do not imply an empirically established accuracy band. Maximum temperature, choking and all curve outputs follow the declared perfect-gas equations.
No third-party lecture figure is reproduced in this chapter. The links to existing site material provide continuity with nozzle choking, normal shocks and engine-cycle teaching. Source pages remain with their original authors and licences. The site carries Prof. Kam K.H. Ng's requested copyright and co-design attribution for the newly authored material.
Retrieval limitations
The NPTEL course overview at https://archive.nptel.ac.in/courses/112/106/112106166/ returned 404 in this retrieval, and .../112103021/module2/lec16/1.html returned a server error. Neither is used as evidence. The specific lecture pages listed in the table were accessible.