๐จ Compressible Fanno Flow with Friction
Model adiabatic compressible duct flow with friction: exit Mach (M2), choking length (Lmax), static and total pressure losses, and temperature variations.
โก Fortran 90 Engine
Double Precision (IEEE 754)
โ ISO / ASME Validated
Cfd
๐ Solver Telemetry
โ ACTIVE
๐๏ธ Views
35
โก Solves
30
๐พ Downloads
322
๐ฆ Fortran Code
4.4 KB
๐
Released
Jun 2026
โฑ๏ธ Latency
< 1 ms
๐ก
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๐จ Adiabatic Duct Flow Acceleration & Sonic Choking Limit (M = 1.0)
Real-time visual simulation of Mach evolution, wall shear friction & static pressure gradient๐ Configuration & Presets
๐จ Compressed Air (M = 0.25)
๐จ Safety Relief (M = 0.55)
โก Supersonic Tunnel (M = 2.0)
๐ฅ Gas Pipeline (50 bar)
Fanno Line Formulations:
โข Choking Parameter: (4fL*/D) = (1โMยฒ)/(ฮณMยฒ) + [(ฮณ+1)/(2ฮณ)] ln[(ฮณ+1)Mยฒ / (2 + (ฮณโ1)Mยฒ)]
โข Max Choking Length: Lmax = (4fL*/D)โ ยท D / (4f) [m]
โข Stagnation Pressure Drop: Pโโ / Pโโ = (Pโ/Pโ*)โ / (Pโ/Pโ*)โ
โข Wall Friction drives subsonic flows toward M=1 and decelerates supersonic flows.
โข Choking Parameter: (4fL*/D) = (1โMยฒ)/(ฮณMยฒ) + [(ฮณ+1)/(2ฮณ)] ln[(ฮณ+1)Mยฒ / (2 + (ฮณโ1)Mยฒ)]
โข Max Choking Length: Lmax = (4fL*/D)โ ยท D / (4f) [m]
โข Stagnation Pressure Drop: Pโโ / Pโโ = (Pโ/Pโ*)โ / (Pโ/Pโ*)โ
โข Wall Friction drives subsonic flows toward M=1 and decelerates supersonic flows.
๐ Fanno Flow Results
Configure inputs and click Compute to view results.
๐ Calculation Methodology & Fanno Flow Standards
Fanno Line Thermodynamics
Adiabatic friction in a constant-area duct drives the flow toward maximum entropy, which always occurs at the sonic state ($M=1$):
4fL*/D = (1โMยฒ)/(ฮณMยฒ) + [(ฮณ+1)/(2ฮณ)] ln[(ฮณ+1)Mยฒ / (2 + (ฮณโ1)Mยฒ)]
Sonic Choking Phenomenon
If actual duct length $L \ge L_{max}$, the flow chokes at the exit ($M_2 = 1.0$), forcing an inlet pressure buildup and mass flow rate reduction.
Key Engineering Assumptions
- 1D steady adiabatic flow of ideal gas in constant cross-section duct.
- Uniform average Fanning friction factor $f$.
- Calorically perfect gas ($\gamma = 1.40$).