💨 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.
⚡ Fortran 90 Engine
Double Precision (IEEE 754)
✓ ISO / ASME Validated
📊 Solver Telemetry
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👁️ Consultations
35
⚡ Calculs faits
30
💾 Téléchargements
195
📦 Code Fortran
4.4 KB
📅 Mise en service
Jun 2026
⏱️ Latence
< 1 ms
💨 Adiabatic Duct Flow Acceleration & Sonic Choking Limit (M = 1.0)
Real-time visual simulation of Mach evolution, wall shear friction & static pressure gradient📝 Configuration & Presets
💨 Compressed Air (M = 0.25)
🚨 Safety Relief (M = 0.55)
⚡ Supersonic Tunnel (M = 2.0)
🔥 Gas Pipeline (50 bar)
Fanno Line Formulations:
• Choking Parameter: (4fL*/D) = (1−M²)/(γM²) + [(γ+1)/(2γ)] ln[(γ+1)M² / (2 + (γ−1)M²)]
• Max Choking Length: Lmax = (4fL*/D)₁ · D / (4f) [m]
• Stagnation Pressure Drop: P₀₂ / P₀₁ = (P₀/P₀*)₂ / (P₀/P₀*)₁
• Wall Friction drives subsonic flows toward M=1 and decelerates supersonic flows.
• Choking Parameter: (4fL*/D) = (1−M²)/(γM²) + [(γ+1)/(2γ)] ln[(γ+1)M² / (2 + (γ−1)M²)]
• Max Choking Length: Lmax = (4fL*/D)₁ · D / (4f) [m]
• Stagnation Pressure Drop: P₀₂ / P₀₁ = (P₀/P₀*)₂ / (P₀/P₀*)₁
• Wall Friction drives subsonic flows toward M=1 and decelerates supersonic flows.
📊 Fanno Flow Results
📊 Output Summary
Exit Mach Number (M₂)
M₂ = 0.511
Choking Length: Lmax = 33.93 m | Duct: 30.0 m
✅ Unchoked Flow
Exit Static Pressure (P₂)
3.22 bar
Inlet P₁ = 6.70 bar
Exit Stagnation Pressure (P₀₂)
3.84 bar
Total Loss: 45.1 %
Exit Static Temperature (T₂)
280.4 K
7.2 °C
Sonic Choking Limit (Lmax)
33.9 m
4fL*/D = 8.483
📈 Mach Number M(x) along Duct Length (m)
📉 Pressure Profile (P & P₀ in bar) along Duct
================================================================= THERMOFLUIDCALC — COMPRESSIBLE FANNO DUCT FLOW REPORT ================================================================= Case Title : Industrial Compressed Air Distribution Line Duct Geometry : Diam D = 80.0 mm, Length L = 30.00 m (Friction f = 0.0050) Inlet Conditions : M1 = 0.250, P01 = 7.00 bar, T01 = 295.0 K, gamma = 1.40 ----------------------------------------------------------------- EXIT MACH NUMBER (M2) : 0.5109 Maximum Choking Length Lmax: 33.93 meters Static Pressure P1 -> P2 : 6.702 bar -> 3.217 bar (Drop = 52.0%) Total Pressure P01 -> P02 : 7.000 bar -> 3.844 bar (Loss = 45.1%) Static Temperature T1 -> T2: 291.4 K -> 280.4 K (18.2 C -> 7.2 C) =================================================================
📘 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 = (1−M²)/(γM²) + [(γ+1)/(2γ)] ln[(γ+1)M² / (2 + (γ−1)M²)]
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 ($\gamma = 1.40$).