💨 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
● ACTIVE
👁️ 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 = 0.179
Choking Length: Lmax = 851.40 m | Duct: 500.0 m
✅ Unchoked Flow
Exit Static Pressure (P₂)
33.10 bar
Inlet P₁ = 49.50 bar
Exit Stagnation Pressure (P₀₂)
33.85 bar
Total Loss: 32.3 %
Exit Static Temperature (T₂)
283.2 K
10.0 °C
Sonic Choking Limit (Lmax)
851.4 m
4fL*/D = 45.408
📈 Mach Number M(x) along Duct Length (m)
📉 Pressure Profile (P & P₀ in bar) along Duct
================================================================= THERMOFLUIDCALC — COMPRESSIBLE FANNO DUCT FLOW REPORT ================================================================= Case Title : Long-Distance Natural Gas High-Pressure Pipeline Duct Geometry : Diam D = 300.0 mm, Length L = 500.00 m (Friction f = 0.0040) Inlet Conditions : M1 = 0.120, P01 = 50.00 bar, T01 = 285.0 K, gamma = 1.40 ----------------------------------------------------------------- EXIT MACH NUMBER (M2) : 0.1792 Maximum Choking Length Lmax: 851.40 meters Static Pressure P1 -> P2 : 49.499 bar -> 33.095 bar (Drop = 33.1%) Total Pressure P01 -> P02 : 50.000 bar -> 33.845 bar (Loss = 32.3%) Static Temperature T1 -> T2: 284.2 K -> 283.2 K (11.0 C -> 10.0 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 ($\gamma = 1.40$).