💨 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

Cfd

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⚡ Solves 30

💾 Downloads 323 📦 Fortran Code 4.4 KB

📅 Released Jun 2026

⏱️ Latency < 1 ms

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💨 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)

📐 Duct Geometry & Friction

Duct Inner Diameter D [mm]:

Duct Length L [m]:

Fanning Friction Factor f: Commercial pipe: 0.004–0.008

Specific Heat Ratio γ:

🚀 Inlet Flow & Stagnation State

Inlet Mach Number M₁:

Inlet Total Pressure P₀₁ [bar]:

Inlet Total Temperature T₀₁ [K]:

Fanno Line Formulations:
• Choking Parameter: (4fL*/D) = (1−M²)/(γM²) + [(γ+1)/(2γ)] ln[(γ+1)M² / (2 + (γ−1)M²)]
• Max Choking Length: L_max = (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
💾 Fortran Source

Exit Mach Number (M₂)

M₂ = 1.000 (CHOKED)

Choking Length: L_max = 1.52 m | Duct: 5.0 m

⚡ Sonic Choke

Exit Static Pressure (P₂) 4.21 bar Inlet P₁ = 8.14 bar

Exit Stagnation Pressure (P₀₂) 7.97 bar Total Loss: 20.3 %

Exit Static Temperature (T₂) 258.3 K -14.8 °C

Sonic Choking Limit (L_max) 1.5 m 4fL*/D = 0.728

📈 Mach Number M(x) along Duct Length (m)

📉 Pressure Profile (P & P₀ in bar) along Duct

=================================================================
 THERMOFLUIDCALC — COMPRESSIBLE FANNO DUCT FLOW REPORT
=================================================================
Case Title                 : High-Speed Safety Relief Blowdown Exhaust Duct
Duct Geometry              : Diam D = 50.0 mm, Length L = 5.00 m (Friction f = 0.0060)
Inlet Conditions           : M1 = 0.550, P01 = 10.00 bar, T01 = 310.0 K, gamma = 1.40
-----------------------------------------------------------------
EXIT MACH NUMBER (M2)      : 1.0000 (SONIC CHOKE AT EXIT)
Maximum Choking Length Lmax: 1.52 meters
Static Pressure P1 -> P2   : 8.142 bar -> 4.210 bar (Drop = 48.3%)
Total Pressure P01 -> P02  : 10.000 bar -> 7.968 bar (Loss = 20.3%)
Static Temperature T1 -> T2: 292.3 K -> 258.3 K (19.2 C -> -14.8 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 ($\gamma = 1.40$).

ThermoFluidCalc Engineering Report