💨 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 = 0.511

Choking Length: L_max = 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 (L_max) 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 ($\gamma = 1.40$).

ThermoFluidCalc Engineering Report