Inputs
All fields are SI units unless noted
Notes: static inputs P₁ and T₁ are absolute. Use Darcy friction factor f. Computation assumes constant area, adiabatic, perfect gas.
Results
| Quantity | Inlet (1) | Outlet (2) | Units |
|---|
Fanno parameter
4 f L / D = —
Max length to choking
L* from inlet = — m
Choking status
—
Example data
Use these inputs to sanity‑check. Click “Load example” above to populate the form.
| γ | R | P₁ (kPa) | T₁ (K) | M₁ | D (m) | f | L (m) | Mode |
|---|---|---|---|---|---|---|---|---|
| 1.40 | 287 | 200 | 300 | 0.30 | 0.10 | 0.020 | 2.00 | Given L → M₂ |
| 1.40 | 287 | 300 | 300 | 0.80 | 0.05 | 0.015 | — | Target M₂=0.95 → L |
| 1.66 | 2077 | 150 | 300 | 1.50 | 0.08 | 0.012 | — | Choking distance |
Formulas used
F(M) = (1 − M²)/(γ M²) + (γ+1)/(2γ) · ln( ((γ+1) M²)/(2 + (γ−1) M²) )
- Dimensionless friction length: 4 f L / D = F(M₁) − F(M₂). To choking from state 1: 4 f L* / D = F(M₁).
- Define B = 2 + (γ−1) M².
- Star‑state ratios (M* = 1): T/T* = (γ+1)/B, P/P* = (1/M)√((γ+1)/B), ρ/ρ* = (1/M)√(B/(γ+1)).
- Velocity: u = M √(γ R T). Mass flow: ṁ = ρ u A, with A = π D²/4.
- Static to stagnation: P₀ = P (1 + (γ−1)M²/2)^{γ/(γ−1)}, T₀ = T (1 + (γ−1)M²/2) (T₀ constant for adiabatic, no shaft work).
- Property ratios between 1 and 2 via star state: e.g., P₂/P₁ = (P₂/P*)/(P₁/P*), similarly for T and ρ.
How to use this calculator
- Select a workflow: given duct length to find outlet Mach, target outlet Mach to find required length, or choking distance check.
- Choose a gas preset or enter γ and R manually.
- Provide inlet static pressure, temperature, Mach number, diameter, and Darcy friction factor.
- Press Compute. The solver checks choking and finds a valid Mach on the correct branch (subsonic increases toward 1, supersonic decreases toward 1).
- Review property tables, Fanno parameter, and L* from the inlet. Use CSV/PDF buttons to export results.
FAQs
It is adiabatic compressible flow in a constant‑area duct where wall friction drives the state along a Fanno line toward Mach 1.
The Darcy friction factor f. If you have relative roughness and Reynolds number, compute f externally (e.g., Colebrook) and enter the value here.
If 4 f L / D exceeds F(M₁), the duct reaches Mach 1 before the exit. The tool reports the distance to choke and flags the case.
Total temperature stays constant (adiabatic, no work). Total pressure decreases along the duct because friction increases entropy.
This version assumes constant f and constant area. For varying f or area changes, segment the duct and apply the solver to each segment.
Use SI: P in kPa absolute, T in kelvin, D and L in meters, R in J/kg·K. The solver computes mass flow using these units.
Yes. For M₁ > 1, friction decelerates the flow toward 1. The solver selects the supersonic branch and enforces a valid bracket during root finding.