Fanno Flow Calculator

Adiabatic compressible duct flow with wall friction. Computes the Fanno parameter fL*/D, maximum duct length to choking, and all property ratios relative to the sonic reference state.

Compressible Flow · Fanno

Gas presets — click to fill γ

Inputs

Inlet Mach number M₁ (dimensionless)

Specific heat ratio γ (dimensionless)

c_p/c_v — use gas presets above

Duct hydraulic diameter D (mm)

Darcy friction factor f (dimensionless)

Darcy f = 4 × Fanning f — use Moody chart value

Specify exit Mach M₂ — computes actual duct length from M₁ to M₂

Theory

Fanno flow relations (adiabatic, constant-area, with friction):

fL*/D = (1−M²)/(γM²) + (γ+1)/(2γ) × ln((γ+1)M²/(2+(γ−1)M²))

T/T* = (γ+1) / (2 + (γ−1)M²)

P/P* = (1/M) × √(T/T*)

ρ/ρ* = (1/M) × √(T*/T) [= V*/V by continuity]

P₀/P₀* = (1/M) × [(2/(γ+1)) × (1 + (γ−1)/2 M²)]^{(γ+1)/(2(γ−1))}

Where:

f = Darcy-Weisbach friction factor (= 4 × Fanning f)
L* = maximum duct length from given M to M = 1 (choking) [m]
D = hydraulic diameter [m]
T*, P*, ρ* = sonic (M = 1) reference conditions
T₀/T₀* = 1 always — Fanno is adiabatic, so T₀ is constant
P₀/P₀* ≥ 1 — total pressure always decreases toward the sonic point

Duct length between two Mach numbers:

fL/D = fL*/D|_M₁ − fL*/D|_M₂

This is always positive since fL*/D decreases as M approaches 1 from either side.

Fanno flow table — air (γ = 1.4):

M	fL*/D	T/T*	P/P*	ρ/ρ*	P₀/P₀*
0.2	14.533	1.190	5.455	4.583	2.964
0.4	2.308	1.163	2.696	2.318	1.590
0.6	0.491	1.119	1.763	1.576	1.188
0.8	0.072	1.065	1.289	1.211	1.038
1.0	0.000	1.000	1.000	1.000	1.000
1.5	0.136	0.828	0.606	0.732	1.176
2.0	0.305	0.667	0.408	0.612	1.688
3.0	0.522	0.429	0.218	0.509	4.235

Fanno flow is driven solely by wall friction in an adiabatic constant-area duct. Both subsonic and supersonic flows are driven toward M = 1 by friction — subsonic accelerates (static P drops), supersonic decelerates (static P rises), but total pressure P₀ always decreases. Exceeding L* causes choking (subsonic) or a normal shock (supersonic).