Rayleigh Flow Calculator

Frictionless compressible duct flow with heat addition. Computes all Rayleigh property ratios, maximum stagnation temperature T₀*, and heat capacity before thermal choking.

Compressible Flow · Rayleigh

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

Inlet total temperature T₀₁ (K)

T₀₁ = 300.00 K

Specify exit Mach M₂ — computes T₀₂ and heat added q/c_p

Theory

Rayleigh flow relations (frictionless, constant-area, with heat):

T/T* = M²(γ+1)² / (1+γM²)²

P/P* = (γ+1) / (1+γM²)

ρ/ρ* = (1+γM²) / ((γ+1)M²) [= V*/V by continuity]

V/V* = (γ+1)M² / (1+γM²) [= ρ*/ρ]

T₀/T₀* = 2(γ+1)M²(1+(γ−1)/2·M²) / (1+γM²)²

P₀/P₀* = (P/P*) × [(2/(γ+1))·(1+(γ−1)/2·M²)]^γ/(γ−1)

Heat added and thermal choking:

T₀* = T₀₁ / (T₀/T₀*)|₁ [maximum T₀ at M = 1]

q/c_p = T₀₂ − T₀₁ = T₀* × (T₀/T₀*|₂ − T₀/T₀*|₁)

q_max/c_p = T₀* − T₀₁ [heat to reach choking]

Rayleigh flow table — air (γ = 1.4):

M	T₀/T₀*	P₀/P₀*	T/T*	P/P*	ρ/ρ*	V/V*
0.2	0.1736	1.2346	0.2066	2.273	11.00	0.0909
0.4	0.5290	1.1566	0.6151	1.961	3.188	0.3137
0.5	0.6914	1.1141	0.7901	1.778	2.250	0.4444
0.8	0.9639	1.0193	1.025	1.266	1.234	0.8101
1.0	1.0000	1.0000	1.000	1.000	1.000	1.000
1.5	0.9093	1.1215	0.7525	0.5783	0.7685	1.301
2.0	0.7934	1.5031	0.5289	0.3636	0.6875	1.455
3.0	0.6540	3.4245	0.2803	0.1765	0.630	1.588

Rayleigh flow models heat addition (combustion, resistive heating) in a constant-area frictionless duct. Heat drives both subsonic and supersonic flow toward M = 1 (thermal choke). T₀* is the maximum stagnation temperature the duct can sustain — adding more heat forces a new lower-Mach upstream state. P₀ decreases with heat addition (entropy increase), even for subsonic flow. Heat removal (cooling) moves M away from 1.