Choked Flow Calculator

Maximum mass flow rate through a sonic (M = 1) throat. Computes ṁ, critical throat conditions T*, P*, ρ*, and throat velocity V*.

Compressible Flow · Choked Flow

Gas presets — click to fill γ and R

Inputs

Total (stagnation) pressure P₀ (kPa)

Total (stagnation) temperature T₀ (K)

T₀ = 300.00 K

Throat area A* (cm²)

Specific heat ratio γ (dimensionless)

c_p/c_v — use gas presets above

Specific gas constant R (J/(kg·K))

R = Rᵤ/M — 287.05 for air, 2077 for helium

Theory

Choked mass flow rate:

ṁ* = A* × P₀ × Γ / √(R·T₀)

Γ = √γ × (2/(γ+1))^{(γ+1)/(2(γ−1))} [flow coefficient, for air: Γ ≈ 0.6847]

Critical throat conditions at M = 1:

T* = T₀ × 2/(γ+1) [for air: T* = 0.833 T₀]

P* = P₀ × (2/(γ+1))^γ/(γ−1) [for air: P* = 0.528 P₀]

ρ* = P* / (R·T*) [for air: ρ* = 0.634 ρ₀]

V* = √(γ·R·T*) [speed of sound at throat]

Where:

P₀ = stagnation pressure [Pa] — upstream total pressure
T₀ = stagnation temperature [K] — upstream total temperature
A* = throat area where M = 1 [m²]
γ = c_p/c_v — specific heat ratio
R = R_u/M — specific gas constant [J/(kg·K)]
ṁ* scales with P₀ and 1/√T₀ — doubling P₀ doubles ṁ*

Critical pressure ratio for choking:

For a converging nozzle, choking occurs when P_back/P₀ ≤ P*/P₀ = (2/(γ+1))^γ/(γ−1). For air this is 0.528 — once back pressure drops below 52.8% of upstream total pressure, the nozzle is choked and further reduction cannot increase ṁ.

Flow coefficient Γ for common gases:

Gas	γ	R [J/(kg·K)]	Γ	P*/P₀	T*/T₀
Air	1.400	287.05	0.6847	0.5283	0.8333
Helium	1.667	2077.1	0.7262	0.4870	0.7500
Hydrogen	1.405	4124.2	0.6862	0.5267	0.8296
CO₂	1.289	188.92	0.6517	0.5457	0.8429
Argon	1.667	208.13	0.7262	0.4870	0.7500