Hava Laboratory Tools

Compressible Flow Calculator

Interactive gas-dynamics relations for course work and preliminary analysis. This version includes perfect-gas relations and reacting-air equilibrium species concentrations for high-temperature estimates.

Isentropic Flow Relations

Perfect gas

Gamma, γ Input Mach number T/T₀ p/p₀ ρ/ρ₀ A/A* subsonic A/A* supersonic Mach angle, deg. Prandtl-Meyer angle, deg. Value

Speed of Sound

a = sqrt(γRT)

Gas Air CO₂ Argon N₂ O₂ Helium Custom Gamma, γ R, J/(kg K) MW, kg/kmol T, K

Normal Shock Relations

Perfect gas

Non Dimensional Analysis

Gamma, γ Input M₁ M₂ p₂/p₁ ρ₂/ρ₁ T₂/T₁ p₀₂/p₀₁ p₁/p₀₂ Value

Dimensional Analysis

M₁ Gamma, γ p₁, Pa T₁, K

Reacting Normal Shock

Hansen equilibrium

M₁ T₁, K p₁, Pa N₂ (X) O₂(X)

Oblique Shock Relations

Perfect gas θ-β-M

Non Dimensional Analysis

Gamma, γ M₁ θ (turn angle), deg.

Dimensional Analysis

Gamma, γ M₁ p₁, Pa T₁, K θ (turn angle), deg.

Conical Shock Relations

Perfect gas Taylor-Maccoll

Gamma, γ M₁ Cone half-angle, deg.

Reacting Oblique Shock

Hansen equilibrium

M₁ T₁, K p₁, Pa θ (turn angle), deg. N₂ (X) O₂(X)

Reacting Cone Shock

Hansen equilibrium Taylor-Maccoll

M₁ T₁, K p₁, Pa Cone half-angle, deg. N₂ (X) O₂(X)

Reacting Air Species

Hansen equilibrium

T, K p, Pa N₂ (X) O₂(X)

Species are reported as mole fraction (X), mass fraction (Y), and mol/m³.
X is mole fraction, Y is mass fraction, and Z is the reacting-air compressibility factor.

Special thanks to Prof. William Devenport and the VT Compressible Aerodynamics Calculator for serving as a source of inspiration for this calculator and for Ozgur Tumuklu’s personal and classroom use over the years in perfect-gas calculations.
For the reacting air model, O. Tumuklu acknowledges the contributions of C. Frederick Hansen, whose algorithm was defined in the NASA TR R-50 technical report, and Semih Olcmen’s group for their recent publication: Axioms paper.