VARIABLE γ · MACH NUMBER · AREA RATIO · FLOW PROPERTIES
📊 Isentropic Flow Calculator
Full isentropic relations for any Mach number and any γ. Includes PM function and Mach angle.
▸ Isentropic Flow Results
📋 Isentropic Flow Table — Custom γ
Enter any γ (e.g. 1.4 for air, 1.3 for combustion gas, 1.67 for monatomic). Set Mach range and step size.
SHOCK WAVE CHARTS
θ-β-M · NORMAL SHOCK PROPERTIES · PRANDTL-MEYER · TOTAL PRESSURE
📉 Interactive Shock Diagrams
All charts computed for γ=1.4. Switch tabs to explore different diagrams.
θ-β-M diagram: each curve = one upstream Mach number. X = shock wave angle β, Y = deflection angle θ. Peak of curve = θ_max (detachment point). Dashed white = sonic line M₂=1 separating weak/strong shock solutions. Highlighted curve (white/bold) = selected M₁.
Normal shock ratios vs M₁ (γ=1.4). P₀₂/P₀₁ drop = entropy increase. M₂ asymptotes to √((γ-1)/2γ) ≈ 0.378.
M₂ vs M₁
P₂/P₁ vs M₁
T₂/T₁ and ρ₂/ρ₁ vs M₁
Total Pressure Recovery P₀₂/P₀₁ vs M₁
PM function ν(M) = turning angle to accelerate isentropically from M=1 to M. Max ν=130.45° for γ=1.4. Mach angle μ = arcsin(1/M).
PM Function ν(M) vs Mach
Mach Angle μ(M) vs Mach
P₂/P₁ and T₂/T₁ through Expansion Fan starting from M₁=2.0
Total pressure recovery P₀₂/P₀₁: normal shock vs oblique shocks at θ=5°,10°,15°,20°. Oblique shocks recover far more total pressure — the fundamental reason supersonic inlets use multiple oblique shocks.