Isentropic Flow Calculator

Isentropic flow is a reversible, adiabatic flow process in which entropy remains constant throughout. It occurs when a gas is compressed or expanded gradually without heat transfer or friction, making it an idealized model used widely in compressible aerodynamics and nozzle design. See also our Enthalpy Calculator (Hess's Law).

For air at standard conditions, γ = 1.4 is the standard value (diatomic gas). For monatomic gases like helium or argon, use γ ≈ 1.667. High-temperature flows may require lower values (around 1.2–1.3) to account for vibrational modes.

A/A* is the ratio of the local cross-sectional area to the throat area (where M = 1). It indicates how much the duct must expand or contract to achieve the given Mach number isentropically. A/A* is always ≥ 1 and equals 1 only at M = 1.

The Prandtl-Meyer angle (ν) represents the total turning angle through which a supersonic flow must expand (around a convex corner) to accelerate from M = 1 to the given Mach number. It is only defined for supersonic flow (M ≥ 1) and is zero at M = 1. You might also find our calculate Thermodynamics (Gibbs Free Energy) Gibbs Free Energy (ΔG) useful.

The Mach angle (μ) is the half-angle of the Mach cone formed by a disturbance moving at supersonic speed, defined as μ = arcsin(1/M). It only has physical meaning for supersonic flows (M > 1). At M = 1, the Mach angle is 90°, meaning the wave is perpendicular to the flow.

p₀/p and T₀/T relate stagnation (total) conditions to static conditions at a given Mach number. Engineers use these to find local static pressure or temperature in a flow given known stagnation conditions — for example, to design nozzles, inlets, or analyze wind tunnel test sections.

Yes. The isentropic relations apply to both subsonic (M < 1) and supersonic (M > 1) flows. For subsonic cases, the Mach angle and Prandtl-Meyer angle are not physically meaningful and are reported as N/A, but the pressure, temperature, density, and area ratios are fully valid.

This calculator assumes a perfect (calorically ideal) gas with constant specific heats, no heat transfer (adiabatic), no friction (inviscid), and a reversible process. Real flows deviate from these ideals, especially at high temperatures, near walls, or in the presence of shocks.