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.

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.

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.