Isentropic Flow Calculator — Compressible Flow Relations

Formula

How this is calculated

Isentropic flow is an idealized model of compressible gas flow in which no heat is exchanged and entropy is constant — equivalently, the flow is reversible and adiabatic. This applies well to flow through nozzles and diffusers away from shocks and boundary layers. The governing equations link the local static conditions (T, P, ρ) to the stagnation (total) conditions (T₀, P₀, ρ₀) that would exist if the flow were decelerated to rest isentropically.

The stagnation temperature ratio T/T₀ = [1 + (γ−1)/2 · M²]⁻¹ follows from the adiabatic energy equation, where γ is the ratio of specific heats (cp/cv). For air at room temperature γ ≈ 1.4; it decreases slightly at high temperature. The pressure and density ratios follow from the isentropic relations for an ideal gas. The area ratio A/A* gives the cross-sectional area relative to the throat (A*) required for a particular Mach number in a nozzle — it equals 1 at M = 1 and increases toward both 0 and ∞ as M moves away from 1.

For supersonic flow (M > 1), the Mach angle μ = arcsin(1/M) is the half-angle of the Mach cone formed by small disturbances. The Prandtl-Meyer angle ν is the total turning angle through which a supersonic flow can be expanded from M = 1 to the given Mach number around a convex corner. These relations assume a calorically perfect gas (constant γ) and inviscid flow; real-gas effects and viscosity become significant at very high Mach numbers or temperatures.