Isentropic Flow
Calculate isentropic flow temperature, pressure, and density ratios from Mach number. Get critical throat properties, Mach angle, and mass flow rate for gas dynamics.
About This Calculator
The Isentropic Flow Calculator computes the key properties of a compressible fluid undergoing an isentropic (constant entropy) process. This is the foundation of gas dynamics used in the design of jet engines, rocket nozzles, wind tunnels, turbines, and diffusers. Aerospace engineers, mechanical engineers, and physics students use isentropic flow relations to determine how pressure, temperature, and density change as a gas accelerates through a converging-diverging nozzle.
The calculator applies the standard isentropic flow equations: the temperature ratio T/T₀ = 1/(1+(γ-1)/2×M²), pressure ratio P/P₀ = (T/T₀)^(γ/(γ-1)), and density ratio ρ/ρ₀ = (T/T₀)^(1/(γ-1)). The area ratio A/A* is computed from the Mach number using the nozzle area-Mach relation. Critical throat conditions (M = 1) are also calculated including the critical pressure, temperature, density, and flow velocity. If a throat area is provided, the mass flow rate and cross-sectional area at the given Mach number are computed.
Regional Notes
Global (SI units): The calculator uses SI units throughout — pressure in bar (1 bar = 100,000 Pa), temperature in Kelvin, area in square meters, and velocity in meters per second. The specific gas constant for dry air R = 287.058 J/(kg·K) is used. For US customary units, convert pressure from psi to bar (1 psi ≈ 0.06895 bar) and temperature from °F to Kelvin (K = (°F + 459.67) × 5/9).
Frequently Asked Questions
What is isentropic flow?
Isentropic flow is a compressible flow process where entropy remains constant (no heat transfer and reversible). It forms the basis of gas dynamics used to design jet engines, rocket nozzles, turbines, and diffusers. The isentropic flow relations relate Mach number to pressure, temperature, and density ratios between stagnation, static, and critical (throat) conditions.
How do I calculate isentropic flow properties?
Enter the Mach number (M), specific heat ratio (γ), stagnation pressure (P₀), and stagnation temperature (T₀). The calculator uses standard isentropic flow equations: T/T₀ = 1/(1+(γ-1)/2×M²), P/P₀ = (T/T₀)^(γ/(γ-1)), and ρ/ρ₀ = (T/T₀)^(1/(γ-1)). Static conditions, critical throat conditions, flow velocity, speed of sound, and mass flow rate are computed automatically.
What is the specific heat ratio (γ) for air?
For dry air (a diatomic gas), the specific heat ratio γ = Cp/Cv is approximately 1.4 at standard conditions. Monatomic gases like helium have γ = 5/3 ≈ 1.667, while polyatomic gases like CO₂ have γ ≈ 4/3 ≈ 1.333. The calculator allows custom γ values for any gas.
What is the critical pressure ratio for isentropic flow?
The critical pressure ratio P*/P₀ at the throat (where M = 1) is given by (2/(γ+1))^(γ/(γ-1)). For γ = 1.4 (air), this ratio is approximately 0.528. This means the static pressure at the throat is about 52.8% of the stagnation pressure. The critical temperature ratio T*/T₀ = 2/(γ+1) ≈ 0.833 for air.
How does Mach number affect isentropic flow?
As Mach number increases, the static temperature, pressure, and density all decrease relative to stagnation conditions. At M = 2 with γ = 1.4, T/T₀ ≈ 0.556 (static temperature is 55.6% of stagnation), P/P₀ ≈ 0.128, and ρ/ρ₀ ≈ 0.230. The area ratio A/A* increases sharply for M > 1, requiring a divergent section after the throat for supersonic flow.
What is the Mach angle for supersonic flow?
The Mach angle μ = arcsin(1/M) represents the angle of the Mach cone formed by disturbances propagating in a supersonic flow. For M = 2, μ ≈ 30°. For M = 3, μ ≈ 19.5°. As Mach number increases, the Mach cone becomes narrower. The Mach angle is only defined for M ≥ 1 (sonic and supersonic flows).
How is mass flow rate calculated in isentropic flow?
The mass flow rate ṁ = ρ* × A* × c* where ρ* is the critical density, A* is the throat cross-sectional area, and c* = √(γRT*) is the critical flow velocity (speed of sound at the throat). The mass flow rate is maximized when the throat reaches sonic conditions (M = 1), which is known as choked flow.
What is the difference between static and stagnation conditions?
Stagnation conditions (P₀, T₀, ρ₀) represent the properties of the fluid when it is brought to rest isentropically (zero velocity). Static conditions (P, T, ρ) are the actual properties at a point in the flow where the fluid has velocity. The ratios P/P₀, T/T₀, and ρ/ρ₀ are always ≤ 1 and depend only on Mach number and specific heat ratio.