Isentropic Flow Calculator

Isentropic Compressible Flow

Isentropic flow describes an ideal, reversible, adiabatic process with no entropy change. In compressible fluid mechanics, temperature changes relate directly to pressure and density changes through the heat capacity ratio γ (gamma).

Formulas

$$\frac{P_2}{P_1} = \left(\frac{T_2}{T_1}\right)^{\frac{\gamma}{\gamma - 1}}$$ $$\frac{\rho_2}{\rho_1} = \left(\frac{T_2}{T_1}\right)^{\frac{1}{\gamma - 1}}$$

$P$ is pressure, $T$ is absolute temperature (Kelvin), $\rho$ is density, and $\gamma = C_p / C_v$ is the ratio of specific heats. For dry air, γ ≈ 1.4.

Applications

These relations apply to nozzles, diffusers, compressors, and shock-free flow regions. They assume ideal gas behavior and no heat transfer. Real flows with friction or heat exchange deviate from isentropic predictions.

Frequently Asked Questions

What value of γ should I use for air?

Use γ = 1.4 for dry air at typical temperatures. Values differ for other gases, for example, γ ≈ 1.67 for monatomic gases and γ ≈ 1.3 for steam.

Must temperature be in Kelvin?

Yes. The ratio T₂/T₁ requires absolute temperature. Using Celsius directly will give incorrect results.

What does isentropic mean?

Isentropic means constant entropy, the process is reversible and adiabatic with no heat exchange and no irreversible losses.

When does pressure ratio exceed temperature ratio?

For γ > 1, the exponent γ/(γ−1) is greater than 1, so a given temperature rise produces a proportionally larger pressure rise.

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Isentropic Compressible Flow

Formulas

Applications

Frequently Asked Questions

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