Isentropic Flow Calculator
For air at Mach 2 the static pressure is 0.127805 of the stagnation pressure, T/T₀ = 0.5556 and A/A* = 1.6875.
Air 1.4; hot combustion gases about 1.3; helium 1.667.
0.127804525462951
Full answer, then cut to fewer decimals (not rounded):
- 0.127804525462951
- 0.12780452546295
- 0.1278045254629
- 0.127804525462
- 0.12780452546
- 0.1278045254
- 0.127804525
- 0.12780452
- 0.1278045
- 0.127804
- 0.12780
- 0.1278
- 0.127
- 0.12
- 0.1
- Temperature ratio T/T₀
- 0.5555555556
- Density ratio ρ/ρ₀
- 0.2300481458
- Area ratio A/A*
- 1.6875
- Mach angle μ
- 30 °
- Prandtl–Meyer angle ν
- 26.37976081 °
- p/p* (to sonic conditions)
- 0.2419249129
Step-by-step solution
- T₀/T = 1 + (γ − 1)/2 × M² = 1.8
- p₀/p = (T₀/T)^(γ/(γ−1)) = 7.824449067
- A/A* = (1/M)[(2/(γ+1))(1 + (γ−1)M²/2)]^((γ+1)/(2(γ−1))) = 1.6875
Isentropic Flow Formula
T₀/T = 1 + (γ − 1)M²/2, p₀/p = (T₀/T)^(γ/(γ−1))
A/A* = (1/M)[(2/(γ+1))(1 + (γ−1)M²/2)]^((γ+1)/(2(γ−1)))
Worked Example
Air (γ = 1.4) at Mach 2:
- T₀/T = 1 + (γ − 1)/2 × M² = 1.8
- p₀/p = (T₀/T)^(γ/(γ−1)) = 7.824449067
- A/A* = (1/M)[(2/(γ+1))(1 + (γ−1)M²/2)]^((γ+1)/(2(γ−1))) = 1.6875
Density ratio ρ/ρ₀: 0.2300481458 · Area ratio A/A*: 1.6875 · Mach angle μ: 30 ° · Prandtl–Meyer angle ν: 26.37976081 ° · p/p* (to sonic conditions): 0.2419249129
GATE tip
Stagnation temperature is constant through shocks and adiabatic ducts; stagnation pressure is constant only where the flow is isentropic. Use that to chain nozzle and shock calculations.
More Compressible Flow Calculators
-
Normal Shock Calculator
M₂² = (1 + (γ−1)M₁²/2) / (γM₁² − (γ−1)/2)
p₂/p₁ = 1 + 2γ(M₁² − 1)/(γ + 1); ρ₂/ρ₁ = (γ+1)M₁²/((γ−1)M₁² + 2)
Example: A normal shock in air at M₁ = 2: Downstream Mach number M₂ = 0.57735.
-
Prandtl-Meyer Expansion Calculator
ν(M) = √((γ+1)/(γ−1)) arctan √((γ−1)(M²−1)/(γ+1)) − arctan √(M² − 1)
expansion by θ: ν(M₂) = ν(M₁) + θ, isentropic
Example: Mach 2 air expanding round a 10° corner: Downstream Mach number M₂ = 2.38489.
-
Nozzle Flow Calculator
ṁ = A* p₀ √(γ/(RT₀)) (2/(γ+1))^((γ+1)/(2(γ−1)))
exit Mach from Aₑ/A* (supersonic branch); vₑ = Mₑ√(γRTₑ); F = ṁvₑ + (pₑ − pₐ)Aₑ
Example: A rocket nozzle with 7 MPa, 3000 K chamber, 100 cm² throat and expansion ratio 10, in vacuum: Mass flow rate ṁ = 44.3031 kg/s.
-
Oblique Shock Calculator
tan θ = 2 cot β (M₁² sin²β − 1) / (M₁²(γ + cos 2β) + 2)
normal component M₁ sin β obeys the normal-shock relations; M₂ = Mₙ₂ / sin(β − θ)
Example: Mach 2 flow turned by a 10° wedge: Shock wave angle β (weak) = 39.3139 °.
Frequently asked questions
Why are there two Mach numbers for one area ratio?
A converging-diverging duct can carry the same A/A* subsonically or supersonically; which one occurs depends on the back pressure.
What is the critical pressure ratio?
p*/p₀ = 0.5283 for air: below it a converging nozzle is choked and the throat is at Mach 1.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Isentropic Flow Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/isentropic-flow-calculator/
IEEE
Scientific Converters, "Isentropic Flow Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/isentropic-flow-calculator/