Isentropic Flow Calculator
Free calculate pressure, temperature, density, and area ratios from mach number for compressible flow.
Input Parameters
M < 1: subsonic, M = 1: sonic, M > 1: supersonic
1.4 for air, 1.67 for monatomic gases, 1.3 for some combustion products
Results
Enter Mach number to calculate
What is Isentropic Flow?
Isentropic flow is a thermodynamic process where a fluid flows without heat transfer (adiabatic) and without friction (reversible), resulting in constant entropy. This is an idealized condition used extensively in compressible flow analysis.
Isentropic flow relations connect the Mach number to various flow properties including pressure, temperature, density, and area ratios. These relationships are fundamental in analyzing nozzles, diffusers, jet engines, and supersonic aircraft.
The isentropic assumption is valid when flow is fast enough that heat transfer is negligible, and friction losses are small. Real flows approximate isentropic behavior in well-designed nozzles and diffusers.
Isentropic Flow Formulas
Pressure Ratio
Temperature Ratio
Density Ratio
Area Ratio
Note: Subscript 0 denotes stagnation (total) conditions. A* is the critical area at M=1.
How to Calculate
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1
Enter Mach number and specific heat ratio
M is the ratio of flow speed to speed of sound. γ is typically 1.4 for air.
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2
Calculate the common term
Compute [1 + (γ-1)M²/2] which appears in all ratio formulas.
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3
Apply formulas for each ratio
Use the appropriate exponent for pressure, temperature, density, and area ratios.
Practical Examples
Example 1: Mach 2.0 Air Flow
Calculate ratios for air (γ=1.4) at Mach 2.0.
Solution:
Term = 1 + (1.4-1)×2²/2 = 1.8
p/p₀ = 1.8^(-1.4/0.4) ≈ 0.128 (12.8%)
T/T₀ = 1.8^(-1) ≈ 0.556 (55.6%)
ρ/ρ₀ = 1.8^(-1/0.4) ≈ 0.230 (23.0%)
Example 2: Sonic Flow (M=1)
At sonic conditions, what are the ratios?
Solution:
At M=1, term = 1 + (γ-1)/2 = (γ+1)/2
For air (γ=1.4): p/p₀ = 0.528, T/T₀ = 0.833, ρ/ρ₀ = 0.634
These are critical ratios at the throat of a nozzle.
Applications
Aerospace
Designing nozzles, analyzing jet engines, understanding supersonic flight, and calculating thrust.
Propulsion
Rocket nozzle design, turbine analysis, and optimizing flow through propulsion systems.
Fluid Systems
Designing compressors, analyzing gas pipelines, and understanding high-speed flow behavior.
Education
Teaching compressible flow dynamics, thermodynamics, and gas dynamics in engineering courses.
Frequently Asked Questions
What does "isentropic" mean?
Isentropic means constant entropy - the flow is both adiabatic (no heat transfer) and reversible (no friction). This is an idealized condition that approximates real flows in well-designed systems.
What is the difference between static and stagnation properties?
Static properties (p, T, ρ) are measured moving with the flow. Stagnation properties (p₀, T₀, ρ₀) are what you'd measure if the flow were brought to rest isentropically - they represent total energy.
Why do ratios decrease as Mach number increases?
As flow accelerates, kinetic energy increases at the expense of pressure and temperature. At higher Mach numbers, more energy is in motion, so static pressure and temperature relative to stagnation values decrease.
What happens at the critical area (A*)?
A* is the area where M=1 (sonic condition). In a converging-diverging nozzle, the throat is the critical area. Flow can only reach M>1 downstream of the throat.
When is the isentropic assumption valid?
Isentropic flow is a good approximation when flow is fast (little time for heat transfer), friction is minimal (smooth surfaces), and there are no shocks. Real flows in nozzles and diffusers often approximate isentropic behavior.