Compressible Nozzle Area Mach Simulator All tools
Interactive simulator

Compressible Nozzle Area Mach Simulator

Evaluate isentropic nozzle area ratio, static pressure ratio, required area, and velocity from Mach number and gas properties.

Parameters
Mach number M
-

Input Mach number M.

Heat-capacity ratio gamma
-

Input Heat-capacity ratio gamma.

Throat area A*
cm2

Input Throat area A*.

Total pressure P0
kPa

Input Total pressure P0.

Total temperature T0
K

Input Total temperature T0.

Results (exit conditions)Not choked
Throat Mach (=1 when choked)
Exit Mach
Area ratio A/A*
Required area A
Static pressure ratio P/P0
Temperature ratio T/T0
Exit velocity
Mass flow ṁ
Converging-diverging nozzle flow (real-time)
M, P, T profiles along the nozzle
Area-Mach relation
Theory & Key Formulas

Area-Mach relation (isentropic, M=1 at the throat):

$$\frac{A}{A^*}=\frac{1}{M}\left[\frac{2}{\gamma+1}\left(1+\frac{\gamma-1}{2}M^2\right)\right]^{\frac{\gamma+1}{2(\gamma-1)}}$$

Isentropic static pressure and temperature ratios:

$$\frac{P}{P_0}=\left(1+\frac{\gamma-1}{2}M^2\right)^{-\frac{\gamma}{\gamma-1}},\quad \frac{T}{T_0}=\left(1+\frac{\gamma-1}{2}M^2\right)^{-1}$$

Choked (M=1 at throat) maximum mass flow:

$$\dot{m}=A^{*}P_0\sqrt{\frac{\gamma}{R\,T_0}}\left(\frac{2}{\gamma+1}\right)^{\frac{\gamma+1}{2(\gamma-1)}}$$

For a given A/A* there are two solutions, subsonic and supersonic (e.g. A/A*=2 → M≈0.31 or M≈2.20). Flow accelerates subsonically in the converging section, reaches M=1 (choked) at the throat, and becomes supersonic in the diverging section. This simplified model assumes isentropic, one-dimensional flow and ignores shocks, boundary layers, and losses.

How to read it

Use the main plot to read the controlling trend, including break points that a single result card can hide.

Use the sensitivity view to find input combinations where margin collapses quickly.

For early design, focus on which input controls margin before trusting the absolute value.

Learn Compressible Nozzle Area Mach by dialogue

🙋
When reading Compressible Nozzle Area Mach, where should I look first? Moving Mach number M changes both the plots and the result cards.
🎓
Start with Area ratio A/A*, but do not treat the number as the whole answer. Use Area ratio versus Mach to confirm the assumed state, then read Pressure, temperature, and velocity ratios for the distribution or trend. Use the main plot to read the controlling trend, including break points that a single result card can hide.
🙋
I can see why Mach number M changes Area ratio A/A*. How should I judge the influence of Heat-capacity ratio gamma?
🎓
Move Heat-capacity ratio gamma in small steps and watch Required area A. That reveals which term is controlling the result. This simplified model captures the main relationship only. Boundary conditions, losses, nonlinear effects, and code-specific corrections still need separate checks. A single operating point is not enough; sweep the realistic scatter range.
🙋
What is Mach-gamma area map for? It feels like the ordinary curve already tells the story.
🎓
Mach-gamma area map is for finding boundaries where the condition becomes risky or margin collapses quickly. Use the sensitivity view to find input combinations where margin collapses quickly. In First-pass comparison of design options before review, the important question is often what happens after a small change, not only the nominal value.
🙋
So if Area ratio A/A* is within the target, can I accept the condition?
🎓
Treat this as a first-pass review. It helps with Narrowing controlling factors and worst-side conditions before detailed analysis and Teaching or explaining the equation, numbers, and visualization under the same inputs, but final decisions still need standards, measured data, detailed analysis, and vendor limits. For early design, focus on which input controls margin before trusting the absolute value.

Practical use

First-pass comparison of design options before review.

Narrowing controlling factors and worst-side conditions before detailed analysis.

Teaching or explaining the equation, numbers, and visualization under the same inputs.

FAQ

Start with Area ratio A/A* and Required area A. Then use Area ratio versus Mach to confirm the assumed state and Pressure, temperature, and velocity ratios to read distribution or bias. Use the main plot to read the controlling trend, including break points that a single result card can hide
Move Mach number M alone, then move Heat-capacity ratio gamma by a comparable amount and compare the change in Area ratio A/A*. Mach-gamma area map shows combinations where margin or performance changes quickly.
Use it for First-pass comparison of design options before review. Instead of trusting a single point, widen the input range and check whether Area ratio A/A* keeps enough margin before moving to detailed analysis.
This simplified model captures the main relationship only. Boundary conditions, losses, nonlinear effects, and code-specific corrections still need separate checks. Final decisions still require standards, measured data, detailed analysis, and vendor limits.

How to Use

  1. Enter Mach number (M) between 0.05 and 4 in the MVal field
  2. Select gas gamma value (γ): 1.40 for air, 1.33 for steam, 1.67 for helium
  3. Input throat area At and total stagnation pressure P0
  4. Move the slider or number input to obtain area ratio A/A*, required nozzle area A, static pressure ratio P/P0, and flow velocity (updates live)
  5. Review isentropic relations for subsonic (M<1) and supersonic (M>1) regimes

Worked Example

Air nozzle accelerating to M=2.5 with γ=1.40, throat area At=50 mm², P0=10 bar, T0=300 K. At M=2.5, the area ratio A/A*=2.637, meaning the nozzle exit requires 131.8 mm² (2.637 × 50). Static pressure ratio P/P0=0.0585, yielding static pressure 0.585 bar. Gas velocity reaches 579 m/s. For supersonic applications like rocket engines, proper throat dimensioning ensures choked flow at critical conditions.

Practical Notes

  1. Choke condition occurs at M=1 where A/A*=1.0; subsonic acceleration requires diverging inlet, supersonic requires diverging exit (de Laval nozzle)
  2. For air jets (γ=1.40) at low Mach (M=0.3), area ratio ≈1.064 and velocity ≈100 m/s; supersonic regimes show dramatic area expansion
  3. Verify gamma selection: combustion gases ~1.25, diatomic gases 1.40, monatomic gases 1.67
  4. Static pressure drops significantly in supersonic regions; use for vacuum generation or high-speed flow control in aerospace applications