PhysSandbox
Classical MechanicsWaves & SoundElectricity & MagnetismOptics & LightGravity & OrbitsLabs
🌙Astronomy & The Sky🌡️Thermodynamics🌍Biophysics, Fluids & Geoscience📐Math Visualization🔧Engineering🧪Chemistry

Related simulators

Continue with similar topics in this category — or all 48 in Engineering.

View category →
NewUniversity / research

Euler Column Buckling

Launch Simulator

Elastic column stability with P_cr = π²EI/(KL)²: choose end conditions, effective length factor K, first mode shape, and load ratio P/P_cr.

NewUniversity / research

Heat Exchanger ε-NTU

Launch Simulator

Parallel and counter-flow heat exchanger calculator: NTU = UA/Cmin, capacity ratio Cr, effectiveness, heat transfer, and outlet temperatures.

NewUniversity / research

Vibration Isolation Transmissibility

Launch Simulator

SDOF base-excitation isolator: transmissibility T(r,ζ), resonance peak, phase lag, and the isolation region above r = √2.

NewUniversity / research

Hertzian Contact Stress

Launch Simulator

Sphere or cylinder on a flat: effective modulus, contact patch, peak pressure p0, elastic approach, and subsurface shear estimate.

NewUniversity / research

Jeffcott Rotor Critical Speed

Launch Simulator

Single disk on a flexible shaft: ω_n = √(k/m), unbalance response, whirl orbit, phase lag, and critical-speed crossing.

NewUniversity / research

Torsional Drivetrain Resonance

Launch Simulator

Two-inertia torsional drivetrain: shaft stiffness and damping, twist angle, first natural mode, resonance response, and optional backlash deadzone.

PhysSandbox

Interactive physics, chemistry, and engineering simulators for students, teachers, and curious minds.

Physics

  • Classical Mechanics
  • Waves & Sound
  • Electricity & Magnetism

Science

  • Optics & Light
  • Gravity & Orbits
  • Astronomy & The Sky

More

  • Thermodynamics
  • Biophysics, Fluids & Geoscience
  • Math Visualization
  • Engineering
  • Chemistry

© 2026 PhysSandbox. Free interactive science simulators.

PrivacyTermsContact
Home/Engineering/de Laval Nozzle Mach Number

de Laval Nozzle Mach Number

Quasi-1D converging-diverging nozzle: area-Mach relation, choking pressure ratio, subsonic/supersonic branches, and a qualitative normal-shock mode.

Gas and geometry

1.4
3.2
8 bar
1.2 bar

Measured values

Back pressure ratio pb/p00.150
Critical ratio0.528
Choked?yes
Ideal exit Mach2.71
Ideal exit pressure0.34 bar
Throat pressure at M=14.23 bar

The model is quasi-1D and mostly isentropic. The shock position is a qualitative teaching overlay; real nozzles need viscous losses, separation, heat transfer, and unsteady shock-cell structure.

Live graphs

About this model

A de Laval nozzle accelerates compressible flow by first converging to a throat and then diverging. In quasi-one-dimensional isentropic theory the area-Mach relation links A/A* to a subsonic or supersonic Mach branch, while choking occurs once pb/p0 falls below the critical pressure ratio (2/(γ+1))^{γ/(γ−1)}. This simulator draws a converging-diverging nozzle, solves the area-Mach relation along the axis, and classifies the flow as unchoked subsonic, choked supersonic, or choked with a qualitative normal-shock overlay for overexpanded back pressures. It omits viscous loss, boundary-layer separation, heat transfer, chemistry, real-gas effects, and unsteady shock cells.

Who it's for: Compressible-flow, propulsion, turbomachinery, and gas-dynamics introductions.

Key terms

  • de Laval nozzle
  • Area-Mach relation
  • Choked flow
  • Normal shock
  • Pressure ratio

How it works

de Laval nozzle sketch using the isentropic area-Mach relation, choking criterion, pressure ratio, and a qualitative normal-shock mode for overexpanded flow.

Key equations

A/A* = (1/M)[(2/(γ+1))(1+(γ−1)M²/2)]^{(γ+1)/(2(γ−1))}
choking when pb/p0 <= (2/(γ+1))^{γ/(γ−1)}; p/p0=(1+(γ−1)M²/2)^{-γ/(γ−1)}

Frequently asked questions

Why are there two Mach numbers for the same area ratio?
The area-Mach relation has a subsonic branch and a supersonic branch joined at M = 1 in the throat. A converging-diverging nozzle can reach the supersonic branch only after choking.
Is the shock position exact?
No. It is a visual teaching cue tied to back pressure. A full shock-location calculation needs mass, momentum, entropy jump, and downstream matching, plus losses and separation.