What Is a Normal Shock Wave?
A normal shock wave is a very thin compression wave that stands perpendicular to a supersonic flow. Across the shock, the flow changes abruptly from supersonic to subsonic.
Static pressure, density, and temperature increase across a normal shock, while Mach number and total pressure decrease. Total temperature remains constant for an ideal adiabatic shock.
Normal Shock Relations
Downstream Mach Number
Pressure Ratio
Density Ratio
Temperature Ratio
Total Pressure Ratio
How to Use the Calculator
- Enter the upstream Mach number M₁. It must be greater than 1.
- Enter γ, the ratio of specific heats. For air, use approximately 1.4.
- Optionally enter upstream temperature and pressure to calculate actual downstream values.
- Use R = 287 J/kg·K for air unless you are using another gas.
- Click calculate to get post-shock Mach number, ratios, and velocities.
Example Calculation
For air with M₁ = 2 and γ = 1.4:
- The downstream Mach number becomes subsonic.
- Static pressure increases strongly.
- Density and temperature increase.
- Total pressure decreases because a shock is irreversible.
Common γ Values
| Gas Type | Typical γ |
|---|---|
| Air near room temperature | 1.4 |
| Diatomic gases, approximate | 1.4 |
| Monatomic gases | 1.67 |
| Combustion gases, approximate | 1.2 – 1.35 |
Important Assumptions
- The shock is normal to the flow direction.
- The gas behaves as a perfect gas.
- γ is constant across the shock.
- The flow is steady, one-dimensional, and adiabatic.
- There is no heat addition, no shaft work, and no chemical reaction.
- At very high temperatures, real-gas effects may become important.
Frequently Asked Questions
What is a shock wave?
A shock wave is a very thin region where pressure, density, temperature, and velocity change abruptly in a supersonic flow.
Why must M₁ be greater than 1?
A normal shock occurs only when the upstream flow is supersonic. The downstream flow becomes subsonic for a perfect-gas normal shock.
Does pressure increase across a normal shock?
Yes. Static pressure increases across a normal shock. Density and temperature also increase.
Does total pressure increase or decrease?
Total pressure decreases across a shock because the shock is irreversible and produces entropy.
Is total temperature constant across a normal shock?
For an ideal adiabatic normal shock with no work or heat transfer, total temperature remains constant.
Is this calculator for oblique shocks?
No. This calculator is for normal shocks. Oblique shocks require shock angle and flow deflection angle.
References
- Anderson — Modern Compressible Flow
- Liepmann & Roshko — Elements of Gasdynamics
- White — Fluid Mechanics
- Munson, Young, Okiishi — Fundamentals of Fluid Mechanics