A shock wave is a sudden disturbance in a fluid that causes abrupt changes in pressure, temperature, and density. Understanding post-shock properties is crucial in supersonic aerodynamics, gas dynamics, and high-speed flow analysis.
Knowing the conditions after a shock wave allows engineers and scientists to:
The Mach number after the shock is:
M2 = √[( (γ - 1) M12 + 2 ) / ( 2 γ M12 - (γ - 1) )]
Post-shock pressure relative to pre-shock pressure:
p2/p1 = ( 2 γ M12 - (γ - 1) ) / ( γ + 1 )
Change in density across the shock:
ρ2/ρ1 = ( (γ + 1) M12 ) / ( (γ - 1) M12 + 2 )
Post-shock temperature relative to pre-shock:
T2/T1 = ( (γ - 1) M12 + 2 ) / ( γ + 1 )
Pre-shock and post-shock velocities are:
u1 = M1 * c1 , u2 = M2 * c2
The speed of sound before and after the shock is calculated as:
c1 = √( γ * R * T1 ), c2 = √( γ * R * T2 )
Use this calculator to quickly compute post-shock Mach number, pressure, density, temperature, and velocities.
Consider air (γ = 1.4) at Mach 2 entering a shock. Using the calculator, you can determine:
A shock wave is a sudden and nearly discontinuous change in fluid properties when the flow speed exceeds the speed of sound.
They are essential for predicting high-speed flow behavior, designing supersonic vehicles, and analyzing compressible fluid systems.
The calculator uses standard gas dynamics equations. For extremely high Mach numbers or unusual gases, specialized tools may be required.
For air, γ ≈ 1.4. Other gases may vary (e.g., 1.67 for monatomic gases, 1.3 for combustion gases).
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