Shock Wave Calculator
Shock Wave Calculator computes post-shock properties (pressure, density, temperature) for a normal shock, with a pressure ratio plot.
Formulas Used in Shock Wave Calculator
The calculator computes properties across a normal shock using Rankine-Hugoniot relations:
Post-shock Mach Number:
\\[ M_2^2 = \frac{M_1^2 + \frac{2}{\gamma – 1}}{\frac{2\gamma}{\gamma – 1} M_1^2 – 1} \\]Pressure Ratio:
\\[ \frac{P_2}{P_1} = 1 + \frac{2\gamma}{\gamma + 1} (M_1^2 – 1) \\]Density Ratio:
\\[ \frac{\rho_2}{\rho_1} = \frac{(\gamma + 1) M_1^2}{(\gamma – 1) M_1^2 + 2} \\]Temperature Ratio:
\\[ \frac{T_2}{T_1} = \frac{P_2}{P_1} \cdot \frac{\rho_1}{\rho_2} \\]Sound Speed:
\\[ c_1 = \sqrt{\frac{\gamma P_1}{\rho_1}} \\]Where:
- \\(M_1, M_2\\): Pre- and post-shock Mach numbers
- \\(P_1, P_2\\): Pre- and post-shock pressures (Pa)
- \\(\rho_1, \rho_2\\): Pre- and post-shock densities (kg/m³)
- \\(T_1, T_2\\): Pre- and post-shock temperatures (K)
- \\(c_1\\): Pre-shock sound speed (m/s)
- \\(u_1 = M_1 c_1, u_2 = u_1 \frac{\rho_1}{\rho_2}\\): Pre- and post-shock velocities (m/s)
- \\(\gamma\\): Specific heat ratio
Example Calculation
Example: \\(M_1 = 2, P_1 = 10000 \, \text{Pa}, \rho_1 = 10 \, \text{kg/m}^3, \gamma = 1.4\\)
\\[
c_1 = \sqrt{\frac{1.4 \times 10000}{10}} \approx 37.4 \, \text{m/s}
\\]
\\[
\frac{P_2}{P_1} = 1 + \frac{2 \times 1.4}{1.4 + 1} (2^2 – 1) \approx 4.5
\\]
\\[
P_2 \approx 4.5 \times 10000 \approx 4.50 \times 10^4 \, \text{Pa}
\\]
\\[
\frac{\rho_2}{\rho_1} = \frac{(1.4 + 1) \times 4}{(1.4 – 1) \times 4 + 2} \approx 2.667
\\]
\\[
\rho_2 \approx 2.667 \times 10 \approx 26.667 \, \text{kg/m}^3
\\]