Discover the temperature ratio across a shock wave with our precise calculator. Utilizing the Rankine-Hugoniot relations, this tool is vital for engineers and physicists analyzing compressible flow and aerodynamic phenomena. Quickly determine critical parameters for supersonic aircraft design and high-speed fluid dynamics applications.
Formula:
The temperature ratio (T₂/T₁) across a normal shock wave can be calculated using the following Rankine-Hugoniot relation for a perfect gas:
T₂/T₁ = [1 + (2γ/(γ+1)) * (M₁² - 1)] * [(2 + (γ-1)M₁²)/( (γ+1)M₁² )]
- T₂: Static temperature downstream of the shock
- T₁: Static temperature upstream of the shock
- γ (gamma): Ratio of specific heats (adiabatic index)
- M₁: Upstream Mach number (must be > 1 for a shock wave to occur)
This formula requires the upstream Mach number and the ratio of specific heats (γ).