Discussion Overview
The discussion centers on determining how the shock wave angle (Beta) varies with changes in the Mach number while keeping the deflection angle (theta) constant. Participants explore the theta-beta-Mach relation and methods for solving the implicit equation involved.
Discussion Character
- Technical explanation
- Mathematical reasoning
- Debate/contested
Main Points Raised
- One participant presents the equation relating shock wave angle and deflection angle, expressing difficulty in solving for Beta.
- Another participant recalls an approximate relationship between Beta and theta for large Mach numbers, referencing a specific text, but notes it may not be applicable for the current problem.
- A third participant indicates that the graphical solutions available in their resources do not provide sufficient detail for higher Mach numbers.
- Some participants suggest using numerical methods, such as fsolve or Newton's method in Matlab, to tackle the implicit nature of the equation.
Areas of Agreement / Disagreement
Participants generally agree that the equation is implicit and that numerical methods may be necessary to solve it. However, there is no consensus on the best approach or the applicability of the referenced relationships for the specific scenario being discussed.
Contextual Notes
The discussion highlights the limitations of existing resources in providing detailed solutions for high Mach numbers and the challenges posed by the implicit nature of the equation.
Who May Find This Useful
This discussion may be useful for students and professionals in gas dynamics, particularly those interested in shock wave behavior and numerical methods for solving related equations.