Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 314 / 4 / a

Table of contents
- Solution a

Solution

The shock speed is

V_{s} = \dot{R} = \frac{C}{3} t^{- 2/3} = \frac{R}{3 t} .

Apply the Strong-shock Rankine-Hugoniot conditions in the shock frame and transform the downstream velocity back to the ambient-medium frame. With the shock compression ratio

χ = \frac{γ + 1}{γ - 1},

the post-shock values are

ρ_{ps} = χ ρ_{0}, u_{ps} = \frac{2}{γ + 1} V_{s}, p_{ps} = \frac{2}{γ + 1} ρ_{0} V_{s}^{2} .

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version