 Home

Codex Wiki

List of universities

University of Cambridge

Course of the University of Cambridge

Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2023

Paper 314

The shock speed is
$$
V_s=\dot R=\frac{C}{3}t^{-2/3}=\frac{R}{3t}.
$$
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>
$$
\chi=\frac{\gamma+1}{\gamma-1},
$$
the post-shock values are
$$
\boxed{
\rho_{\rm ps}=\chi\rho_0,
\qquad
u_{\rm ps}=\frac{2}{\gamma+1}V_s,
\qquad
p_{\rm ps}=\frac{2}{\gamma+1}\rho_0V_s^2}.
$$

Solution

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

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

 Ancestors (11)

 Discussion (0)

 Articles by others on the same topic (0)

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

 Ancestors (11)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)