- #1

orochimaru

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## Homework Statement

For the case of a strong shock propagating into a gas with [tex]\gamma=7/5[/tex] What is the ratio [tex]\rho2/\rho1[/tex]

## Homework Equations

[tex]\rho\ u=constant[/tex]

[tex]P+ \rho\ u^2=constant[/tex]

[tex]\frac{1}{2} u+ \frac{\gamma }{\gamma -1}\frac{\ P}{\rho} = constant [/tex]

## The Attempt at a Solution

I can use the 3 equations in this form to get [tex]\rho2/\rho1=6[/tex] but my problem is how do I arrive at the 3rd equation in the given form

we were given equation 3 in the form [tex]\frac{1}{2} u+ \frac{5}{2}\frac{\ P}{\rho} = constant [/tex] but this is only valid for [tex]\gamma=\frac{5}{3}[/tex]

I would like some advice on how to prove the adaption of equation 3 for different values of [tex]\gamma[/tex]

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