J shock in a gas for gamma = 7/5

In summary, the conversation is discussing the Rankine-Hugoniot condition for energy flow in a gas with a given value of \gamma=7/5. The question is how to arrive at the third equation, \frac{1}{2} u+ \frac{\gamma }{\gamma -1}\frac{\ P}{\rho} = constant, for this specific value of \gamma. The suggestion is to simply plug in the value of \gamma into the equation, but the asker is seeking advice on how to prove this adaptation.
  • #1
orochimaru
8
0

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]
 
Last edited:
Physics news on Phys.org
  • #2
Hi oro,

Apologies but I don't quite understand what you're question is. If you wanted to solve the Rankine-Hugoniot condition for energy flow for something other than a monatomic gas, what's the problem with just plugging in a different value of [tex]\gamma[/tex] into equation 3 in your list?
 

Related to J shock in a gas for gamma = 7/5

1. What is J shock?

J shock refers to a type of shock wave that occurs in a gas when there is a sudden and significant increase in the gas's pressure and temperature. It is often seen in high-speed flows and can lead to dramatic changes in the gas's properties.

2. What is gamma in relation to J shock?

Gamma, also known as the adiabatic index, is a measure of the gas's heat capacity ratio. In the context of J shock, it is used to calculate the gas's speed and pressure behind the shock wave.

3. How is J shock calculated with a gamma of 7/5?

J shock can be calculated using the Rankine-Hugoniot equation, which takes into account the gas's properties before and after the shock wave and the gamma value. With a gamma of 7/5, the equation will return the speed and pressure of the gas behind the shock wave.

4. What factors can lead to J shock in a gas with a gamma of 7/5?

J shock can occur in a gas with a gamma of 7/5 when there is a sudden change in flow velocity, a sudden change in the gas's properties, or when a gas encounters an obstacle or boundary. It can also occur in high-speed flows or supersonic aircraft.

5. What are the applications of studying J shock in a gas with a gamma of 7/5?

Understanding J shock in a gas with a gamma of 7/5 has many practical applications, such as in aerodynamics, astrophysics, and engineering. It can help in the design of supersonic aircraft and spacecraft, as well as in predicting and preventing shock waves in industrial processes and explosions.

Similar threads

  • Advanced Physics Homework Help
Replies
4
Views
878
  • Advanced Physics Homework Help
Replies
4
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Advanced Physics Homework Help
Replies
2
Views
647
  • Advanced Physics Homework Help
Replies
3
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Biology and Chemistry Homework Help
Replies
1
Views
56
  • Advanced Physics Homework Help
Replies
5
Views
1K
  • Advanced Physics Homework Help
Replies
2
Views
2K
Back
Top