Shock wave system of equations

In summary, the conversation is about solving a system of equations related to Rankine-Hugoniot conditions at a hydrodynamic shock front. The equations are attached and the person is struggling to solve for three unknowns using algebra. They question if they are missing an assumption and eventually solve the problem.
  • #1
fabianprewett1
2
1

Homework Statement


This is Rankine-Hugoniot conditions at a hydrodynamic shock front. Where P2=0 v2=0.

The problem is attached. I need to solve a system of equations. I thought it would be relatively straight forward solving for the three unknowns but I'm struggling. I know it's possible to solve but maybe not just rearranging the equations as I've been trying. Am I missing an assumption or something?

Homework Equations


The equations are attached.

The Attempt at a Solution



I just want to know if simply using algebra will work for rearranging/solving this system. All I can solve for so far is P1/V1=Vs*ρ2 from the first two equations. Anything I try with w in equation 3 gives me multiple terms with the variables I'm trying to solve for. I feel like something should be 0 or some other assumption.
 

Attachments

  • Shock.PNG
    Shock.PNG
    7.5 KB · Views: 355
  • eq astr.PNG
    eq astr.PNG
    1.2 KB · Views: 338
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  • #2
You need to show us your actual calculations if you want us to comment on them. Your description is too vague to do anything with, the section "Attempt at a Solution" is meant to actually show the work you've done toward a solution.
 
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  • #3
Thanks. I solved it. I was missing something basic.
 
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1. What is the shock wave system of equations?

The shock wave system of equations is a set of mathematical equations used to describe the behavior of shock waves, which are sudden and large changes in pressure, density, and temperature in a fluid, such as air or water.

2. How is the shock wave system of equations derived?

The shock wave system of equations is derived from the fundamental laws of fluid dynamics, including conservation of mass, momentum, and energy. These equations are then simplified and specialized to describe the specific conditions of a shock wave.

3. What are the applications of the shock wave system of equations?

The shock wave system of equations has many practical applications, including understanding the behavior of supersonic aircraft, designing efficient rocket engines, and studying the formation of shock waves in explosions and other high-speed events.

4. How does the shock wave system of equations account for non-ideal effects?

The shock wave system of equations can be expanded to include non-ideal effects, such as viscosity and heat conduction, by adding additional terms to the equations. These terms account for the dissipative processes that occur in real-world shock waves.

5. Are there any limitations to the shock wave system of equations?

While the shock wave system of equations is a powerful tool for understanding shock waves, it does have limitations. For example, it assumes that the fluid is in a state of thermodynamic equilibrium, which may not always be the case in highly dynamic events. Additionally, it does not account for chemical reactions that may occur in the shock wave.

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