Help plotting the Rayleigh line for a flow?

So in summary, the task at hand is to plot the Rayleigh line for a flow with given conditions, using the equation of state for a perfect gas. The attempt at a solution involves plotting the change in entropy as a function of Mach number, but it appears that the correct equation to plot is the equation of state for a perfect gas, which is P*V=n*R*T.
  • #1
kawf
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0

Homework Statement



I need to plot the Rayleigh line for a flow that has the following conditions at one point
(Perfect gass assumption holds, R=287 J/kgK, gama=1.4)
p = 101.3 kPa
T = 300 K
s = 6.867*10^3 J/kgK
M = .25

My question is what equation am I actually supposed to plot for a Rayleigh line?

Any help is appreciated. TIA

Homework Equations



change in entropy seen here as S_R
http://upload.wikimedia.org/math/7/0/e/70eca7a87051faef8ba16009e8f46fe2.png

The Attempt at a Solution



So far i have tried plotting the change in entropy as a function of mach number but that does not seem to be right (seen here as S_R http://upload.wikimedia.org/math/7/0/e/70eca7a87051faef8ba16009e8f46fe2.png)
 
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  • #2
I believe the equation I am supposed to plot is the equation of state for a perfect gas, which is P*V=n*R*T.
 

1. What is the Rayleigh line for a flow?

The Rayleigh line for a flow is a graphical representation of the pressure and temperature relationships for a compressible fluid flow. It shows the changes in these properties as the fluid moves through different stages of the flow process.

2. How is the Rayleigh line plotted?

The Rayleigh line is typically plotted by first determining the specific enthalpy and specific entropy of the fluid at different points in the flow process. These values are then used to plot points on a pressure-temperature graph and connect them with a line.

3. Why is the Rayleigh line important in fluid dynamics?

The Rayleigh line is important because it provides valuable information about the characteristics of a fluid flow, such as the efficiency of a turbine or compressor. It also allows for the identification of different flow regimes and helps in the design and analysis of various fluid systems.

4. What are the limitations of using the Rayleigh line?

One limitation of using the Rayleigh line is that it assumes a perfect gas behavior, which may not always be the case in real-world applications. It also does not take into account factors such as friction or heat transfer, which can affect the properties of the fluid in the flow process.

5. How can the Rayleigh line be used to improve fluid flow processes?

The Rayleigh line can be used to optimize fluid flow processes by identifying areas of inefficiency and designing systems to operate closer to the ideal conditions represented by the line. It can also be used to troubleshoot and diagnose issues in existing fluid systems.

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