Help on how to plot the Rayleigh line for a flow?

[kawf]

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

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)

 

[nate808]

After doing some research, it seems that the Rayleigh line is a plot of the change in entropy (s) as a function of the change in pressure (p) and temperature (T) at a constant Mach number. In order to plot this, you will need to use the following equation:

s2/s1 = (p2/p1)^((gamma-1)/gamma) * (T2/T1)^(-1/(gamma-1))

where s is entropy, p is pressure, T is temperature, and gamma is the specific heat ratio (in this case, 1.4). M is the Mach number, which is already given as 0.25.

To plot the Rayleigh line, you will need to choose a range of p2 and T2 values and use the equation to calculate the corresponding s2 value. Then, plot s2 as a function of p2 and T2. This will give you a curve that represents the change in entropy at a constant Mach number.

I hope this helps! Let me know if you have any further questions.