How to present pressure ratio of nozzle as a function of area ratio?

[dokeun]

Hi
During my study on the text book "Rocket propulsion elements" I got a problem to progress on nozzle theroy.

Here is a question.

Thrust coefficent contains Pressure ratio which is Pressure in chamber divided by exit pressure. I wanted to represent this pressure ratio not as a function of Mach # but as a function of area ratio. So..I reformulated pressure ratio equation as below using some equations for the isentropic process(

p0=p*POW[1+0.5*(k-1)*M^2, k/(k-1)],

A_exit/A_throat = 1/M_exit*sqrt[POW[{1+(k-1)/2*M_exit^2}/{[{1+(k-1)/2}, (k+1)/(k-1)]]

).

result was....

POW[P, (k^2-1)/k^2] - POW[P, (k+1)/k] = {(k-1)/2}*POW[(k+1)/2, (k+1)/(k-1)]*?

here,
k = specific heat ratio
? = area ratio = A_exit/A_throat
P = pressure ratio = p_chamber/p_exit

As you can see above, this equation can be sovled by equation solver or some other progams... And, for now, I can't confirm that my approach to plot the Cf versus nozzle area ration for given k.

Is this right approach?!

PS. I got hint from presentation from the GeorgiaTech AE4451 Propulsion(see attachment or

http://soliton.ae.gatech.edu/people/jseitzma/classes/ae4451/thrust_coefficient2.pdf)

Thank you in advance =)

 

[CarbonRod]

A really good book to look at would be Saad's compressible fluid flow. It really goes deep into the algebra of getting one ratio like static to stagnation pressure in terms of another and contains lots of information that was useful in solving problems in my compressible flow class which used a different book.

 

[IRstuff]

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FAQ731-376