How to present pressure ratio of nozzle as a function of area ratio?
How to present pressure ratio of nozzle as a function of area ratio?
(OP)
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)]*ε
here,
k = specific heat ratio
ε = 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 htt p://solito n.ae.gatec h.edu/peop le/jseitzm a/classes/ ae4451/thr ust_coeffi cient2.pdf)
Thank you in advance =)
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)]*ε
here,
k = specific heat ratio
ε = 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 htt
Thank you in advance =)





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