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As you know, the Ideal Thrust Coefficient of convergent-divergent nozzle is calculated using this equation:

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But what about a convegent nozzle? Is there any equation to calculate the Ideal Thrust Coefficient for a convergent nozzle?

Image from: this link

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It’s exactly the same equation, but now the throat is at the exit. So, Ae = A*, and so the areas disappear from the last term.

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  • $\begingroup$ What about Pe? are you sure about your answer? Do you know how this equation is drived? $\endgroup$ – Roh Dec 2 '18 at 11:54
  • $\begingroup$ @Roh. Although the exit is now at the throat, the exit is still the exit. So, Pe is still Pe. Yes, I did look at the derivation, given by your link.(Thanks fir that, it was very useful). A convergent- divergent nozzle is a more complex geometry. So, a formula for that can be reduced to the simpler situation of a convergent only nozzle, but not the other way around. $\endgroup$ – Penguin Dec 3 '18 at 8:06
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One must be careful when working with those coefficients, they account for many losses that make differ the ideal thrust from de real one (components of exhaust velocity in a radial direction, presence of boundary layer friction, mass flow leakage, etc.), and those losses may vary depending on the author.

I don't know how this equation was derived, but when I studied jet engines a factor in $C_f$ expression was from a empirical basis, so maybe you cannot use only your math skills to get there.

Respect your question, I think the equation can be used directly considering that $A_e=A^*$ if the nozzle is choked ($M_e=1$) and using the proper expression for $p_e$.

Note: anyway, for a rocket, the relation between total pressure at the entry of the nozzle and the ambient pressure is so great that a con-di nozzle is always used (I've never seen a rocket fitted with a convergent one).

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