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


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

Image from: this link


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.

  • $\begingroup$ 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

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).


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.