# Isentropic Efficiency - Nozzle

VooDoo
Hey guys,

I have been given that the isentropic efficiency of a nozzle = 90%. Inlet condictions are: 5MPa and 550°C and exit: 100kPa.

Now $$\eta_{n}(h_{i}$$ - $$h_{0}$$) = $$V^{2}_{i}$$/2

h(o) - h(i) is the enthalpy drop across the turbine.

Now next they say that s(o) = s(i). Now how can the entropy at the entrance of the nozzle be equal to the entropy at the exit if the isentropic efficiency of the nozzle is not equal to one!

Here is a picture of my notes:
http://img259.imageshack.us/img259/6140/111nm6.jpg [Broken]

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jaap de vries
Maybe there is heat transfer out of your nozzle?

The isentropic efficiency is a type of efficiency that is defined by dividing the actual work output or KE output to the isentropic output. Why do you assume for your nozzle that it is isentropic when you are given the efficiency?

Jupiter6
Hey guys,

I have been given that the isentropic efficiency of a nozzle = 90%. Inlet condictions are: 5MPa and 550°C and exit: 100kPa.

Now $$\eta_{n}(h_{i}$$ - $$h_{0}$$) = $$V^{2}_{i}$$/2

h(o) - h(i) is the enthalpy drop across the turbine.

Now next they say that s(o) = s(i). Now how can the entropy at the entrance of the nozzle be equal to the entropy at the exit if the isentropic efficiency of the nozzle is not equal to one!

Reiterating what FredGarvin was saying...the term "isentropic efficiency" refers to a comparsion between actual performance and the ideal isentropic performace. If s(o) = s(i), then yes, the efficiency would be 100%. I think you just misunderstood the usage of the words.
\frac{V_{2}^2/2}{(V_{2}^2/2)_{s}}
OR
\frac{h_{1}-h_{2}}{h_{1}-h_{2s}}

Mechaniac
let me get this straight ,the question is wrong isn't it ?..cos his notes clearly mention that inlet entropy is equal to outlet entropy=7.131 kj/kgK and yet the question says that isentropic efficiency is 90 % how can both of this be true ?

90 % would mean a curved expansion graph, in which the initial entropy would be different from final entropy which means S(I) and S(O) can't be same ,right ?

Jupiter6
let me get this straight ,the question is wrong isn't it ?..cos his notes clearly mention that inlet entropy is equal to outlet entropy=7.131 kj/kgK and yet the question says that isentropic efficiency is 90 % how can both of this be true ?

90 % would mean a curved expansion graph, in which the initial entropy would be different from final entropy which means S(I) and S(O) can't be same ,right ?

Yes, the notes are unclear and seem to have no relevance to the problem stated by the original poster. Turbine...nozzle...which is it?