# Thermodynamics:based on first law

## do you know the answer

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1. Feb 27, 2015

### anisha

1. The problem statement, all variables and given/known data
In an adiabatic steam nozzle,steam is expanded from 10 bar and 473k to an exit pressure of 5 bar.nozzle has an isentropic efficiency of 90%.neglect kinetic energy at the inlet.assuming equilibrium condition at exit,find the velocity of nozzle at exit? given data : i)at nozzle inlet: enthalpy=2828KJ/Kg ; entropy = 6.70KJ/KgK
ii)saturated liquid properties at nozzle exit: enthalpy=640 KJ/Kg;entropy=1.86KJ/KgK
iii)saturated vapour properties at nozzle exit: enthalpy=2750 KJ/Kg;entropy=6.82KJ/KgK

2. Relevant equations
energy equation for nozzle: (h1/2)+((c1)^2/2)=(h2/2)+((c2)^2/2)
isentropic efficiency of nozzle : (h1-h2)/(h1-h2s)
where h2s is isentropic enthalpy at nozzle exit

3. The attempt at a solution
i didn't understand what is the use of giving the efficiency here and how it's related in finding the exit velocity.the isentropic enthalpy i found is h2s=2741.333KJ/Kg,h1=2828KJ/Kg,h2=2750KJ/Kg (given).the correct answer is482 m/s
please do help me ,any hint will be of great use and appreciated!

Last edited: Feb 27, 2015
2. Feb 27, 2015

### SteamKing

Staff Emeritus
With regard to the isentropic efficiency:

η = (h1-h2)/(h1-h2s)

Now, if η = 1, that would imply η = 1 = (h1-h2)/(h1-h2s), which would only be true if h2 = h2s.

If η = 0.9, then you are given a hint how to calculate h2 given h1 and h2s.

3. Feb 27, 2015

### anisha

Thanks,but there is no h2s given,instead h2 value is there.i am totally confused now.

4. Feb 28, 2015

### rock.freak667

You found h2s=2741.333KJ/Kg

Using this formula, and the fact that you were told that the isentropic efficiency = 90 %, can you put

5. Feb 28, 2015

### anisha

6. Feb 28, 2015

### anisha

7. Feb 28, 2015

### anisha

sir,if i take given exit enthalpy to be h2s then my answer is 374 m/s as exit velocity were as the actual one is 482 m/s.

8. Feb 28, 2015

### anisha

Can anyone tell me whether given enthalpy at the exit is h2s or h2,cause if it's h2s it's not giving me the right answer

9. Feb 28, 2015

### SteamKing

Staff Emeritus
h2s is the enthalpy at the nozzle exit assuming that the expansion is isentropic, which the problem statement tells you it is not. In order to find h2s, you use the value of entropy at the inlet condition, namely s1 = 6.70 kJ/kg-K, and the saturated vapor and liquid conditions at the exit pressure of 5 bar, as given in the problem statement. Due to expansion thru the nozzle, the steam exiting may be a mixture of vapor and saturated liquid.

Having found h2s and knowing the isentropic efficiency of the nozzle, you should be able to find the enthalpy at the exit of the nozzle, h2.

In order to keep going back and forth on this point, please post your calculations, not just the final velocity of the steam.

10. Mar 2, 2015

### anisha

kindly explain in more detail!