Steam enters an adiabatic turbine at 7 MPa, 600°C, and 80 m/s and leaves at 50 kPa, 150°C, and 140 m/s. If the power output of the turbine is 6 MW, determine...
a.) the mass flow rate of the steam flowing through the turbine
b.)the isentropic efficiency of the turbine
7 comments:
Hi Dr. B,
I got part A, but for part B...
In the equation x = [s - s(sat liq)]/s something
What is the s something?
Where is this in our ThermoCD?
I am finding it hard to find some of the equations on a lot of these probelms...
Thanks for your help.
Oops, I figured it out, its Svap - Sliq, but I'm still wondering where these equations are in ThermoCD.
Tyler 12:17 PM
Quality was introduced in Lesson 2B and in an example problem I derived one of the two relationships between quality and specific properties of sat'd liquid and vapor. The other relationship (the one you needed here) was derived in class. It does not appear in Thermo-CD except in examples and quizzes. I will fix that.
We didn't derive that equation in my class and I am totally lost. What are we supposed to do for part b?
Katie 8:53 PM
The relationship Tyler was talking about is:
x = (Hsatmix - Hsatliq) / (Hsatvap - Hsatliq)
Where H is really Hhat. This equation works with any specific property,not just H. It works with V, U and S as well.
When dealing with isentropic efficiency, you are going to analyze a hypothetical turbine that is isentropic...S2 = S1. You use this fact to determine H2 and then use the 1st Law to determine the shaft work produced by the isentropic turbine...Wisen. Then, the isentropic efficiency is Wactual / Wisen.
Its strange that i worked this problem and got correct answers without considering changes in KE. Is this a coincidence? I just realized that. Were we supposed to use -Wactual=mdot(deltaH+deltaKE)?
AdamAnt 2:54 PM
The change in kinetic energy is very small compared to the change in H. This is true here even though the velocity changed from 140 m/s to 80 m/s. H changed by almost 900 kJ/kg, but Ekin changed by just 6.6 kJ/kg. The change in Ekin often (but not always) gets lost in the round-off error.
But, YES, you are supposed to consider changes in kinetic energy in this problem !
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