Thermodynamics - Need Help on Turbine Engines

[paul1234]

Hey Guys,

I'm trying to solve the problem below:

Steam enters a turbine with a velocity 120 m/s at 600°C and 600kPa. The steam leaves the turbine as saturated vapor at 200 kPa with a velocity of 180 m/s. Heat is transferred from the turbine to the surroundings in the amount of 30 kJ for every kilogram of steam flowing through the turbine. The mass flow rate of steam through the turbine is 20 kg/s (1 kJ/kg = 1000 m2/s2)
Find the work and power.

I'm given the T, v, p initial and p, v final. I think I need to find T final to solve the problem.
How do I go about finding T final? Also, I don't know whether to assume the system is isentropic or adiabatic. Can someone help me on this?

 

[BishopUser]

I think this is a homework problem so try the homework forums next time. Saturated vapor is the clue to finding Tfinal. The problem gives you enough info to know how much energy is entering the turbine and how much is leaving the turbine. The differnece is probably how much power the turbine is putting out (assuming 100% efficient turbine since no efficiency is given).

 

[paul1234]

I think this is a homework problem so try the homework forums next time. Saturated vapor is the clue to finding Tfinal. The problem gives you enough info to know how much energy is entering the turbine and how much is leaving the turbine. The differnece is probably how much power the turbine is putting out (assuming 100% efficient turbine since no efficiency is given).

Yeah Thats what I thought. But Do i just cancel out the the change in enthalphy?
I was trying to find Tfinal to find hfinal. I got hinitial from the steam tables.

Can i just use KEf-KEi-Q=work
and to find power do use p=mass flowrate*work

or do i need to use hi + kei - kef - h2 = Q - W in order find work?

 

[Mech_Engineer]

This is obviously homework, but I'll try to give you some pointers. I've split your problem statement up to help make it more obvious what you're being given:

Steam enters a turbine with a velocity 120 m/s at 600°C and 600kPa. (State 1)

The steam leaves the turbine as saturated vapor at 200 kPa with a velocity of 180 m/s. (State 2)

Heat is transferred from the turbine to the surroundings in the amount of 30 kJ for every kilogram of steam flowing through the turbine. (System)

The mass flow rate of steam through the turbine is 20 kg/s (1 kJ/kg = 1000 m2/s2) (System)

Find the work and power. (System)

It could help to draw a system diagram, with all of the parameters listed. You should review in your textbook what a system diagram for a steam power cycle looks like (http://en.wikipedia.org/wiki/Rankine_cycle" ).

Also, I don't know whether to assume the system is isentropic or adiabatic.

An adiabatic process is a thermodynamic process in which no heat is transferred to or from the working fluid. Since it is explicitly stated in the problem statement that heat is being transferred from the turbine to the surroundings, it is obviously not an adiabatic process.

 

[BishopUser]

Yeah Thats what I thought. But Do i just cancel out the the change in enthalphy?
I was trying to find Tfinal to find hfinal. I got hinitial from the steam tables.

Can i just use KEf-KEi-Q=work
and to find power do use p=mass flowrate*work

or do i need to use hi + kei - kef - h2 = Q - W in order find work?

The problem provides you with the final pressure, and the fact that the steam is saturated. That is enough information to find tfinal (and hfinal) via steam tables.

Just use conservation of energy, that is the most important concept. Imagine the turbine - you know how much kinetic energy and thermal energy is being put into the turbine per unit time. You also know how much kinetic energy and thermal energy is leaving the turbine per unit time. The difference between those two values has to be the work per unit time (power) that the turbine is putting out.

I don't know how to calculate work from what is given; that would require some time limitation (i.e. how much work is done over a period of 60 seconds).