Calculating Steam Turbine Work & Power from 2 Unknowns

[JSBeckton]

A steam turbine has an inlet of 2kg/s water at 1000kPa and 350C and velocity of 15m/s. The exit is at 100kPa, 100% quality and very low velocity. Find specific work and power produced.

I have done a lot of these problems but it usually says adiabatic or the inlet and exit temp is the same. How do i solve with the energy equation when I have 2 unknowns? (q and w)

thanks

 

[Andrew Mason]

A steam turbine has an inlet of 2kg/s water at 1000kPa and 350C and velocity of 15m/s. The exit is at 100kPa, 100% quality and very low velocity. Find specific work and power produced.

What does 100% quality mean? Check the question carefully. One has to have a temperature of the exit steam/water in order to determine the loss of energy of the steam.

AM

 

[JSBeckton]

I understand that that gives me the exit temp, I just do not understand how to solve the energy equation for work when I have heat loss as well. Is the heat loss just the difference in internal energy between those two temperatures and pressures?

 

[Andrew Mason]

I understand that that gives me the exit temp, I just do not understand how to solve the energy equation for work when I have heat loss as well. Is the heat loss just the difference in internal energy between those two temperatures and pressures?

The first law of thermodynamics:

$$dQ = dU + dW = nC_vdT + PdV$$

where dQ is the heat removed from the hot reservoir, applies only to systems in thermodynamic equilbrium. Here you have a dynamic element: moving steam, so you have to take into account the kinetic energy of the steam as well.

I still don't understand how you get the exit temperature. What does "100% quality" mean?

AM

 

[Cyrus]

A steam turbine has an inlet of 2kg/s water at 1000kPa and 350C and velocity of 15m/s. The exit is at 100kPa, 100% quality and very low velocity. Find specific work and power produced.

I have done a lot of these problems but it usually says adiabatic or the inlet and exit temp is the same. How do i solve with the energy equation when I have 2 unknowns? (q and w)

thanks

The heat flow is zero. Turbines under steady state are adiabatic unless otherwise specified. You have one unknown, solve for it.

AM, 100% quality means the liquid is a saturated vapor, x=1.0, and the specific enthalpy is equal to the value of Hg at said temperature.

Beckton and his never ending slew of thermo questions, aye caramba.

 

[JSBeckton]

Thanks guys, sorry about all of the thermo questions, just studying for an exam and doing a bunch of problems that were not assigned so I sometimes come across something that was not covered and haven't seen that situation before, but that helps me the more situations I see, the more I understand the underlying concepts.

 

[JSBeckton]

I figured it out and found that without taking into account the velocity, the anwser is 482.19 kj/kg, and 482.303 kJ,kg with the velocity considered (the right anwser in the back of the book). Is this not negligible?

 

[Cyrus]

What do you think?

 

[JSBeckton]

It seems to me that we should almost always neglect kinetic energy. Should there be a rule of thumb or something?