From Robert Balmer\'s Modern Engineering Thermodynamics, chapter 9, problem 8: A

Question

From Robert Balmer's Modern Engineering Thermodynamics, chapter 9, problem 8:

A steam turbine is limited to a maximum inlet temperature of 800°C. The exhaust pressure is 0.0100 MPa, and the moisture in the turbine exhaust is not to exceed 9.00%.

a. What is the maximum allowable turbine inlet pressure if the flow is adiabatic and reversible?
b. What is the maximum power output per unit mass flow rate?

I'm kind of at a loss as to where to start. Any help would be appreciated. I will rate lifesaver for an answer that explains the process to further my learning. Thanks for the help.

Explanation / Answer

I think quality given is wrong, it has to be 90 %

and am taking 90%, as 9 % is not practically possible

T1 = 800 C

At P2 = 0.010 pa and quality = 90% = 0.9

h2 = h f@0.01MPa + 0.9 x h fg@0.01 Mpa,

and s2 = s f@0.01MPa + 0.9 x s fg@0.01 Mpa,

We take values of hf and hfg, and sf and sfg from mollier diagram, or steam table

h2 = 191.9 + 0.9 x 2393 = 2345.6 KJ/Kg.K

s2 = 0.6964 + 0.9 x 7.5013 = 7.45 KJ/Kg.K

Now, for maximum work, process has to be isentopic,(adiabatic and reversible) i.e. dS = 0.

S1 = S2 = 7.45 KJ/Kg.K

At inlet at T1 = 800 C and s1 = 7.45 KJ/Kg.K,

from mollier diagram (or steam table)..

a) Pressure = P1 = 9.2 MPa

b)

At inlet at T1 = 800 C and s1 = 7.45 KJ/Kg.K,

from mollier diagram (or steam table)..

h1 = 4118.46 KJ/Kg

mass flow rate = m_rate = 1kg/s

maximum work done = m_rate x (h1 - h2)

W = 1 x (4118.46 - 2345.6)

   = 1772.86 KW

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