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Rankine Cycle - Net Power, Thermal Efficiency and Heat Transfer

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Water is the working fluid in a vapor power cycle with reheat, superheat and reheat.

Superheated steam enters the first turbine stage at 8 MPa, 480 C and expands to 0.7 MPa. It then is reheated to 480 C before entering the second turbine stage, where it expands to the condenser pressure of 8 KPa. The mass flow rate of steam entering the first turbine stage is 2.63*10^5 Kg/h. Each turbine stage operates with an isentropic efficiency of 58%. The pump operates with an efficiency of 80%.

Determine the net power developed, the cycle thermal efficiency and the rate of heat transfer to the cooling water passing through the condenser.

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This solution is provided in approximately 626 words and attached in a .doc file. It uses step-by-step equations and diagrams to further understand and solve the problem.

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Solution:

Notations and assumptions:

[ ]* = total features (like p*, T*, h*)
[ ]id = ideal states
[ ]L = referring to liquid state
[ ]V = referring to vapor state
k = adiabatic exponent (for superheated steam k = 1.3)
R = gas constant (for steam R = 461.9 J/kg.K)
= steam mass flow rate [kg/s]
LT , LP = turbine and water pump specific work [kJ/kg]

The diagram of the full cycle is shown in the figure below:

(see attachment)

a) The net power developed can be computed by formula:
(see attachment for equation) ( 1)
The steam mass flow rate is
(see attachment for equation) ( 2)
Now, we need to use the Steam Tables.
State 5: At p = 8 MPa and T = 480 C we find:
(see attachment for equation) ( 3)
We have to check now where is located state 6id (under or above the saturation line)
For s = 6.661 kJ/kg.K, we find on saturation line:
(see attachment for equation) ( 4)
Since p6id = 0.7 MPa = 7 bar < p5s, the state (6id) will be under the saturation line, that is within wet steam area
For p = 0.7 ...

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