EML 3015C Thermal-fluids I  Sample Test #3                                              fall 1999

 

1.     (45%)Considering the ideal Rankine power plant as shown.  The steam mass flow rate is 60 kg/s.  The steam is first heated in the boiler at a constant pressure of 8 MPa and expands in the first turbine to become 100% saturated vapor before it is reheated again at a constant pressure of 0.8 MPa before entering the second turbine.  Finally, the heat is rejected to a condenser unit operating at a pressure of 10 kPa.   In order to remove the heat in the condenser unit, cooling water enters at 20°C and leaves at 60°C at a mass flow rate of 750 kg/s.  Determine (a) The power input of the pump, (b) The heat rejection of the condenser unit, (c) The work output of the first stage turbine, (d) the work output of the second stage turbine, (e) the total heat transfer into the power plant, (f) thermal efficiency of the power plant.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


P(MPa)

T(°C)

x (%)

h (kJ/kg)

s (kJ/kgK)

v (m3/kg)

1

0.01

45.8 (C-2)

0

191.8

 

0.00101

2

8

 

 

199.9

 

 

3

8

 

 

3352.5

6.6636

 

4

0.8

170.4(C-2)

100

2769.1

6.6636

 

5

0.8

 

 

3056.4

7.236

 

6

0.01

45.8 (C-2)

87.8

2291.8

7.236

 

 

A-6

 

A-6

 

A-5

 

 

 

 

 

 

 

 

 

 


 

2.     (25%)Steam enters the turbine steadily at 8 MPa and 400°C and leaves at a pressure of 1 MPa.  Determine (a) the work output if the process is isentropic.  If the actual turbine is operating at 70% isentropic efficiency, determine (b) the actual work output, (c) the actual exit temperature of the steam, (d) the entropy generation (assume adiabatic). Base your calculation on 1 kg/s of steady steam flow.

 

 

 

 

 

 

 

 

 

 

 

 

 


 

3. (30%) A cylinder and piston assembly, containing 1 kg of air, is undergoing a complete cycle consisting of three reversible processes: 1-2 is an isentropc compression; 2-3 is an isothermal expansion from a pressure of 1 MPa to 100 kPa; and 3-1 is a constant pressure compression to a temperature of 50°C.   Sketch the T-s and P-v diagrams representing this cycle.  Determine the total work and heat transfer of the cycle.  Assume ideal gas (Cp=1 kJ/kg K, Cv=0.72 kJ/kg K, R=0.287 kJ/kg K, k=Cp/Cv=1.4)

 

 

 

 

 

 

 

 

 

 

 


P (MPa)

T (K)

v (m3/kg)

1

0.1

323

0.927

2

1

623.6

0.179

3

0.1

623.6

1.790

 

 


Formula Sheet