Question

The following diagram illustrates a simple steam power plant. A 10kg/s flow of liquid water at T1=25°C enters the pump at a pressure of P1=100kPa and is then pumped to a pressure of P2=2MPa. The boiler then heats the water at constant pressure to produce superheated vapour at T3=450°C. The steam is then expanded in the turbine to a final pressure of P4=100kPa. The turbine and pump are well insulated and may be considered reversible.

a) Find the turbine exit state (quality or temperature, whichever is appropriate). (6 marks)

b) Determine the turbine power output. (4 marks)

c) Evaluate the power required to operate the pump. (3 marks)

d) Find the water temperature T2 at the exit of the pump. (4 marks)

e) Calculate the required heat input for the boiler. (3 marks)

f) If the flow velocity in the pipe at the turbine inlet is 50m/s, what is the pipe diameter? (2 marks)

g) Illustrate this cycle (identifying states 1 to 4) on a T-s diagram. (2 marks)

3 W Turbine Boiler 4 Pump 2 1 Wp

1)Identify the system / control volume
2)List the known variables
3)Assumptions
4)Relevant equations (Mass conservation, 1st Law, 2nd Law, etc)
5)Lookup required values in tables and/or do calculations

Answer 1

Giveni The following diagram, 3 (3 twr T= 25c Turbin P, = 100 kPa Boiler b = 2mpa 4 11 pump T3 = 450 c pump o turbine are well insulsted and reversible. from stam table at T = 450c, p= 2mpu h = 3350 kikg, s = 7.25 wlkgg pressun p=lov KPC • Vf = 0.601043 m 1kg hf = 417 Sklicy, hy = 2675 111 sf = 1.3026101g, Sg = 7.3589 lolig Turbine exit sote "T, from steam table @p=1W KP a T4 = gg. 6c Ts = 99.6°C proiez 3-4 gre isentropic S3 = sq a 7.25 1.3026 +21.7.3589-1303) x = 0.98 Turbine power output (W) ha= hitelhghs) w = mil hz-ha) - 417.5t 9812675- 417) W =1013350-2634) = 7158 kW ha = 2634 ks lcg power required to operate pump wp = mil Po-Pc) y Vs 19.217 KW wp = 10x (2000-160) *0.2010 43 = Water Tempereture at eit of pump (T2)- alsuum (p = 4.18 ha hy - Ty Cpu) (200-Ts) 417.2+1-96 = 908 R$ 4.18 (212-T 142 = 116°c)