Question

Steam at 5MPa and 300°C enters a turbine in a steady flow manner, from the turbine the steam expands to 200kPa with a quality of 90%. Find the following:

1. The work done by the steam to the turbine in kj/kg
2. The amount of steam flow rate needed in kg/hr if the turbine produces 200kW of power
3. The efficiency of the expansion process

Answer 1

Ans

At state 1 (5 MPa and 300 ^oC)

h₁ = 2925.6 kJ/kg

s₁ = 6.2109 kJ/kg K

At state 2s ( 200 kPa)

s_2s = s₁ = 6.2109 kJ/kg K

s_f + x_2s(s_g - s_f) = 6.2109

1.53 + x_2s(7.127 - 1.53) = 6.2109

x_2s = 0.836

Therefore,

h_2s = h_f + x_2s(h_g - h_f)

= 504.7 + 0.836(2707 - 504.7)

= 2345.82 kJ/kg

At state 2a ( 200 kPa and x_2a = 0.9 )

h_2a = h_f + x_2a(h_g - h_f)

= 504.7 + 0.9(2707 - 504.7)

= 2486.77 kJ/kg

(a)

Work done by the steam turbine per kg = h₁ - h_2a

= 2925.6 - 2486.77

= 438.83 kJ/kg (ans)

(b)

Steam flow rate needed for producing 200 kW of power, m = 200 / Work done by the steam turbine per kg

= 200 / 438.83

= 0.45576 kg/s

= 0.45576 * (3600) kg/hr

= 1640.73 kg/hr (ans)

(c)

Efficiency of the expansion process,

  

  

= 75.69 % (ans)