Question

300 kg/hr of superheated steam is used to drive a turbine at a velocity of 50 m/s. the superheated steam enters the turbine at 60 bar and 400°C . The stream leaves the turbine as a saturated steam with a velocity of 100 m/s at 1.5 bar. The turbine delivers work and the heat loss from the turbine is 10 KW.

a) Calculate the net kinetic energy of the system (delta kE) and determine the work done by the turbine in KW.

Answer 1

Energy balance at inlet and outlet at steady state conditions

h1 + gz1 + 0.5 V1² + Q/m = h2 + gz2 + 0.5 V2²? + W/m

z1 = z2

At inlet velocity V1 = 50 m/s

Outlet velocity V2 = 100 m/s

Net kinetic energy = 0.5(V2² - V1²)

= 0.5(100*100 - 50*50) m2/s2

= 3750 m2/s2 x (1N/1kg-m/s2) x (1kJ/1000N-m)

= 3.75 kJ/kg

At 400 °C and 60 bar (superheated steam)

Enthalpy h1 = 3177 kJ/kg

At 1.5 bar (saturated steam)

Enthalpy h2 = 2693.11 kJ/kg

heat loss Q = - 10 kW

Q/m = W/m + 2693.11 - 3177 + 3.75

Q/m = W/m - 480.14

Q = W - 480.14 kJ/kg x 300 kg/hr x 1hr/3600s

Q = W - 40.01

W = Q + 40.01

W = - 10 + 40.01

W = 30.01 kW