A steam power plant operating in an ideal Rankine cycle has a high pressure of 5MPaand a low pressure of 15 kPa. The turbine exhaust state should have a quality of at least95% and the turbine power generated should be 7.5MW. Find the necessary boiler exittemperature and the total mass flow rate
Below I write you a code for the software EES (Engineering Equation Solver). Download and install the trial version of said software if you don't have it already. !----Begin EES--------- {Unit settings: be sure to set it up as: kJ; mass basis; kg; C; kPa} State labeling: State 1: pump inlet, condenser outlet State 2: boiler inlet, pump outlet State 3: turbine inlet, boiler outlet State 4: condenser inlet, turbine outlet Data W_dot_out = 7500 [kW] P[1] = 15 [kPa] P[3] = 5000 [kPa] x[4] = 0.95 Assumptions: 1. turbine and pump are both adiabatic and isentropic 2. pressure variation across all heat exchangers and piping is negligible 3. all velocity effects are negligible 4. saturated liquid enters the pump (no subcooling) x[1] = 0 Strategy: Equate pressures across heat exchangers P[1] = P[4] P[2] = P[3] Trivial entropy and enthalpy h[1] = enthalpy(Steam, P=P[1], x=x[1]) s[1] = entropy(Steam, P=P[1], x=x[1]) h[4] = enthalpy(Steam, P=P[4], x=x[4]) s[4] = entropy(Steam, P=P[4], x=x[4]) Equate entropy across pump and turbine s[1] = s[2] s[3] = s[4] Complete the table h[2] = enthalpy(Steam, P=P[2], s=s[2]) h[3] = enthalpy(Steam, P=P[3], s=s[3]) T[1] = Temperature(Steam, P=P[1], s=s[1]) T[2] = Temperature(Steam, P=P[2], s=s[2]) T[3] = Temperature(Steam, P=P[3], s=s[3]) T[4] = Temperature(Steam, P=P[4], s=s[4]) Energy balance equations W_dot_out = m_dot*(h[3] - h[4]) W_dot_in = m_dot*(h[2] - h[1]) W_dot_net = W_dot_out - W_dot_in Q_dot_in = m_dot*(h[3] - h[2]) Q_dot_out = m_dot*(h[4] - h[1]) eta = W_dot_net/Q_dot_in !----End EES---------
