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+// Example 24_18

+clc;funcprot(0);

+//Given data 

+P=200;// Power plant capacity in MW

+T_6=1000;// K

+T_8=900;// K

+p_1=1;// bar

+T_1=27+273;// K

+p_r=5;// bar

+e=0.7;// The effectiveness of heat exchanger

+n_c=1;// Isentropic efficiency of  both compressors

+n_t=0.9;// Efficiency of both turbines

+n_com=0.95;// Combustion efficiency

+n_m=0.92;// Mechanical efficiency of compressor and generator shafts

+CV=40000;// kJ/kg

+C_p=1;// kJ/kg.°C

+r=1.4;// Specific heat ratio for air and gases

+

+//Calculation

+p_2=p_1*p_r;// bar

+p_i=sqrt(p_1*p_2);// bar

+T_7a=T_6*(p_1/p_2)^((r-1)/r);// K

+n_t2=n_t;

+T_7=T_6-(n_t2*(T_6-T_7a));// K

+W_g=C_p*(T_6-T_7)*n_m;//Work done per kg of air in generator-turbine in kJ/kg

+m_2=CV/W_g;// The mass of exhaust gases in kg/sec

+T_2=T_1*(p_i)^((r-1)/r);// K

+W_c=2*C_p*(T_2-T_1);//Work done per kg of air in both compressors in kJ/kg

+T_4=T_2;// K

+// Assume m_1=y(1);T_5=y(2)

+function[X]=massflow(y);

+    X(1)=(m_2*C_p*(y(2)-T_8))-(y(1)*C_p*(T_8-T_4));

+    X(2)=((y(1)*C_p*(T_8-T_4))/(m_2*C_p*(y(2)-T_4)))-(e);

+endfunction

+y=[100 1000];

+z=fsolve(y,massflow);

+T_5=z(2);// K

+m_1=z(1);// kg/sec

+T_9a=T_8/(p_i)^((r-1)/r);// K

+n_t1=n_t;

+T_9=T_8-(n_t1*(T_8-T_9a));// K

+m_c1=(((m_1*(T_8-T_9))/((T_2-T_1)*n_m))-m_1)/2;// Air taken from atmosphere in kg/sec

+m_c2=m_c1+m_1;// kg/sec

+//Assume m_f=y(1)

+function[X]=massoffuel(z);

+    X(1)=((m_c2+z(1))*C_p*(T_5-T_4))/(CV*n_com)-z(1);

+endfunction

+z=[10];

+y=fsolve(z,massoffuel);

+m_f=y(1);// Mass of fuel used per second

+n_o=((P*10^3)/(CV*m_f))*100;// Over all efficiency of the plant in %

+Ctc=(m_1*C_p*(T_8-T_9))/1000;// Compressor-turbine capacity in MW

+printf('\n(a)Air taken from atmosphere per second=%0.0f kg/sec \n(b)Fuel required per second=%0.2f kg/sec \n(c)Over all efficiency of the plant=%0.1f percentage \n(d) Compressor-turbine capacity=%0.0f kW',m_c1,m_f,n_o,Ctc*1000);

+// The answer vary due to round off error