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+//clear//

+clear;

+clc;

+

+//Example 6.2

+//Given

+Tr = 1000; //[R] 

+pr = 20; //[atm]

+Ma_a = 0.05;

+gama = 1.4;

+gc = 32.174; //[ft-lb/lbf-s^2]

+M = 29;

+R = 1545;

+//(a)

+//Using Eq.(6.45)

+A = 2*(1+((gama-1)/2)*Ma_a^2)/((gama+1)*Ma_a^2);

+fLmax_rh = (1/Ma_a^2-1-(gama+1)*log(A)/2)/gama  

+

+//(b)

+//Using Eq.(6.28), the pressure at the end of the isentropic nozzle pa

+A = (1+(gama-1)*(Ma_a^2)/2); 

+pa = pr/(A^(gama/(gama-1)))  // [atm]

+//From Example 6.1, the density of air at 20atm and 1000R is 0.795 lb/ft^3

+//Using Eq.(6.17), the acoustic velocity 

+Aa  = sqrt(gc*gama*Tr*R/M) //[m/s]

+//The velocity at the entrance of the pipe 

+ua  = Ma_a*Aa //[m/s]

+//When L_b = L_max, the gas leaves the pipe at the asterisk conditions, where 

+Ma_b = 1;

+// Using Eq.(6.43)

+A = (gama-1)/2;

+Tstar = Tr *(1+A*Ma_a^2)/(1+A*Ma_b^2) // [K]

+// Using Eq.(6.44)

+rho_star = 0.795*Ma_a/sqrt(2*(1+(gama-1)*Ma_a^2/2)/(2.4)) //[lb/ft^3]

+//Using Eq.(6.39)

+pstar = p0*Ma_a/sqrt(1.2) // [atm]

+//Mass velocity through the entire pipe

+G = 0.795*ua //[lb/ft^2-s]

+ustar = G/rho_star //[ft/s]

+

+//(c)

+//Using Eq.(6.45) with f_Lmax_rh = 400

+

+err = 1;

+eps = 10^-3;

+Ma_ac = rand(1,1);

+i =1;

+while((err>eps))  

+  A = 2*(1+((gama-1)/2)*Ma_ac^2)/((gama+1)*Ma_ac^2);

+  B = gama*400+1+(gama+1)*log(A)/2;

+  Ma_anew  = sqrt(1/B);

+  err = Ma_ac-Ma_anew;

+  Ma_ac = Ma_anew;

+end

+Ma_ac;

+uac  = Ma_ac*ua/Ma_a //[ft/s]

+Gc = uac*0.795 //[lb/ft^2-s]