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+//Solution 8-05
+WD=get_absolute_file_path('8_05_solution.sce');
+datafile=WD+filesep()+'8_05_example.sci';
+clc;
+exec(datafile)
+//simultaneous equations method
+function [Z] = equation(X)
+ V = X(1);
+ Re = X(2);
+ f = X(3);
+ Vdot = X(4);
+ Z(1) = V - Vdot / (%pi / 4 * D**2);
+ Z(2) = Re - V * D / nu;
+ Z(3) = 1 / sqrt(f) + 2.0 * log10(epsilon / D /3.7 + 2.51 / Re / sqrt(f));
+ Z(4) = h_L - f * L * V**2 / (2 * g * D);
+endfunction
+epsilon = 0.0;
+funcprot(0);
+[X, v, info] = fsolve([1;1e5;0.02;0.1], equation);
+Vdot = X(4);
+Vdot_drop = Vdot_old - Vdot
+printf("Drop in flow rate through duct is %1.2f m^3/s",Vdot_drop); \ No newline at end of file