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+//Example 13_1
+clc;clear;
+// given values
+b=0.4;// Width in m
+v=0.2;// Flow rate in m^3/s
+y_1=0.15;// Flow depth in m
+g=9.81;// m/s^2
+
+// Calculation
+A_c=y_1*b;// m^2
+V=(v/A_c);//The average flow velocity in m/s
+printf('The average flow velocity,V=%0.2f m/s\n',V);
+y_c=(v^2/(g*b^2))^(1/3);// The critical depth  in m
+printf('The critical depth for this flow,y_c=%0.3f m\n',y_c);
+printf('Therefore, the flow is SUPER CRITICAL since the actual flow depth is y=0.15 m, and y<yc.\n');
+Fr=(V*sqrt(g*y_1));// The Froude number
+E_s1=y_1+((v^2/(2*g*b^2*y_1^2)));//The specific energy for the given condition in m
+//Then the alternate depth is determined E_s1=E_s2; y_2=y(1)
+function[X]=depth(y);
+    X(1)=(y(1)+((0.2^2)/(2*9.81*0.4^2*y(1)^2)))-0.7163;
+endfunction
+y=[0.5];
+z=fsolve(y,depth);
+printf('The alternate depth y_2=%0.2f m\n',z);