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+// Example 10_6

+clc;clear;

+//Given data

+// Assume (vdot/L)_1=V1,(vdot/L)_2=V2;

+V1=2.00;// m^2/s

+V2=-1.00;// m^2/s

+gamma1=1.50;// m^2/s

+x_1=0;

+y_1=1;

+x_2=1;

+y_2=-1;

+x=1.0;

+y=0;// where all spatial coordinates are in meters.

+

+//Calculation

+//From fig.10-53,The vortex is located 1 m above the point (1, 0) and vortex velocity has positive i direction

+r_vortex=1.00;// m

+V_vortex=[gamma1/(2*%pi*r_vortex) 0];// m/s

+//Similarly, the first source induces a velocity at point (1, 0) at a 45° angle from the x-axis as shown in Fig. 10–53.

+r_source1=sqrt(2);// m

+V_source1=(V1)/(2*%pi*r_source1);// Resultant vector in m/s

+theta=45;// angle between two vectors

+// Function to find the velocity vector in i and j direction from resultant vector

+ function [X]=fric(f)

+    X(1)=f(1)^2 + f(2)^2-V_source1^2; // modulus(r)=sqrt(x^2+y^2)

+    X(2)=tand(theta)*f(1)-f(2);// theta=tan^-1(y/x)

+ endfunction

+

+    f=[0.01 0.01]; // Initial guess to solve X

+    V_source1_vec=fsolve(f,fric);// m/s (Calculating friction factor)

+    

+//Finally, the second source (the sink) induces a velocity straight down i.e in the negative j direction 

+r_source2=1.00;/// m

+V_source2=[0 (V2)/(2*%pi*r_source2)];// m/s

+V=V_vortex+V_source1_vec+V_source2;//The resultant velocity in m/s

+printf('\nThe resultant velocity, V = %0.3fi %1.0fj\n',V);

+