A velocity field is defined by V(x, y) = [2] Three paths C, C2 and C3...

 

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A velocity field is defined by V(x, y) = [2] Three paths C₁, C2 and C3 are shown below, where C₁ is a circular arc with its centre at the origin, x is constant along C₂ and y is constant along C3. O 2 Figure Q3 Evaluate directly the line integral of V(x, y) along the path C₁. (12 marks) (b) Evaluate directly the line integral of V(x, y) along the path C₂. (6 marks) Using Green's theorem, evaluate the line integral of V(x, y) along the path C3. (6 marks) A velocity field is defined by V(x, y) = [2] Three paths C₁, C2 and C3 are shown below, where C₁ is a circular arc with its centre at the origin, x is constant along C₂ and y is constant along C3. O 2 Figure Q3 Evaluate directly the line integral of V(x, y) along the path C₁. (12 marks) (b) Evaluate directly the line integral of V(x, y) along the path C₂. (6 marks) Using Green's theorem, evaluate the line integral of V(x, y) along the path C3. (6 marks)