5. Consider a two-dimensional fluid flow characterised by the velocity field V(r, y, 2) = (2² – 2y)i + (3a² – 2ry)j. (a) Verify that the vector field V is solenoidal, i.e. V. V = 0. (b) Evaluate the...

5. Consider a two-dimensional fluid flow characterised by the velocity<br>field<br>V(r, y, 2) = (2² – 2y)i + (3a² – 2ry)j.<br>(a) Verify that the vector field V is solenoidal, i.e. V. V = 0.<br>(b) Evaluate the circulation of V over the path C defined by<br>a(t) = cos(t), y = 3 sin(t), 0<t< 27,<br>%3D<br>where the integration<br>· dr<br>is taken in the anti-clockwise direction.<br>

Extracted text: 5. Consider a two-dimensional fluid flow characterised by the velocity field V(r, y, 2) = (2² – 2y)i + (3a² – 2ry)j. (a) Verify that the vector field V is solenoidal, i.e. V. V = 0. (b) Evaluate the circulation of V over the path C defined by a(t) = cos(t), y = 3 sin(t), 0<>< 27,="" %3d="" where="" the="" integration="" ·="" dr="" is="" taken="" in="" the="" anti-clockwise="">

Jun 04, 2022

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5. Consider a two-dimensional fluid flow characterised by the velocity field V(r, y, 2) = (2² – 2y)i + (3a² – 2ry)j. (a) Verify that the vector field V is solenoidal, i.e. V. V = 0. (b) Evaluate the...

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