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 æ(t) = cos(t), y = 3 sin(t), 0

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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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 circulation of V over the path C defined by
a(t) = cos(t), y = 3 sin(t), 0<t< 27,
%3D
where the integration
· dr
is taken in the anti-clockwise direction.
Transcribed Image 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<t< 27, %3D where the integration · dr is taken in the anti-clockwise direction.
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