(Solved): Consider a fluid flow characterised by the velocity field in cylindrical coordinates \( (r, \theta, ...

Consider a fluid flow characterised by the velocity field in cylindrical coordinates \( (r, \theta, z) \) \[ \mathbf{V}(r, \theta, z)=2 r \cos (2 \theta) \mathbf{e}_{r}-2 r \sin (2 \theta) \mathbf{e}_{\theta}+6 z \mathbf{e}_{z} . \] (a) Verify that the vector field \( \mathbf{V} \) is conservative, i.e. \( \nabla \times \mathbf{V}=0 \). [10 marks] (b) Derive the representation for the velocity potential for this fluid flow. [15 marks]