3. Consider a fluid flow in spherical coordinates (p, 0,0). (a) Assuming that the velocity field...

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3. Consider a fluid flow in spherical coordinates (p, 0,0). (a) Assuming that the velocity field V is characterised by the velocity potential (p), derive the representation for V in terms of and show that V xe,=0. [12 marks] (b) For a particular case when the velocity potential has the form $(p, 0,0) = -p-¹, show that when p 0 the velocity field is given by V = p ² ep₁ and evaluate div V. [13 marks] 3. Consider a fluid flow in spherical coordinates (p, 0,0). (a) Assuming that the velocity field V is characterised by the velocity potential (p), derive the representation for V in terms of and show that V xe,=0. [12 marks] (b) For a particular case when the velocity potential has the form $(p, 0,0) = -p-¹, show that when p 0 the velocity field is given by V = p ² ep₁ and evaluate div V. [13 marks]