In a two-dimensional velocity field with velocities u and

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In a two-dimensional velocity field with velocities u and v along the x and y directions respectively, the convective acceleration along the x-direction is given by

1. u ∂V + v ∂u
  ∂x ∂y
2. u ∂u + v ∂v
  ∂x ∂y
3. u ∂u + v ∂u
  ∂x ∂y
4. u ∂u + u ∂u
  ∂x ∂y

Correct Option: C

Two dimensional velocity field with velocities u, v and along x and y direction.
∴ Acceleration along x direction, a_x = a_convective + a_{temporal or local}

= u	∂u	+ v	∂u	+ w	∂u	+	∂u
	∂x		∂y		∂z		∂t

Since, (∂u/∂z) = 0 for 2-dimensional field, therefore

Convective acceleration u	∂u	+ v	∂u
	∂x		∂y