A two dimensional velocity field is given by

V = (x² – y² + x) i – (2xy – y) j

The convective acceleration at (x, y) = (1, 2) is

Concept:

Convective acceleration in the x-direction is given by

Where u, v and w are the velocities in the x, y and z-direction respectively.

Calculation:

V = (x² – y² + x) i – (2xy – y) j = u i + v j + w k

u = (x² – y² + x),  v = – (2xy – y), and w = 0

We need to find out the convective acceleration at (x, y) = (1, 2)

At point (1, 2) x component

y, Component,

At point (1, 2) y component

Total convective acceleration,

a = a_x i + a_y j = 2 i + 10 j

Hence the magnitude of acceleration,

So no option matches.