Step: 1

Write the expression for steady, two dimensional, incompressible velocity field.

Write the velocity components u and v.

Find the differentiation of velocity components.


Find the differentiation of velocity components with respect to time.

Step: 2

Check the velocity field satisfies the two dimensional, incompressible continuity equation or not.
Write the two dimensional continuity equation.

Substitute for and for 

Hence continuity equation satisfied.

Step: 3

Write the x-component of the two dimensional incompressible Navier-Stokes equation.

Here,  is density, is gravity along x direction, and is dynamic viscosity.
Substitute 0 for , 0 for , 0 for ,  for , for , for u, for v,  for , 0 for , and 0 for 

Now, differentiate the above equation with respect to y.

Now, take the y-component of the two dimensional incompressible Navier-Stokes equation.

Substitute 0 for , 0 for , 0 for ,  for , for , 2ax for , for u, for v, 0 for , 0 for , and 0 for 

Now, differentiate the above equation with respect to x.

Since Hence P is not a smooth function of x and y.
Therefore, the pressure as a function of x and y cannot be calculated.