Africtionless, incompressible steady flow field is given by v = 2xyi − y2j (2) in arbitrary units. let the density be rhoo = constant and neglect gravity. find expressions for the pressure gradients in both the x and y directions.

pressure gradient in x direction:

pressure gradient in y direction:

Explanation:

Here the gravity is neglected and the field velocities is time independent, so we can use a simplify equation to Navier-Stokes.

V: Field Flow

ρ: Density

p: pressure

Before finding the pressure, let's define the components of the field vector.

Now, the x component pressure gradient will be:

We can apply the same analyze to find the y component of the pressure gradient. We just need to take the partial derivative from v.

I hope it helps you! :)