Consider a steady, two-dimensional, incompressible flow of a newtonian fluid in which the velocity field is known: u=-2xy, v=y 2 - x 2 , w=0. (a) does this flow satisfy conservation of mass? (b) find the pressure field, p(x, y) if the pressure at the point (x=0, y=0) is equal to pa.

The flow is 2-dimensional and incompressible. Its velocity field is


Part (a)
Because the flow is incompressible, conservation of mass requires that



The flow satisfies the conservation of mass

Part (b)
Note that

Therefore the pressure field is given by

Also,


Therefore


Because p(0,0) = ρa, therefore
f(0) = g(0) = -ρa.


 

A., d., and f i think