Problem $2$

Consider a $3$D steady flow of a Newtonian liquid, with a velocity field given as$-$

$u=$axhat$(i)+$ayhat$(j)-2$azhat$(k)$

There are no body forces acting on the flow and the pressure at the origin $(0,0,0)$ is a stagnation pressure $p_0.$

a$)$ Prove that the flow is incompressible.

b$)$ Prove that the flow can be treated as inviscid.

c$)$ Determine the pressure field, noting that the pressure at the origin is po$.$ Show detailed work.