Question

If an incompressible fluid rotates like a rigid body with an angular velocity, θ ˆ q = ωR , about a vertical zaxis
and gravity, g, is the only external force acting, prove that,
a) −∇gz − 
 ∇p = ∇ 
 ωR − 2ωRR.
b) The pressure at any point in the fluid is given by,



 = r w R - g z + constant
2
1
p 2 2 ,
where ω is a constant and R is the distance from the axis.