If an incompressible fluid rotates like a rigid body with an angular velocity, θ ˆ q = ωR , about a vertical zaxis

Question

and gravity, g, is the only external force acting, prove that,
a) −∇�gz� − �
� ∇p = ∇ ��
� ω�R�� − 2ω�RR�.
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.