$(25$ pts$)$ Read Example Problem $10-3$ in the text carefully, and then do the following:

$($a$)$ Write out all the terms of the $r,,$ and $z$ components of the Euler equation in cylindrical coordinates.

$($b$)$ Verify that the velocity and pressure fields of Example Problem $10-3$ satisfy the continuity equation and all thre components and $z)$ of the Euler equation, showing all your work.

$($c$)$ Calculate the vorticity vector. Is this flow rotational or irrotational?