Solution
= Solution
The radial momentum equation makes $p$ independent of $r$. The axial <Navier-Stokes equation> reduces to
$$
\boxed{0=-\frac{dp}{dz}
+\mu\frac1r\frac d{dr}\left(r\frac{du}{dr}\right)+\rho g}.
$$
The no-slip boundary conditions are
$$
\boxed{u(\alpha R)=V,\qquad u(R)=0}.
$$