Long's solution (Q. Jl Mech. Appl. Math. 9 (1956) 385-393) for steady flow
of a rotating liquid into a hydrodynamic sink at the base of a cylinder is
extended to the case where the sink is elevated above the cylinder base. Th
e solution satisfies the nonlinear Euler equations exactly for all sink hei
ghts and for swirl ratios (inverse Rossby numbers) less than a finite criti
cal value. Flow above the elevated sink is qualitatively similar to that in
Long's original solution, while flow beneath the sink is comprised of a ve
ry weak meridional circulation and an intense nearly-potential vortex.