Superfluid vortex dynamics on the surface of an infinite cylinder differs significantly from that on a plane. The requirement that a condensate wave function be single valued upon once encircling the cylinder means that such a single vortex cannot remain stationary. Instead, it acquires one of a series of quantized translational velocities around the circumference. The dynamics of a single vortex on a finite cylinder provides a hydrodynamic analog of Laughlin pumping. A cylinder is topologically equivalent to a planar annulus, and on an annulus Laughlin pumping may be more accessible to experimental observation.