We present an experimental and numerical study of a rotating fluid with a zonal flow produced from small-scale eddies, a common feature of many planetary systems. The apparatus consists of a water-filled annular tank with a sloped bottom. Flow is forced mechanically at small, non-axisymmetric scales. Potential vorticity is materially conserved and well-mixed. This implies the existence of nonzero axisymmetric vorticity and therefore of zonal flow, which has three zones in this case. The strength of zonal flow has an upper bound imposed by complete depletion of the beta-plane potential vorticity reservoir.