The problem of the through-flow across annuli of fine clearance has been investigated both theoretically and experimentally. The study includes the effects due to the relative motion of the walls and to varying degrees of eccentricity of the bounding surface. The experimental work was carried up to a Reynolds number, based on the diametral clearance, of 30,000. The theoretical results are presented both graphically and in the form of equations. Nomographs are included for rapid solution of certain engineering problems.