For the tangential velocity u measured in the free vortex flow region in a turbulent non-baffled agitated vessel with a paddle impeller or a pitched blade paddle impeller, the dimensionless velocity (u/nu(theta),)(beta D/md) was well correlated with the dimensionless radius 2r/D, where the correlation parameter m was expressed by m=2.5(r(c)/,r(d))(2) using the radius of cylindrically rotating zone r(c) and the impeller radius r(d). The tangential velocity near the side wall of the vessel u(D) satisfied the relation (u(D)/nu(theta))(beta D/md)=1.