For the turbulent boundary layer at the side wall of an agitated vessel without baffles, new dimensionless variables u(++) and y(++) were derived as u(theta)(+) (beta D/1.7d) and y(+)(beta D/1.7d), respectively, instead of the dimensionless variables u(theta)(+) and y(+), in the universal velocity distribution law. The correlation of the measured tangential velocity at the side wall of an agitated vessel without baffles with u(++) and y(++) satisfied the logarithmic expression of the universal velocity distribution law in the range 20 < y(++) < 70 for the paddle impeller having a larger value of the impeller similarity parameter than 0.1. This meant that the mixing length for an agitated vessel was beta D/1.7d times that for a flat plate. Besides the tangential velocity at the turbulent boundary layer edge u(D). and the boundary layer thickness y(D)) were roughly expressed as 0.85(d/D)U-D and 0.030(1.7d/beta D)L, respectively.