A damper floating ring seal with round hole pattern surfaces is suggested for better leakage control. The flat plate test of the round hole pattern surfaces has been performed to yield an empirical friction factor model. The exact predictions of the lock­up position of the damper floating ring, the leakage performance, and the rotordynamic coefficients of the seal are necessary to evaluate the rotordynamic performance of the turbo pump unit. The governing equations including the empirical friction factor model for round hole pattern surfaces are solved by the Fast Fourier Transform method. The lock­up position, leakage flow rate, and rotordynamic coefficients are evaluated according to the geometric parameters of the damper floating ring seal. Theoretical results show that the damper floating ring seals yield less leakage and better rotordynamic stability than the floating ring seal with a smooth surface.