Incompressible turbulent flow in a single cavity of the stepped multi-cavity labyrinth seal is numerically analyzed to investigate an effect of the shaft speed on the leakage. SIMPLER algorithm is used to solve governing equations, and low-Reynolds k-$varepsilon$ turbulence model as outlined by Launder and Sharma is adopted to predict turbulent flow. Pressure drops for the cavity with and without the groove are evaluated for four different Reynolds numbers and three different shaft speeds.