The turbomachine comprises a stationary casing with a rotating member configured to rotate about a rotation axis in the stationary casing. The turbomachine further includes a rotating balance drum, arranged for co-rotation with the rotating member. A stationary sleeve is arranged in a fixed relationship with the stationary casing and surrounds the balance drum. The stationary sleeve comprises a plurality of consecutively arranged sleeve sections. A fluid channel is defined by an outer surface of the balance drum and an inner surface of the stationary sleeve. Between at least one pair of sequentially arranged upstream sleeve section and downstream sleeve section an annular chamber is provided, fluidly coupled to the fluid channel. Shunt holes are arranged on the upstream sleeve section, each shunt hole having a shunt hole inlet on an inner surface of the upstream sleeve section, and a shunt hole outlet in the annular chamber.