Estimation of the Leakage through a Labyrinth Gland

Abstract

The usual theory gives leakage per unit clearance area but this assumes that the successive pressure drops are all small, and further, ignores the fact that with decreasing back pressure the quantity flowing cannot go on increasing indefinitely, but reaches a maximum, and thenceforth any further decrease of back pressure p_n has no effect. Its critical ratio to the initial pressure p ₀ is given in a diagram which also serves to give the progressive pressures along the gland.

For calculating the leakage quantity a method is given, more accurate than the usual formula above. For the case where the kinetic energy of the fluid is not completely destroyed at each stage, the consequent increase of leakage can be assessed by a correction factor given by a formula made to agree with some test results, but based on the fundamental idea that the stream spreads out conically from the cylindrical surface at a small angle.