Although the leakage flow through labyrinth seals under stationary con
ditions has been examined by many investigators a reliable prediction
of the effect of various labyrinth parameters on leakage rate has not
been reported so far. The theoretical models for the seals proposed in
most of the previous literature provided results with considerable di
fferences and contradictions in some cases. The structure of the lamin
ar incompressible flow and the performance of a number of seals of var
ious shapes for both stationary and rotating conditions are investigat
ed in this paper. The theoretical treatment is based on the formulatio
n of three-dimensional axisymmetric momentum and continuity equations
for labyrinth shapes having small height to radius ratio as is always
the case in turbomachinery, rotodynamic pumps and many hydraulic devic
es. It is found in this paper that shaft rotation is only beneficial f
or the up-the-step seal, has no effect on grooved shaft and grooved ca
sing seals and has an adverse effect on the down-the-step seal. It is
also found that the use of a smaller clearance size at the entrance ma
kes some improvement in the performance of the grooved shaft and down-
the-step seals depending on the value of the height to width ratio of
the seal. Copyright (C) 1996 Elsevier Science Ltd