 
Summary: Turning Moment of Rotating Inner Cylinder
in the Entry Region of Concentric Annuli*
M.A.L. ELSHAARAWI* *, M.O. BUDAIR**
and M.S.A. ALQAHTANI* *
This paper is concerned with calculating the tangential shear stress and the torque
required to turn the inner shaft of concentric annuli having a laminar flow with
simultaneously developing tangential and axial boundary layers. The nondimensional
governing equations have been numerically solved over a wide range of the annulus
radius ratio (N=0.5  0.95) and the ratio of the square of Reynolds nurnber to Taylor
number (Re2/Ta=0.3  10). The results clarify the effect of these two controlling
pararneters ( N and Re2/Ta) on the torque and show that the assumption of whole
channel fully developed flow leads to a considerable underestimation of the values of
the torque.
Key Words: Annulus, Rotating Inner Boundary, Turning Torque
1. Introduction
Fluid flow between concentric cylinders with
inner rotating walls is of practical importance in
many industrial applications. In the field of electric
motors and generators, knowledge of the
hydrodynamic features of such fluid flow is needed to
