A mathematical analysis has been carried out for the axial flow of a Bingham
plastic fluid, in the Concentric Cylinder Viscometer which consists of a cylindrical
sample holder (the cup) and a cylindrical spindle (the bob) coaxial with the cup. The
fluid to be tested flows through the annular gap of the cup and the bob system,
sheared by the rotation of the inner cylinder, while the outer cylinder is held
stationary. This is a case of helical flow in an annular region. An attempt has been
made to direct the analysis toward an examination of the relationship between
moment (M) and angular velocity (?) at the inner cylinder. Since M and ? are
proportional to the shear stress and shear rate respectively, we may thus investigate
the relationship between shear stress and shear rate and the dependence of this on
axial flow rate. We have shown using numerical solutions that axial flow has no
effect on shear rate. A definition for an approximate viscosity has been presented
and a comparison has been made between predicted approximate and true viscosity