Unsteady flow of a viscous fluid through an annulus

One boundary of an annulus is fixed, and other boundary is subjected to a series of pulses. The fluid in the annulus, therefore acquires a velocity, relative to the annulus, due to the transfer of momentum from the boundary by viscous stresses. The flow relative to the annulus is determined when a constant pressure gradient and a series of pulses act together. The velocity profiles for unsteady motion, are plotted for various times and for a fixed radii ratio.