Flow between Long Concentric Cylinders

Consider the flow in an annular space between two fixed, concentric cylinders as shown in Fig. 5.3.3. The fluid is having constant density and viscosity . The inner cylinder rotates at an angular velocity and the outer cylinder is fixed. There is no axial motion or end effects i.e. and no change in velocity in the direction of θ i.e. . The inner and the outer cylinders have radii , respectively and the velocity varies in the direction of only.

Fig. 5.3.3: Flow through an annulus.

The continuity and momentum equation may be written in cylindrical coordinates as follow;

(5.3.5)