SOURCES AND SINKS AT AXIS OF A VISCOUS ROTATING FLUID

Theoretical and experimental investigations have been made for the problem of a source or sink at the axis of a viscous, incompressible, steady, unbounded rotating fluid. For the sake of generality, the theoretical portion of this paper also includes a uniform axial velocity. It is found that the velocity distributions have similarity forms at the distant wake along the axis of rotation using the Fourier transform technique. An inverse coordinate expansion technique is then used. This procedure not only brings out the nature of the approximation very clearly but also allows higher-order solutions to be calculated. The zeroth-order solution indicates that there exists a withdrawal viscous core which grows in radius with the axial distance x* from the sink at the rate x*1/3. The first-order solutions are also calculated. The experimental results agree very well with the theoretical predictions.