Pressure distribution in unsteady sink and source flows

Basic flow generated in a viscous incompressible fluid by a "point" sink (source) of mass is revised. In practice, such flow can be modeled by sucking (pushing) fluid from a thin tube with a small porous sphere at one end. Intuitively, by sucking (pushing) fluid, one creates low (high) pressure near the origin and a positive (negative) radial pressure gradient drives the fluid to (from) the origin. A simple analysis, however, shows that the pressure distribution for both steady flows is the same. Then a question arises: How does the fluid "know" in what direction to flow? To explain this "paradox" an unsteady flow is considered and the pressure terms responsible for the flow direction are derived.