Since liquids are incompressible, the amount of liquid inside a closed volume is constant; if there are no sources or sinks inside the volume then the flux of liquid out of "S" is zero. If the liquid is moving, it may flow into the volume at some points on the surface "S" and out of the volume at other points, but the amounts flowing in and out at any moment are equal, so the "net" flux of liquid out of the volume is zero.