Sink flow is the opposite of source flow. The streamlines are radial, directed inwards to the line source. As we get closer to the sink, area of flow decreases. In order to satisfy the continuity equation, the streamlines get bunched closer and the velocity increases as we get closer to the source. As with source flow, the velocity at all points equidistant from the sink is equal.
The velocity of the flow around the sink can be given by –
The stream function associated with sink flow is –
The flow around a line sink is irrotational and can be derived from velocity potential. The velocity potential around a sink can be given by –