Circular Flow in A Bowl or Cup
When water in a circular bowl or cup is moving in circular motion the water displays vortex flow – the water at the center of the bowl or cup spins at relatively high speed, and the water at the perimeter spins more slowly. The water is a little deeper at the perimeter and a little more shallow at the center, and the surface of the water is not flat but displays the characteristic depression toward the axis of the spinning fluid. At any elevation within the water the pressure is a little greater near the perimeter of the bowl or cup where the water is a little deeper, than near the center. The water pressure is a little greater where the water speed is a little slower, and the pressure is a little less where the speed is faster, and this is consistent with Bernoulli's principle.
There is a pressure gradient from the perimeter of the bowl or cup toward the center. This pressure gradient provides the centripetal force necessary for the circular motion of each parcel of water. The pressure gradient also accounts for a secondary flow of the boundary layer in the water flowing across the floor of the bowl or cup. The slower speed of the water in the boundary layer is unable to balance the pressure gradient. The boundary layer spirals inward toward the axis of circulation of the water. On reaching the center the secondary flow is then upward toward the surface, progressively mixing with the primary flow. Near the surface there may also be a slow secondary flow outward toward the perimeter.
The secondary flow along the floor of the bowl or cup can be seen by sprinkling heavy particles such as sugar, sand, rice or tea leaves into the water and then setting the water in circular motion by stirring with a hand or spoon. The boundary layer spirals inward and sweeps the heavier solids into a neat pile in the center of the bowl or cup. With water circulating in a bowl or cup, the primary flow is purely circular and might be expected to fling heavy particles outward to the perimeter. Instead, heavy particles can be seen to congregate in the center as a result of the secondary flow along the floor.
Read more about this topic: Secondary Flow, Examples of Secondary Flows
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