The diagrams shown represent the boundaries of the layers of a viscous liquid that move at different speeds when the liquid flows through a pipe. Which of the diagrams correctly represents the boundaries of the layers for the liquid?
In these two diagrams, (A) and (B), we see the outline of the pipe that these layers of liquid flow through. And in the solid lines between these outlines, we see the purported boundaries of the fluid layers. If we were to look at these two pipes end on, then the boundaries would look a bit like this. In diagram (A), the boundaries between layers of liquid are concentric circles. In diagram (B) though, the fluid seems to move in horizontal layers through the pipe.
An important point to realize about separate layers in an overall flow pattern is that the different layers represent different flow speeds. So, for example, in our sketch of diagram (A), this outer layer of the liquid will flow through the pipe at a different speed than this layer next to it, which will flow through the pipe at a different speed than this layer and so on. Since the outer layer in sketch (A) is in contact with the surface of the pipe, it makes sense that this whole layer would move with the same speed, and then the same thing is true for interior layers of the fluid flow.
If we look at scenario (B) though, we see that the layers are divided up in a surprising way. By arranging the boundaries in this horizontal line pattern, we’re saying that this layer of liquid moves at a different speed than this one which moves at a different speed than this one, and then this one, and so on. We would expect, though, that all the parts of the liquid that are in contact with the pipe would be flowing at the same speed. And then it’s reasonable to think that the layer interior to that outer layer would also be flowing through the pipe at the same speed.
We’re finding then that the boundary pattern depicted in sketch (A) makes more physical sense than that in sketch (B). Because the shape of the pipe itself is a circle, we would expect that the boundaries between layers of liquid flowing through the pipe are also in the shape of circles. This pattern of concentric rings is demonstrated in diagram (A). This is the diagram that correctly represents the boundaries of the layers for this liquid.