Question about fluid statics and dynamics

[farleyknight]

This is not a homework assignment but a general question about something I found in my textbook. It pertains to fluid statics and dynamics and it says that:

We can make the flow of a fluid visible by adding a tracer. This might be a dye injected into many points across a liquid stream or smoke particles added to a gas flow. Each bit of a tracer follows a streamline, which is the path that a tiny element of the fluid would take as the fluid flows. Recall from Chapter 4 that the velocity of a particle is always tangent to the path taken by the particle. Here the particle is the fluid element, and it's velocity v is always tangent to the streamline. For this reason, to streamlines can never intersect; if they did, then an element arriving at their intersection would have two different velocities simultaneously - an impossibility.
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Why is this last statement impossible? Is it saying that two particles floating in water will never touch (something that many people have witnessed, I'm sure)? Or is it more abstract / general than that?

 

[ehild]

Real particles can touch each other as they have some finite size. The streamline is imagined to contain abstract, point-like particles with zero extension.

ehild

 

[farleyknight]

Real particles can touch each other as they have some finite size. The streamline is imagined to contain abstract, point-like particles with zero extension.

ehild

Ah, okay, that makes sense. Thanks for answering.