I am confused by this idea. If a flow is steady, its streamlines are unchanging. Taking the typical example of an airfoil, there is (at least) one streamline which will hit the leading edge of the airfoil and stagnate. Stagnation point is defined as:
a point in a flow field where the local velocity of the fluid is zero.
Now my question is, if the velocity here is zero, and fluid particles that pass through the streamline which results in a stagnation point have nonzero velocity upstream, where do these fluid particles go? Since they are on the streamline, they have to reach the stagnation point? Does this not defy the conservation of mass law?
Further, an online Fluid Mechanics course I have been following has in one lecture shown streamlines going away from the stagnation point. If the velocity at this point is precisely zero (and is unchanging since the flow is steady), then how can the fluid particles go in other directions?
I must be missing something, do enlighten me.