We know that velocity in stream direction (u) gradually decreases along the axial distance on a flat plate or del (u)/del (x) is negative. So, using equation of continuity this means for an incompressible 2d flow, del v/del y should increase. But physically we don't observe any flow in y direction. How to explain this?
Dear Svsr, I suppose that x-direction is the normal axial direction to the plate, while (y, z) are direction on the plate surface. The stream is a 3D flow, therefore dv/dy + dw/dz is increasing, not only dv/dy. On the plate, flow has a radial component. Gianluca
For the 2D BL flow (x- streamwise direction, y- normal to wall direction), the well known Prandtl solution shows that it exists a component v in the BL. But the order of magnitude is smaller compared to u and becomes as much disregardeble as the viscosity diminuishes.
If the experimental measure was accurate, you will see a small deviation of the stream-line from the x-direction.
Have a look to Chap.10 in the book of Kundu.
As Filippo mentioned, if you mean developing flow over a flat plate, there must be a small velocity component in the orthogonal or normal direction since the velocity near the plate surface in the boundary layer decreases. Otherwise, the flow could not satisfy the continuity equation. In laminar flow, the boundary layer (in theory) continues to grow with increasing distance along the wall, which means the normal velocity component remains finite. However, if the boundary layer becomes turbulent, the normal component can eventually become zero.
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