In which direction does the shear stress act on the face AB of the fluid element shown near the plate?

Question

The velocity profile across a boundary layer on a flat plate may be approximated as linear

$V_{x}\left ( x,y \right )=\frac{V_{0}y}{\delta \left ( x \right )}$

Where V₀ is the velocity far away and d(x) is the boundary layer thickness at a distance x from the leading edge, as shown below.

 

(a) Use an appropriate control volume to determine the rate of mass influx into the boundary layer up to x.  (b) Obtain the momentum thickness into the boundary layer up to x.

(c) In which direction (up or down) does the shear stress act on the face AB of the fluid element shown near the plate?