Boundary-layer flows: the effect of cross-stream velocity

Boundary-layer flows: the effect of cross-stream velocity. Consider the flow past a flat plate. Here we examine the effect of a superimposed velocity vy0 at the plate surface. This can be done by the integral method with only minor changes in the equations. Verify that the velocity in the y-direction is now given by vyδ = vy0 − 0∫δ ( ∂vx /∂x) dy (15.88) This adds an extra term vy0v∞ to the integral form of the x-momentum balance. The resulting equation can be derived as d/ dx 0∫δ  (v2 x − v∞vx)dy + vy0v∞ = −τw ρ (15.89) Apply a cubic profile and integrate the above equation to get an (implicit) relation for the boundary-layer thickness. Derive this equation and discuss how the boundary-layer thickness changes with the blowing or suction velocity v0.