Chapter 5, Problem 32P

The velocity field within a laminar boundary layer is approximated by the expression

$\stackrel{\to }{V}=\frac{AUy}{x^{1/2}}\hat{i}+\frac{AU{y}^2}{4x^{3/2}}\hat{j}$

In this expression, A = 141 m^-1/2, and U = 0.240 m/s is the free-stream velocity. Show that this velocity field represents a possible incompressible flow. Calculate the acceleration of a fluid particle at point (x, y) = (0.5 m, 5 mm). Determine the slope of the streamline through the point.