4. (10 Points) Consider the set of scaled, nondimensional variables for a boundary layer over a flat plate I x* L y* = 1 u vL = P* Uo8 P-P PUZ where L is the length of plate, & is the thickness of the boundary layer, U is the velocity parallel to the surface at a height 8 above the surface, p is the fluid density, and P is the pressure far away from the plate. (a) For each term in the y-component of the Navier-Stokes equation Iv Iv u- +v. 1 Jv Jv +v- +v 2 give the scale in terms of the parameters L, 8, U and v. (1) (b) Based on relative scales of each term, argue that only the pressure gradient term should be retained when considering the boundary layer approximation 8/L <1. Hint: recall that the Reynold's number ReL = UL/v 1 when the boundary layer approximation is applicable.