XI. Thwaites' Integral method for Laminar Incompressible Boundary Layers

	This is an empirical method based on the observation that most laminar boundary layers obey the following relationship (Ref: Thawites, B., Incompressible Aerodynamics, Clarendon Press, Oxford, 1960).:

(1)
	Thwaites recommends A = 0.45 and B = 6 as the best empirical fit.

	The above equation may be analytically integrated yielding

(2)
	For blunt bodies such as airfoils, the edge velocity ue is zero at x=0, the stagnation point. For sharp nosed geometries such as a flat plate, the momentum thickness q is zero at the leading edge. Thus, the term in the square bracket always vanishes.

	The integral may be evaluated, at least numerically when ue is known.

	After q  is found, the following relations are used to compute the shape factor H and the shear stress at the wall tw.

(3)
and,

	Despite the empiricism involved in the above formulas, Thwaites' integral method is considered to be the best of a variety of integral boundary layer methods.