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).:

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

The above equation may be analytically integrated yielding
 
 

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.

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.