The Momentum Integral Equation of the Boundary Layer

(Two Dimensional Steady Flow)

Consider an element of the boundary layer, AB CD, of unit length normal to the xy plane; the element is defined by two sections AB and CD normal to the surface AD, where AD is a small distance and BC is the edge of the boundary layer. We suppose AB and DC continued to E and F where AE = DF = h, say, and h is slightly greater than the local boundary layer thickness. The surface is flat but the following argument can be readily generalized to slightly curved surfaces and the same resulting formulae apply.

The rate of mass flow across AE into AEFD

and the corresponding rate of mass flow across DF and AE, out of AEFD

smaller terms of order

Hence the net rate of mass flow across DF and AE, out of AEFD

terms of order