Editing Boundary layer (section)

===Von Kármán momentum integral===
[[Theodore von Kármán|Von Kármán]] derived the integral equation by integrating the boundary layer equation across the boundary layer in 1921.<ref>{{Cite journal|doi = 10.1002/zamm.19210010401|title = Über laminare und turbulente Reibung|year = 1921|last1 = von Kármán|first1 = T.|journal = Zeitschrift für Angewandte Mathematik und Mechanik|volume = 1|issue = 4|pages = 233–252|bibcode = 1921ZaMM....1..233K|url = https://zenodo.org/record/1447403}}</ref> The equation is

:<math>\frac{\tau_w}{\rho U^2 } = \frac{1}{U^2}\frac{\partial }{\partial t}(U\delta_1) + \frac{\partial \delta_2}{\partial x} +\frac{2\delta_2+\delta_1}{U} \frac{\partial U}{\partial x} + \frac{v_w}{U} </math>

where

:<math>\tau_w = \mu \left( \frac{\partial u}{\partial y}\right)_{y=0}, \quad v_w = v(x,0,t), \quad \delta_1 = \int_0^\infty \left(1- \frac{u}{U} \right) \, dy, \quad \delta_2 = \int_0^\infty \frac{u}{U} \left(1- \frac{u}{U}\right) \, dy</math>

:<math>\tau_w</math> is the wall shear stress, <math>v_w</math> is the suction/injection velocity at the wall, <math>\delta_1</math> is the displacement thickness and <math>\delta_2</math> is the momentum thickness. [[Kármán–Pohlhausen Approximation]] is derived from this equation.