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A schematic diagram of the Blasius flow profile. The streamwise velocity component () / is shown, as a function of the similarity variable .. Using scaling arguments, Ludwig Prandtl [1] argued that about half of the terms in the Navier-Stokes equations are negligible in boundary layer flows (except in a small region near the leading edge of the plate).
Schlichting proposed an equivalent substitution that reduces the thermal boundary-layer equation to an ordinary differential equation whose solution is the same incomplete gamma function. [22] Analytic solutions can be derived with the time-dependent self-similar Ansatz for the incompressible boundary layer equations including heat conduction. [23]
The first formula is sometimes called Blasius–Chaplygin formula. [4] The theorem is named after Paul Richard Heinrich Blasius, who derived it in 1911. [5] The Kutta–Joukowski theorem directly follows from this theorem.
The boundary layer thickness, , is the distance normal to the wall to a point where the flow velocity has essentially reached the 'asymptotic' velocity, .Prior to the development of the Moment Method, the lack of an obvious method of defining the boundary layer thickness led much of the flow community in the later half of the 1900s to adopt the location , denoted as and given by
Source: [3] Falkner and Skan generalized the Blasius boundary layer by considering a wedge with an angle of / from some uniform velocity field .Falkner and Skan's first key assumption was that the pressure gradient term in the Prandtl x-momentum equation could be replaced by the differential form of the Bernoulli equation in the high Reynolds number limit. [4]
Self-similar solutions appear whenever the problem lacks a characteristic length or time scale (for example, the Blasius boundary layer of an infinite plate, but not of a finite-length plate). These include, for example, the Blasius boundary layer or the Sedov–Taylor shell .
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The Blasius correlation is the simplest equation for computing the Darcy friction factor. Because the Blasius correlation has no term for pipe roughness, it is valid only to smooth pipes. However, the Blasius correlation is sometimes used in rough pipes because of its simplicity. The Blasius correlation is valid up to the Reynolds number 100000.