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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).
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. [1] [2]
Paul Richard Heinrich Blasius derived an exact solution to the above laminar boundary layer equations. [25] The thickness of the boundary layer δ {\displaystyle \delta } is a function of the Reynolds number for laminar flow.
Equation for which the elliptic functions are solutions [12] Euler's differential equation: 1 ... Blasius boundary layer [25] Chandrasekhar's white dwarf equation: 2
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]
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
The above equation, which is derived from Prandtl's one-seventh-power law, [6] provided a reasonable approximation of the drag coefficient of low-Reynolds-number turbulent boundary layers. [7] Compared to laminar flows, the skin friction coefficient of turbulent flows lowers more slowly as the Reynolds number increases.
Paul Richard Heinrich Blasius (9 August 1883 – 24 April 1970) was a German fluid dynamics physicist.He was one of the first students of Prandtl.. Blasius provided a mathematical basis for boundary-layer drag but also showed as early as 1911 that the resistance to flow through smooth pipes could be expressed in terms of the Reynolds number for both laminar and turbulent flow.