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Since the static pressure is independent of , then pressure at the edge of the boundary layer is the pressure throughout the boundary layer at a given streamwise position. The external pressure may be obtained through an application of Bernoulli's equation .
The tendency of a boundary layer to separate primarily depends on the distribution of the adverse or negative edge velocity gradient / < along the surface, which in turn is directly related to the pressure and its gradient by the differential form of the Bernoulli relation, which is the same as the momentum equation for the outer inviscid flow.
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
In fluid dynamics, an adverse pressure gradient is a pressure gradient in which the static pressure increases in the direction of the flow. Mathematically this is expressed as dP/dx > 0 for a flow in the positive x-direction. This is important for boundary layers.
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).
The basis of the Falkner-Skan approach are the Prandtl boundary layer equations. Ludwig Prandtl [2] simplified the equations for fluid flowing along a wall (wedge) by dividing the flow into two areas: one close to the wall dominated by viscosity, and one outside this near-wall boundary layer region where viscosity can be neglected without significant effects on the solution.
This turbulent boundary layer thickness formula assumes 1) the flow is turbulent right from the start of the boundary layer and 2) the turbulent boundary layer behaves in a geometrically similar manner (i.e. the velocity profiles are geometrically similar along the flow in the x-direction, differing only by stretching factors in and (,) [5 ...
At least one author takes a different approach in order to avoid a need for the expression freestream static pressure. Gracey has written "The static pressure is the atmospheric pressure at the flight level of the aircraft". [15] [16] Gracey then refers to the air pressure at any point close to the aircraft as the local static pressure.