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The displacement thickness, or , is the normal distance to a reference plane representing the lower edge of a hypothetical inviscid fluid of uniform velocity that has the same flow rate as occurs in the real fluid with the boundary layer. [6]
The displacement thickness, δ D , is the distance at which the undisturbed outer flow is displaced from the boundary by a stagnant layer of fluid that removes the same mass flow as the actual boundary layer
A second measure of the boundary-layer thickness, and one in which there is no arbitrariness, is the displacement thickness, which is commonly denoted δ ∗ or δ 1. It is defined as the thickness of a layer of zero-velocity fluid that has the same velocity deficit as the actual boundary layer.
The displacement thickness, δ1, and momentum thickness, δ2, are often used as a measure of the thickness of the boundary layer but are not actually the boundary layer thickness; these two are important parameters in the analysis of the frictional forces on the surface.
Solution to Boundary Layer on a Free Surface (PDF) This section provides readings, class notes, videos seen during class, and problems with solutions for two lectures on boundary layers, separation, and drag.
Definition of Displacement Thickness. δ * = the distance that a streamline just outside the BL is deflected away from the wall due to the effect of the BL; the distance in which the outer flow is “displaced” away from the wall. streamlines. lines of δ and δ * Figures. Alternate Definition:
Displacement thickness, often represented as \(\delta^*\), is a fundamental concept in the realm of fluid dynamics, particularly in the study of boundary layer theory. This concept is pivotal in understanding how a fluid flow is affected by the presence of a solid surface.
Determine the mass flow rate through the channel in terms of the displacement thickness. H/2 H/2 core velocity, U’ boundary layer velocity, u(y) free stream velocity, U
One can define the thickness of the boundary layer to be the amount of this displacement. The displacement thickness depends on the Reynolds number which is the ratio of inertial (resistant to change or motion) forces to viscous (heavy and gluey) forces and is given by the equation : Reynolds number (Re) equals velocity (V) times density (r ...
99% boundary layer thickness, or 99%. This thickness definition is the most commonly used definition. The boundary layer thickness, , is defined as the distance from the boundary at which the fluid velocity, u, is 99% that of the outer velocity, U (Figure 9.2), displacement thickness, D or ⇤.