Laminar boundary layer flow perpendicular

In terms of hydrodynamics, the boundary layer thickness is measured from the solid surface (in the direction perpendicular to a particle s surface, for instance) to an arbitrarily chosen point, e.g., where the velocity is 90-99% of the stream velocity or the bulk flow ((590 or (599, respectively). Thus, the breadth of the boundary layer depends ad definitionem on the selection of the reference point and includes the laminar boundary layer as well as possibly a portion of a turbulent boundary layer. 

The velocity of laminar flows (discussed in Chap. 6) and of boundary-layer flows (discussed in Chap. 11) changes rapidly with distance perpendicular to the flow, so that the flow into or out of a system must always be calculated by an integral of the form of Eq. 3.14. However, in most industrial flows in pipes or channels, the velocity is practically constant across the entire cross section of the pipe or channel (except in a very thin layer near the pipe or channel wall). The density and velocity of these flows may be considered constant across the cross section, and then the integrations in Eqs. 3.13 and 3.14 can be easily performed, giving... 

The properly (equation [1.31]) of bormdary layers regarding the pressure gradient is of the same nature as the property of pressure uniformity in planes perpendicular to the flow direction, which was observed for the Poiseuille and Couette solutions. Figure 1.6(a) shows that the bormdary layer thickness on a flat plate grows with increasing values of x. At a sufficient distance from the inlet of a pipe, the boundary layer thickness eventually exceeds the diameter of the pipe. The flow reverts to the Poiseuille type solutiou presented previously, if the Reynolds number is sufficiently low to allow the flow to remain laminar. Such flows are termed established laminar flows or developed flows , as the velocity field does not change any more when traveling downstream in the pipe, because the boundary... 

Within the flow channel, a parabolic flow profile is created because of the laminar flow of the liquid. As a result, the stream moves slower closer to the boundary edges than it does at the center of the channel flow. When a perpendicular force field, in this case, fluid cross-flow, is applied to the flowing, laminar stream, the analytes are driven toward the boundary layer of the channel. 

Movement of a soluble chemical throughout a water body such as a lake or river is governed by thermal, gravitational, or wind-induced convection currents that set up laminar, or nearly frictionless, flows, and also by turbulent effects caused by inhomogeneities at the boundaries of the aqueous phase. In a river, for example, convective flows transport solutes in a nearly uniform, constant-velocity manner near the center of the stream due to the mass motion of the current, but the friction between the water and the bottom also sets up eddies that move parcels of water about in more randomized and less precisely describable patterns where the instantaneous velocity of the fluid fluctuates rapidly over a relatively short spatial distance. The dissolved constituents of the water parcel move with them in a process called eddy diffusion, or eddy dispersion. Horizontal eddy diffusion is often many times faster than vertical diffusion, so that chemicals spread sideways from a point of discharge much faster than perpendicular to it (Thomas, 1990). In a temperature- and density-stratified water body such as a lake or the ocean, movement of water parcels and their associated solutes will be restricted by currents confined to the stratified layers, and rates of exchange of materials between the layers will be slow. 

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