Special importance in Fluid Mechanics have thin shear layers or slender longitudinal shear regions with one dominating flow direction, characterised by large transverse slope
/ of the velocity profile = f(). Quite often these flows possess direct practical significance in technology - we have already learned about the submerged jet and its applications, which is an example of such flows. Another example is the boundary layer, which develops at the wall of a body. Processes (such as flow separation or transition to turbulence) that take place in the boundary layer may have a decisive influence upon the whole flowfield.
Fig.I-1 Schematic representation of the shear flow between two streams having
different velocity. There is a dominant flow in one direction, aligned with which is
the axis . Typical is small transverse dimension - thickness - and substantial
change of velocity in transverse direction.
According to Fig. D-5 the transverse gradient
/ is associated with (in laminar flow it is proportional to) shear stress. Large acting shear stress may give rise to extraordinary phenomena. Especially important phenomenon is turbulence - which can evolve and exist permanently only in a shear region. The key importance of shear flows is the reason why they are in the focus of attention in contemporary Fluid Mechanics. Some of their aspects, however, are extremely complicated - and e.g. turbulence belongs among the least understood phenomena in science.
For any deep study of shear flows, the one-dimensional approach followed in the present textbook cannot be sufficient. Nevertheless, even within its frame it is possible to show some basic concepts and relations. We shall learn some simplest cases in which the results can be obtained by integration along a single axis - even if the integration path will here often follow the transverse co-ordinate . The general equation of shear flows is not presented - instead, its particular forms for simplified situations will be derived in each individual case by following force balance on an infinitesimal fluid volume.
First we shall study elementary problems in which the friction forces, generated by the shear flow, are in equilibrium with pressure forces and gravity forces. Of real interest, however, in advanced studies of shear flows are the regions in which the frictional forces are balanced by inertial forces.


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This is page Nr. I01 from textbook Vaclav TESAR : "BASIC FLUID MECHANICS"
Any comments and suggestions concerning this text may be mailed to the author to his address tesar@fsid.cvut.cz

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