Laminar Flows. These exist in several types, depending on the
geometrical constraints. Some examples are shown in Figure 5.1. An
important characteristic of laminar flow is thevelocity gradientC, defined in
the figure. Figure 5.1a shows purerotational flow(circular streamlines); here,
a volume element in the center will only rotate and not be displaced
(‘‘translated’’) nor deformed. The rotation rate equals the velocity gradient.
Figure 5.1c shows hyperbolic streamlines, an example ofelongational flow
(also called extensional flow). A volume element in the center will be
deformed by elongation, as depicted in Figure 5.2. The velocity gradient is in
the direction of the flow. There is no rotation. Figure 5.1b depicts what is
calledsimple shear flow (straight streamlines), although it is not such a
FIGURE5.1 Cross sections through three types of laminar flow. The upper row
gives the streamlines, the second row the velocity profiles. The flows are two-
dimensional, implying that the patterns do not change in the z-direction
(perpendicular to the plane of the figure).C¼velocity gradient,v¼linear flow
velocity,R¼rotation rate,o¼rotation frequency.