simple flow type. Layers of liquid appear to slide over each other. A volume
element is sheared, as depicted in Figure 5.2, but it is also rotated (its
diagonal rotates). Simple shear is a rotating flow, and the rotation rate is
half the velocity gradient. The gradient is in a direction perpendicular to the
direction of flow.
Most people envisage simple shear when laminar flow is considered,
but it is not the most common type of flow. To begin with, intermediate
types generally occur. An example is the flow type in Figure 5.1a. In the
center it is purely rotating, but moving away from the center of rotation, i.e.,
at increasingr, the flow becomes ever more similar to simple shear. Also
when going from either axis outwards in Figure 5.1c, an increasing amount
of shear flow is introduced.
Moreover, most flows are not two-dimensional as in Figure 5.1, where
the flow pattern does not change in thez-direction. Consider Figure 5.1c and
rotate it around one of the axes: it then representsaxisymmetric flow.By
rotation around the x-axis, uniaxial elongational flowin thex-direction
results; a practical example is flow through a constriction in a tube. By
rotation around they-axis,biaxial elongational flowin thex,z-plane results;
a practical example is squeezing flow between two closely approachingFIGURE5.2 Explanation of the type of strain occurring in a volume element
subjected to simple shear (shear strain) or to elongation (strain expressed as Hencky
strain).