Chapter 4, Problem 68P

Consider the steady, incompressible, two-dimensional flow field of Prob. 4—66. Using the results of Prob. 4—66(a). do the following:
(a) From the fundamental definition of shear strain rate (half of the rate of decrease of the angle between two initially perpendicular lines that intersect at a point), calculate shear strain rate in the xy-plane. (Hint: Use the lower edge and the left edge of the fluid particle, which intersect at 900 at the lower-left corner of the particle at the initial time.)
(b) Compare your results with those obtained from the equation for e in Cartesian coordinates, i.e.,
${\epsilon }_{xy}=\frac{1}{2}\left(\frac{\partial u}{\partial y}+\frac{\partial v}{\partial x}\right)$