$($a$)$ Verify that the velocity distribution $($c$)$ in Problem $1$B$\mathrm{.}1$ describes a fluid in a state of pure

rotation; that is$,$ the fluid is rotating like a rigid body. What is the angular velocity of

rotation?

$($b$)$ For that flow pattern evaluate the symmetric and antisymmetric combinations of velocity

derivatives:

$($i$)($vy$/$x$)+($vx$/$y$)$

$($ii$)($vy$/$x$)($vx$/$y$)$

$($c$)$ Discuss the results of $($b$)$ in connection with the development in $1\mathrm{.}2.(1)$ Velocity profiles and the stress components

Do problem $1$B$.1$ in $TrPh$; however, replace the velocity profiles given in the

problem statement by

$v_x={}^{}y$ and $v_y=a{}^{}x$ where $a$ is a constant which describes flow type

and ${}^{}$ is the shear rate which we will take as a constant for this problem.

$($a$)a=0$

$($b$)a=1$

$($c$)a=-1$

and skip part $($d$).$

$(2)$ A fluid in a state of rigid rotation

Do problem $1$B$.2$ in $TrPh.$

Note that this problem should now refer to part $($c$)$ as done above in Problem $(1).$