$4\mathrm{.}14$ Consider the points in a fluid with the Cartesian

coordinates given below $($Figure $4\mathrm{.}17)$:

$A(0,0,0),B(1,0,0),C(1,1,0)$

$D(0,1,0),E(0,0,1),$

Figure $4\mathrm{.}17$ Flow domain for Problem $4\mathrm{.}14.$

$($a$)$ At $t=0$ a shear flow given by $v_{?}$ below is

imposed on the flow domain above:

$v_{c\frac{m}{s}}=([3y],[0],[0]{)}_{xyz}$

Where will points $A,B,C,D,$ and $E$ be after $10$

seconds?

$($b$)$ Where would the points be after $10$ seconds

if instead the following elongational flow were

imposed at $t=0?$

$v_{?}=([-x],[-y],[2z]{)}_{xyz}$

$($c$)$ Calculate the rate$-$of$-$deformation tensor ${}_{{?}_{?}}$ and

the magnitude of the rate$-$of$-$deformation tensor

${}^{}-=|{}_{{?}_{?}}|$ for each of the above flows.

$($d$)$ Comment on the similarities and differences be$-$

tween these two flows.