Additional Problem $2.$

Given: Uniaxial extensional flow is relevant in several manufacturing processes, such as the stretching flow used to make polypropylene fibers for your N$95$ mask. Consider an idealized velocity field for steady uniaxial extension flow defined by the elongational velocity component

$\backslash [$

v$\_\{$z$\}=\backslash$dot$\{\backslash$varepsilon$\}$ z

$\backslash ]$

where $\backslash (\backslash$dot$\{\backslash$varepsilon$\}\backslash )$ is a constant $($this parameter is known as the extensional strain rate.

Find: Find the other velocity components assuming incompressible flow. Make a sketch of the $3$D velocity field.