$-$ The critical Reynolds number, $\backslash ($ R e$\_\{$c$\}\backslash )$ is associated with the laminar$-$turbulent transition, in which a laminar flow becomes turbulent.

$-$ As mentioned during the lecture, $\backslash ($ R e $\backslash )$ depends on the geometry of the flow.

$1.$ Identify what is the "characteristic dimension" based on the following geometry.

$-$ Flow in a pipe

$-$ Flow over the flat plate

$-$ Flow across a sphere