A nonionic organic molecule $$A$$ is dissolving and diffusing into a pure carrier

solvent $$B$,$ which is flowing with a certain velocity across a flat surface of pure A$.$ The

dissolution and transfer of A is driven by this fluid flow. The flat surface is $10$ cm long $($x

direction$).$ The height is represented here by the y$-$direction. The kinematic viscosity of B is $6$e$-3$

cm$^2/$s$,$ the diffusivity of A in B is $3$e$-6$ cm$^2/$s$,$ the solubility of A in B $($surface value$)$ is $1$

g$/$cm$^3,$ and the molar mass of A is $200$ g$/$mol$.$ The flow rate across the surface is $2$ L$/$min and

the cross$-$sectional area of this flow is $2$ cm by $10$ cm$.$

$($a$)$ Write out the equation for the Schmidt number and solve. Is Sc above or below $1?$

$($b$)$ Write out the Sherwood number equation and state the known and unknown variables

needed to calculate Sh$.$

$($c$)$ Write out the equation for the Reynolds number. There are some options for the $$length$$

variable $-$ choose the direction across the flat surface. State the known and unknown variables

needed to calculate Re$\_$L and Re$\_$x$.$ You will need to include a value for v$\_$infinity and cA$\_$infinity.

$($d$)$ Write out the Blasius version of the equation for Sherwood number as a function of other

dimensionless numbers, at an arbitrary point $$x$$ along the flat surface $($x $=0$ at the starting edge

of the point, x increasing in the direction of flow$).$ What is the Sherwood number at x $=5$ cm$?$