A sphere with diameter $d,$ soaked with ethanol, is kept still in a stream of air. Show by

dimensional analysis that the expression which relates the mass transfer coefficient of the

ethanol evaporation, $k,$ to the sphere diameter $d,$ the mean air velocity, $u,$ the diffusion

coefficient of the ethanol in the air, $D,$ and the air properties, density $$ and viscosity $,$ is of

the form:

$Sh=f(Re,Sc)$

where $Sh=\frac{kd}{D}$ is the Sherwood number, $Re=\frac{du}{}$ is the Reynolds number

and $Sc=\frac{}{D}$ is the Schmidt number.

b$)$ A sphere, $5cm$ in diameter, soaked in ethanol, is within a stream of air. Experiments have

given the following values of the mass transfer coefficient of the ethanol in the air:

For what range of air velocities can the above results be used for a sphere of $2cm$ in diameter

in the same air stream?

c$)$ What would be the mass transfer coefficients in this case?

Air properties: density $=1\mathrm{.}21kg{m}^{-3},$ viscosity $=1\mathrm{.}78{10}^{-5}kg{m}^{-1}{s}^{-1}.$

Diffusion coefficient of ethanol in air $=1\mathrm{.}26{10}^{-5}{m}^2{s}^{-1}.$