Pasta can be bought fresh or dry. Fresh pasta has a high moisture content, which makes it susceptible to grow microorganisms. Because of its long shelf life, dry pasta is widely available. Spaghetti strands coming out of an extrusion process are dried by exposing them to a continuous flow of relatively dry air. Drying would be faster at high temperatures but tem$-$ peratures above $60\backslash$deg C are known to modify the starches in pasta to a point that flavor and texture are compromised.

Consider a long, cylindrical spaghetti strand $($D $=2\mathrm{.}4$ mm$).$ The spa$-$ ghetti comes out of the extruder with a moisture content cA$0=0\mathrm{.}55$ g water$/$cm$3.$ A flow of air at $55\backslash$deg C and relative humidity of $5\%$ is estab$-$ lished perpendicular to the spaghetti. The air velocity far from the spa$-$ ghetti is $10$ cm$/$s$.$ For a fluid flowing perpendicular to a cylinder in laminar flow, the mass transfer coefficient can be estimated from the empirical correlation

Sh $=(0\mathrm{.}4$Re$1/2+0\mathrm{.}06$Re$2/3)$Sc$0\mathrm{.}4$

where the velocity in the Reynolds number is the velocity far from the cyl$-$ inder, and the characteristic length used in the definition of the Reynolds and Sherwood numbers is the cylinder diameter.

Estimate the time that the spaghetti must spend in the air flow to remove $80\%$ of its initial water content.