Question

a circular disk of radius r is used in an evaporator and is rotated in a vertical plane. If it is to be partially submerged in the liquid so as to maximize the exposed wetted area of the disk, show that the center of the disk should be positioned at a height r/sqrt(1+pi^2) above the surface of the liquid

Answer 1

@amistre64

Answer 2

@SithsAndGiggles

Answer 3

first thought is:

assume y=0 is the water line

set a circle (x-h)^2+y^2=r^2 so that it rides along the y axis

but i feel im missing some information as to what the whetted area has to do with evaporation in order to complete the thought

Answer 4

it would seem to me that any calculation as is to assess the max exposed area of the circle would amount to any h greater than r

Answer 5

or do we assume that the whetted portion forms a "washer" type area on the disc and are trying to create an optimal from that