Optimizing Disk Submersion Height for Maximum Wetted Area

[fghtffyrdmns]

Homework Statement

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 liquids as to maximize the exposed wetted area of the disk, show that the center of the disk should be positioned at a height $$r/ \sqrt{1+\pi^2}$$

The Attempt at a Solution

I do not know how to start this. Would I differentiate and then determine the when it is zero?

 

[lanedance]

start by picturing the disk in the fluid

the way i have, as it rotates, there will be a disk of wet section, with part of that disk submerged, first calculate the area of the disk, then calculate the area on the submerged section, the difference is the exposed evaporator