Optimizing Wetted Area in a Rotating Disk Evaporator

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SUMMARY

The discussion focuses on optimizing the wetted area of a circular disk in a rotating disk evaporator. The optimal positioning of the disk's center is established at a height of r/sqrt(1+pi^2) to maximize the exposed wetted area. Participants share insights on deriving the equation for the submerged portion of the disk, emphasizing the importance of understanding the geometry involved in the optimization process.

PREREQUISITES
  • Understanding of fluid dynamics principles
  • Familiarity with geometry and trigonometry
  • Knowledge of evaporator design and operation
  • Basic calculus for deriving equations
NEXT STEPS
  • Research the principles of fluid dynamics in rotating systems
  • Study the geometry of submerged surfaces in circular disks
  • Explore mathematical derivation techniques for optimization problems
  • Learn about the design considerations for disk evaporators
USEFUL FOR

Engineers, researchers, and students involved in chemical engineering, particularly those focusing on evaporator design and optimization techniques in fluid systems.

momu
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A circular disk of radius r is used in an evaporator and is rotated in a vertical plane. 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 height r/sqrt(1+pi^2)

ok i absolutely know how to do this question but I'm having a tough time deriving the equation for the submerged portion.. if i can get help on that i would be greatful thanks.
 
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Nevermind haha
 
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