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Does Energy transfer from a rotating disk at a constant RPM into ambient fluid depend on disk material density?

Why?

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1 Answer 1

I'll confess that I haven't thought about it very long, but I believe the answer is: no, the energy transfer rate in the scenario you have described does not depend on the disk material density. The energy transfer is dictated by the velocity of the disk, a function of the disk's (constant) rotation rate and disk radius (and thickness), and the viscosity of the ambient fluid. While a disk of higher density would maintain a more uniform transfer rate in isolation, if you are holding the disk at a constant RPM through a driving torque, then only the disk geometry (and identity of the fluid) matters.

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If higher power is required to maintain a constant RPM for disk with higher material density than that of lower material density, where does the additional input energy go and how? @KDN –  kuki Feb 14 '13 at 19:19
    
Higher power isn't required to maintain constant RPM for a disk with higher density. More energy is required to get it to that speed (a heavier disk is more energetic than a lighter disk with the same geometry). However, once it is up to speed, the power (energy per unit time) required to keep the disk rotating in the fluid does not depend on the density of the disk. If there were no fluid (i.e., the disk is spinning in a vacuum) and no mechanical losses (perfect bearings), then both disks would maintain constant RPM without any power input. –  KDN Feb 14 '13 at 22:32
    
@kuki: Where the disk with higher density does distinguish itself is in the amount of work it can do from a fixed RPM. If two disks of different density are spinning at the same RPM, the disk of lower density will slow down much faster in a viscous fluid. The more dense disk will still slow down, but it will transfer more energy to the fluid, and it will slow down over a longer period of time. –  KDN Feb 14 '13 at 22:34
    
Thanks @KDN for the nice simple explanation. –  kuki Feb 15 '13 at 21:31

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