colcob t1_j5pe6hk wrote
Yes. The rate of slowing of the spinning water must be a function of the kinetic energy of the water against the drag of the side walls.
Even if the max velocity of the water is the same in the pool (ie a very slow rotation rate) then the energy of the water will scale somewhat with the volume of the water, ie cubicly, while the drag of the walls will scale somewhat with the area of the side walls, ie. squared, therefore the larger the cup, the more the kinetic energy of the water outweighs the drag of the sides.
If you do actually stir at the same rotational rate, then as the other commenter says, the max velocity of the water will be very significantly higher than in the coffee cup, and as energy scales to the square of the velocity then you'll have vastly more energy proportional to drag than in the coffee cup.
Plus anecdotally, as a kid we used to run around those circular backyard swimming pools and get the water spinning faster and faster, and they kept going for ages!
imbluedabedeedabedaa t1_j5qdycm wrote
Otherwise known as the square-cube law!
Another great (but completely unrelated) example of this law explains the design differences between large and small animals. As a creature gets larger, its mass increases at a cubic rate (volume, m^3) but muscle/bone strength is proportional to their cross sectional area (m^2). This is why an elephant has such massive muscles/bones when (proportionally) compared to a dog.
It also impacts body temperature--since heat generation is proportional to body volume, but the ability to reject heat is proportional to the skin area. This explains the elephants' massive ears, and also why most cold blooded animals are very small.
If you scaled a dog up to elephant size it would collapse under its own weight before dying of heat. If you scaled an elephant down to dog size it would probably freeze to death. All because of math!
silvercup011 t1_j5r3fa1 wrote
How do baby elephants not freeze to death? They are the size of a dog…
imbluedabedeedabedaa t1_j5r6yvl wrote
There's a big difference between a baby elephant and a scaled down adult elephant
cobywaan t1_j5remzo wrote
Baby elephants are like 250-300 lbs when born, that is much larger than all but the most massive outliers of the biggest breeds of dogs
crackaryah t1_j5r4hxl wrote
It wouldn't freeze. Endotherms regulate their body temperatures by modulating their metabolisms. Not to mention that modern elephants don't live in cold places. Ancient elephants (mammoths) were highly insulated. Metabolism can be modulated a lot. There are small "warm blooded" animals that have a body temperature above 37 C in the summer, but hibernate during the winter, dropping their body temperatures to below 0 C. They don't freeze and they certainly don't die. There is even some evidence that hibernation contributes to longevity.
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blind_ninja_guy t1_j675xlf wrote
Good to know that the dog sized elephants that you could hold in whatever that moovie was where they go find atlantus before it again falls into the see is not realistic.
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ShelfordPrefect t1_j5qzs5e wrote
Another factor in favour of the big pool: at the same rotational rate, the big pool will have less shear because the difference in speed between two points a given distance apart is smaller than the same two points in the small cup, so I would imagine less energy would be lost to turbulence
Bebilith t1_j5rc9jz wrote
Tested and verified. Source I was a kid/teen with access to an above ground swimming pool.
uncleawesome t1_j5rmbzu wrote
Making a whirlpool and getting in the middle and jumping up and down making a wave pool were the funnest parts of an above ground pool
jordanmindyou t1_j609t3x wrote
Why did I never get in the middle and jump up and down?
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Starbucks__Coffey t1_j5ppyy6 wrote
>Even if the max velocity of the water is the same in the pool (ie a very slow rotation rate) then the energy of the water will scale somewhat with the volume of the water, ie cubicly, while the drag of the walls will scale somewhat with the area of the side walls, ie. squared, therefore the larger the cup, the more the kinetic energy of the water outweighs the drag of the sides.
The centripetal force increases friction aswell angular momentum. So it increases the energy lost due to friction aswell as the increase in surface area.
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Starbucks__Coffey t1_j5vv1pp wrote
Yea I was just informing that the surface area increase also correlates with an increase in normal force. Idk how it interacts just that it was missed.
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Old_comfy_shoes t1_j5sazqq wrote
Wdym by rotational rate? You mean equivalent tangential velocity of the spoon going around?
colcob t1_j5sdytd wrote
So by rotational rate i mean the angular velocity, ie. degrees per second, RPM, not the tangential velocity.
I guess I would stir a cup of about 1 revolution per second, so I'm imagining that if you stir the swimming pool cup at 1 revolution per second, the water's going pretty damn fast at the edge!
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Fantastic-Arrival556 t1_j5uw36v wrote
What if the energy put into the stir is equivalent for both cups?
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