Understanding Pascal's Principle: Water Dispenser for Pets

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The water dispenser for pets operates based on Pascal's Principle, where the pressure from the water in the inverted bottle pushes water into the bowl as it is consumed. The bowl's design prevents overflow by balancing the water levels. The height of the water in the bottle does indeed depend on the surface area of the water in the bowl; a smaller surface area results in a higher water level in the bottle when water is consumed. This relationship is due to the pressure exerted by the water column in the bottle. Understanding these principles clarifies how the dispenser maintains a steady supply of water without overflowing.
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I can't seem to wrap my ahead around this question! Please help me understand.

A water dispenser for pets has an inverted plastic bottle. When a certain amount of water is drunk from the bowl, more water flows automatically from the bottle into the bowl. The bowl never overflows. Explain the operation of the dispenser. Does the height of the water in the bottle depend on the surface area of the water in the bowl?
 
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ZoeGab said:
I can't seem to wrap my ahead around this question! Please help me understand.

A water dispenser for pets has an inverted plastic bottle. When a certain amount of water is drunk from the bowl, more water flows automatically from the bottle into the bowl. The bowl never overflows. Explain the operation of the dispenser. Does the height of the water in the bottle depend on the surface area of the water in the bowl?

So what are your thoughts on it?
 
here goes!

I am thinking if a given volume of water is taken away then the height of the water in the bottle would be more for smaller surface area of the water in the bowl. This is so confusing just trying to put it into words! I am so confused!
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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