How does weight distribution work in water?

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Idea04
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Lets say we put a large weight on top of a large amount of water. And it didn't sink, It just sat on top of the water applying force to the water beneath it. How would the force of the weight be distributed through out the water beneath it?
 
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yes that is what I mean.
 
so how is the weight distributed through the water?
 
Exactly as you would expect: there is a pressure equal to the weight of the object divided by it base area. Throughout the water you would have pressure equal to the pressure of the water, at that depth, itself plus the added pressure.
 
but another thing I wanted to know is let's say that the piston wasn't evenly balanced. so if you have a 20 square inch surface area piston with a few square inches being quite light and a few square inches being heavy. Would the pressure be higher below the heavy part and lower below the lighter part of the piston or would the piston distribute the weight evenly through out the water below
 
I don't quite understand your example with the non-uniform piston, but the increase in pressure is evenly distributed at any given level beneath the piston.

Going back to your original example might make the point more clearly. Imagine you are swimming along underwater. If you swam under a huge battleship that was floating on the surface, would you feel an increase in pressure as you passed under the ship? No.