Buyoant force confusion

[bluequestions]

So the buoyant force is defined at force pushed up by fluid molecules - force pushed down on object by fluid above it. When Khan Academy was deriving the equations, it shows that F upwards = (hydrostatic gauge P_upwards) (SA of object) and F downward = (hydrostatic gauge pressure_downward) (SA of object), and that the gauge pressure_bottom = rho (g) (the depth the bottom of object is at). Can someone explain why the height now is the depth of object's bottom measured from the top? When I imagine gauge pressure exerting upwards on the object, I was thinking it's the fluid molecules beneath the object pushing against the object bottom, so we want the weight of those molecules x SA of object to get the pressure at bottom of object. Thanks!

https://www.khanacademy.org/science...uoyant-force-and-archimedes-principle-article

here's the link for the khan academy explanation btw. Thanks!

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[sazerac]

The water molecules on top of the can push down on the upper surface, based on the height of all the water above them.

The water molecules on the bottom of the can push up on the lower surface, based on the height of the water above them. Note that this is a slightly deeper depth.

The net force acting on the can is based on the difference between these two forces. You can measure the difference in heights as (depth of bottom of can - depth of top of can), or just acknowledge that this value is exactly equal to the height of the can itself.