Buoyancy of Vertical Columns
I am having trouble understanding why the point of application of a
buoyancy force (center of buoyancy) is the center of volume for the submerged
part of the body. Is there a proof for this statement somewhere? Also, it is
nice to say that the buoyancy force is equal to the weight of displaced water
but is this true for bodies that have their horizontal surfaces resting on a
bottom? 1. Imagine a partially submerged cube. The pressure forces on the side
walls balance out, leaving only the distributed pressure forces acting of the
bottom face. The resolution of the distributed forces yields a single pressure
force acting at the geometric center of the bottom face. In the vertical
direction, is it not also acting at the bottom face? This is where the
distributed pressure forces acted, but this is not the center of volume
for the submerged section of the body. 2. Imagine a large, upright pillar
submerged in a lake and that rests on the lake bottom with its top at the
lake's surface. I would expect that, in theory, there should not be any
vertical forces acting on the submerged body since the pillar's base presents
no surface area to the water, and so there should be no buoyancy. All the
pressure forces are acting along the pillar's circumference. So does this
pillar really have no buoyancy despite being entirely submerged?
A long awaited reply, but here are the considerations.
1. The net point of the buoyancy force (the center of buoyancy) occurs because
if the submerged object is in any other orientation, there will be a net force
and the object will rotate until the net forces are zero. The geometric center
and the buoyancy center need not coincide if the object does not have uniform
2. The argument that a submerged column has no buoyant force is flawed. Gravity
is pulling the pillar down, and buoyancy is presenting a vertical force tending
to lift the column. That does not depend on the pillar's base not presenting a
surface area to the water. The buoyant force depends upon the weight of
displaced water and acts in a direction opposite to the force of gravity.
Shape does not matter.
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Update: June 2012