jim rozen wrote:

In article ,
says...

The reason why a balloon floats in still air is because of the
pressure gradient between the top and the bottom of the balloon.

I really don't understand this. Are you talking about
the pressure gradient in the atmosphere?

If that were the case then even a ballon filled with air
would float, because it sees the same gradient as one filled
with helium. But air-filled ballons don't float
because the amount of lift from that effect is very,
very tiny.

The pressure differential is only half of the equation. It has to be
balanced against the weight of the balloon. In the case of a
helium-filled balloon that rises, the net force resulting from the
pressure differential is greater than the weight of the balloon, so it
pushes the balloon up. For an air-filled balloon, the weight of the
balloon is greater than the resultant buoyant force, so the balloon
sinks.

The amount of force involved is not as tiny as you think. At sea level
at 59 deg F, the pressure gradient is about 0.000531 psi / ft, or
0.0765 psf / ft. To simplify calculations, let's assume we have a
balloon in the shape of a cube 1 ft on each side. The difference in
the upward pressure acting on the bottom square foot and the downward
pressure acting on the upper square foot is therefore 0.0765 lb, or
1.22 oz, acting in an upward direction. (Note that these numbers are
the same as the weight of one cubic foot of air under these conditions
-- this isn't a coincidence!) This force is greater than the combined
weight of a cubic foot of helium (at near ambient pressure) and a
balloon; it's less than the combined weight of a cubic foot of air and
a balloon. (An empty balloon this size would probably weigh 1/3 to 1/2
oz, based on the weight of a smaller balloon I had lying around.)

Things float because the volume of fluid they displace,
weighs less than their own mass. This is true even in
incompressible fluids, like water for example.

The weight of the fluid displaced is simply an easily computed
surrogate for the force due to the pressure differential. Both values
turn out to be exactly the same (regardless of whether the fluid is
compressible or not). But physically speaking, the balloon moves
because of the forces acting on it, and the force acting on it due to
the surrounding atmosphere is transmitted through pressure (which is
the result of individual gas molecules impinging on the balloon).

Bert