# How does buoyancy work?

Discussion in 'Electronic Design' started by Pimpom, Feb 18, 2013.

1. ### PimpomGuest

Gravity and depth. The underside of the immersed body is at
a greater depth than the upper side. Therefore the pressure
on the lower part is greater than on the upper side, so
there's an upward thrust. That's why the body feels lighter
even if it has a density greater than that of the fluid.
Working out the math from that should be simple for an
engineer.

2. ### mikeGuest

I know this isn't the right group for this question, but I want
an answer an electrical engineer can understand.

I understand the simple model of buoyancy. If something weighs
less than the medium it displaces, it floats.

The question is, "why?"
If you stick a ping pong ball under water and let go, it floats.
What's the mechanism? The water has no idea what's inside the
ball. We have water molecules banging into the ball on all sides.

Is there a simple explanation, in layman's terms, of what's actually
going on to force the ball up?

I really want to understand how convection works in a chimney,
but water should be easier to grasp.

3. ### Martin BrownGuest

The simple answer is that the system is rearranging itself to obtain the
lowest energy configuration possible. If the ball is too heavy this is
with the ball at the bottom of the tank. Otherwise the ball will
displace water and raise the water level in the tank against gravity
until the net force it experiences is zero. That is once it has
displaced its own weight of water it floats. Pushing it down or raising
it from this equilibrium position increases its potential energy.

The ping pong ball is accelerated by the vertical pressure difference
across its diameter so if it is lighter than the water it displaces then
upwards it goes. Various modern executive bubble toys exploit the
behaviour of viscous oils and air bubbles a revamp of the lava lamps
popular in the 1960's.
Warm air rises because it is less dense and the heavier cold air falling
can thereby lose some potential energy.

4. ### Sylvia ElseGuest

As you say, there are water molecules banging into the ball on all
sides. But consider a horizontal slice of the water, one centimetre
thick, at some arbitrary depth. It is being banged into by water
molecules from above and from below, but it doesn't go anywhere, despite
its weight, so its weight has to be balanced by a difference between the
net forces generated by the molecules above and below it. The
implication is that the rate at which molecules hit from below is
greater than the rate at which they hit from above by an amount
sufficient to create the required net force.

This is just another way of saying the pressure rises as you go deeper
into the water.

So now if we go back to your immersed ping pong ball, it is apparent
that the forces generated by the molecules banging on the ball are not
balanced, because the forces on the lowerhalf of the ball are greater
than the forces on the upper half. Thus there is a net upwards force on
the ball.

So how much net force is there? Well, if the pingpong ball were not
there, then in its place would be a sphere of water. Since the water
wouldn't go anywhere, the net force on that sphere must be equal to its
weight. Thus the force on the pingpong ball is equal to the weight of
the water that would have been there had the ping pong ball not been.

Sylvia.

5. ### SoothSayerGuest

The reason why is gravity tugs one way ALL THE TIME. The molecules of
one gaseous or liquid medium push against each other with a force based
on their masses.

So liquids or gasses introduced into this would rise or fall to
whichever place their masses would put them with respect to the other
members of the matrix.

SOLID items, or solid items with a hollow inside and a gas of a
particular pressure level filling that, will rise or fall to a particular
place in the matrix based on what the mass of that exact same volume it
displaces of the material it happens to be in at the time.

So a one cubic foot displacing solid element in our sea level air has
a zero point if it weighs the exact amount one cubic foot of sea level
air weighs. If it weighs less, it will get pushed upward by the air
around it (a balloon with Helium in it), until it reaches an equilibrium
point that matches the weight it has against the matrix it is in (pretty
high up).

If it is in water, same rule applies. If that one cubic foot item
weighs less than one cubic foot of sea surface, sea level water, it gets
pushed UPWARD, and rides on said surface (in this case). as we cross
into the realm where the one cubic foot device weighs more than the water
it is in, it sinks (think submarine) toward the center of the earth, by
gravity, and the fact that the molecules of water around it are pushing
up less than said gravitational pull is pulling down.

In free space, it merely changes the way said one foot cube would
'slosh" through a given medium, based on relative velocities.
as there would be no gravitational attractor in space. Down here, we
merely get to examine how things move through slurries, and from that we
can understand gravity. They found the Higgs Boson particle... maybe
they'll see the gravity particle next.

Ever see that surfer dude's multi-dimensional layout of the sub-atomic
particles?

Anyway... gravity is the answer. and molecular pressure.

6. ### SoothSayerGuest

In other words, it only sinks a small bit because that small bit of
volume, in the form of water, would weigh the same as the ping pong ball.

So, if it displaces one teaspoon (for the sake of the analogy), then the
weight of one teaspoon of water and one ping pong ball would balance on a
scale (be the same).

On the Moon, it would sink far less. And the water wouldn't last long
either! (unless you were aboard The Eagle).

7. ### Jeroen BellemanGuest

You may want to think about that last statement a little longer....

Jeroen Belleman

8. ### SoothSayerGuest

About the sinking, the water, or the Eagle?

9. ### Jeroen BellemanGuest

The sinking, specifically.

Jeroen

10. ### mikeGuest

Thanks, guys, for the inputs.
Those are the classical arguments. I accept them as true and useful
models for everyday use.

But, I'm still not satisfied.

Throw a sheet of thin plywood into the swimming pool.
If you put sufficient force on it, it sinks.
Now turn it vertical and push it down.
The force to submerge it should not change.
But the direction of force applied by all the molecules banging
on the side do not obviously have a net upward force.

The thing I'm trying to get my brain around is convection.
If I have a 20 foot chimney and build a fire in the firebox,
air gets sucked in the box and goes up the chimney.
If I cut a hole in the bottom and stack it on top of a
similar chimney (close up the front), does the same amount
of air get sucked into the bottom (cold) fireplace?
My intuition says it does.
And that means that if you're interested in ventilation,
it doesn't matter where the heat gets into the pipe.
Solar collector should work for that. And the distance
to the space to be ventilated should be irrelevant???

OK, so now, put an S-curve in the pipe, kinda like a P-trap.
Can you make a passive thermostat out of it? Suck air
only when the sun shines?

11. ### rickmanGuest

Uh, what? Well, no the vector of the force on the long sides now are
opposing and so cancel out. But the unit area force on the bottom,
small edge is much greater because it is at a greater depth. So the
total force is the same. In the general case you have to integrate the
forces over the entire surface. The rectangle of the plywood makes that
easy. Do you know how to express this as an equation? It will be area
(the bottom edge of your rectangle) times the unit area force
(proportional to the depth).

In the chimney case, as long as the temperature of the hot air being
sucked in does not change a taller chimney will create a greater force
because of the higher difference in air pressure from the top to the
bottom just like in the water.

I like Sylvia's way of looking at it. How much does the air in the
chimney weigh vs. the air that would otherwise be in the chimney weigh.
That is the total force pushing the air up the chimney.

How fast it moves is another matter. A longer chimney will have more
resistance but that may or may not be directly proportional to the
length of the chimney. Air resistance is a complex subject.

I'm not sure what you are thinking here. What would the S-curve in the
pipe do? Are you putting water in it, or cold air, or what? Any sort
of gas would just diffuse away I expect. Even a little water would
create a huge barrier to air movement. That's how a water trap works on
your sink. A water trap could work if it were shallow enough. But it
wouldn't really act as a thermostat to maintain temperature in the room.
It would just allow differences in pressure to be equalized with a
minimum of air movement.

12. ### Guest

(snip to the real issue)
OK, now think about why the air does that. Hint; buoyancy and
convection are about *density*, not *mass*.

Also, crack a window somewhere in the house or the chimney won't
draw. Remember, this is a circuit and the fire is your potential
source. ;>)
IOW the chimney is now 40' tall. Fine.
Intuition will usually get you into trouble in technical topics.
What does your intellect say will be different with a longer chimney?
Think resistors.
Now you've built a fire on top of the chimney. My intuition mentions
carts and horses.
Wait, we've moved from heating (what fireplaces are usually designed
for) to just moving air? How do you plan on coupling the heat from the
solar collector to the chimney?
An air version of a lambda diode? Interesting.

Mark L. Fergerson

13. ### Sylvia ElseGuest

Convection works because, other things being equal, warm air is less
dense than cold air. Since it's less dense, the pressure drop with
height is less than the pressure drop for the same height in cold air.

With a chimney, you then have the situation where the pressure at the
bottom has to equal the pressure of the outside air at the bottom, and
the pressure at the top has to equal the pressure of the outside air at
the top, but the pressure change from the bottom to the top is
different. The apparent impossibility is resolved by accelerating the air.

The effect is thus dependent on the height of the column of warm air,
and is consequently very dependent on where the heat is introduced.
Well, if the convection is solar powered, then it will only occur when
the sun is shining, regardless of the shape of the pipe. When it exists,
the effect depends on the difference in altitude of the inlet and
outlet. The only effect of an S-curve is to lengthen the pipe, and thus
increase the frictional forces that slow the air down.

Sylvia.

14. ### Roberto WaltmanGuest

For a "layman engineer," generic calculations involving integrating
the hydrostatic pressure outside the submerged body should be easy to
grasp.
Analyzing simple shapes (cylinders, cubes etc.) can make it trivial.

See:

http://en.wikipedia.org/wiki/Buoyancy
http://videolectures.net/mit801f99_lewin_lec28/
http://ocw.mit.edu/high-school/physics/fluid-mechanics/buoyancy/

15. ### Martin RiddleGuest

Laws of physics.....
Leftists like to change Laws.

Cheers

16. ### Robert BaerGuest

No, water will trickle out of the hand..

17. ### SoothSayerGuest

One might guess that the sinking would be exactly the same.

I suppose it pretty much would be exactly the same sinking.

But NO! The gravity is less, so it would *have* to sink less, and the
rule includes that the water is standard Earth sea level density water.

There is, however, no additional atmosphere to push down on it either.
so, it would seemingly sink even less still. And the water would have to
be lees dense than sea level Earth water. Hmmmmmm.

Of course, it would also be boiling.

Except, as I stated, within the pressurized confines of The Eagle.

No air on top is about the only thing I see I could have missed
including the effects of. But that should make my statement more true,
not less.

The ping pong ball would be bigger in a reduced pressure environ too,
as it is filled with air.

I don't get it. Don't see what I missed. You'll have to tell me.

Nut floats on Mercury. What height does it float at here? On the
moon?

18. ### Tom Del RossoGuest

H ow do you define 'pressure differential of the surrounding atmosphere'?

Like starting an upside-down siphon, almost.

19. ### SoothSayerGuest

Again humor has been achieved.

20. ### Tom Del RossoGuest

That's one of those laws of nature that seems to 'cause' things to happen as
if they understand the law.