Buoyant force

[Saber]

When  you  push a  piece  of wood  down in the  water  for example.....  the  buoyant  force  pushes  it  upwards  till the  piece  of wood  reaches the  surface.......

Is  that   the  same  force that  pushes  up a  hot air balloon  in the  air ?  I mean  are  these two  forces  from a  same type ?   less dense  object  submerged  in a  more  dense  one ?

 

And  if yes  whats the  source of those  forces ?   Where does that  buoyant  force come from and  originate ?

 

Thanx.........

Edited January 28, 2023 by Saber

[Lorentz Jr]

Yes, it's the same force. The net downward force on any object immersed in air or water, or any other fluid, is the difference between the weight of the object and the weight of the fluid that would otherwise fill up the volume that's currently occupied by the object. So it's a buoyant force (i.e. upward) if the object is less dense than the fluid.

Generally speaking, the difference between the pressures at two points in a fluid that are separated by a height [math]h[/math] is equal to [math]\rho g h[/math], where [math]\rho[/math] is the fluid's density. It's just the weight of any column of fluid of height [math]h[/math] divided by the column's cross-sectional area.¹ If you integrate that difference over a submerged object's horizontal cross section, calculating [math]h[/math] at each point from the vertical distance between the object's upper and lower surfaces above and below the point,² you get the total weight of the displaced water, and the net upward force on the object is that force minus the object's weight.

 

¹ For a tall object in a gas (e.g. air), you may have to take the gas's altitude-dependent density into account.

² Of course, this assumes the surfaces aren't too convoluted, i.e. it assumes there's no fluid in the space between the upper and lower surfaces. If there are any holes in the sides of the object, you'll have to compensate for them in the same way, by calculating the volumes of water in them and subtracting their weights from the total.

Edited January 28, 2023 by Lorentz Jr

[Saber]

Thank you  very much  Mr Lorents  

Reading  your post  i understood  that the  Buoyant force  is actually originated by the  pressure  difference between the fluid underneath &  above the  object

Have i  understood it  right ?

[Lorentz Jr]

Yes, that's right. And the pressure difference is caused by the weight of the surrounding fluid.

[studiot]

7 hours ago, Saber said:

Is  that   the  same  force that  pushes  up a  hot air balloon  in the  air ?

Not quite, the hot air ballon is a special case that is more complicated.

Lorenz' analysis applies to rigid bodies. The hot air balloon is a deformable body.

I can explain it fully if you can do high school maths for science ?

But it is basically due to the fact that the pressure inside a hot air balloon must be greater than the pressure outside, except at one point.

Can you see why this is true ?

Edited January 28, 2023 by studiot

[Genady]

6 hours ago, Saber said:

the  Buoyant force  is actually originated by the  pressure  difference between the fluid underneath &  above the  object

Have i  understood it  right ?

To see if you have understood it right, think about the following question.

Take a pencil 20 cm long and 0.5 cm thick. Compare the buoyancy in these two cases:

1) you push it under water while holding it vertically,

2) you push it under water while holding it horizontally.

In the case 1, the pressure difference between the water underneath and above the pencil is greater than in the case 2. Is the buoyant force different in these two cases?

[studiot]

47 minutes ago, Genady said:

To see if you have understood it right, think about the following question.

Take a pencil 20 cm long and 0.5 cm thick. Compare the buoyancy in these two cases:

1) you push it under water while holding it vertically,

2) you push it under water while holding it horizontally.

In the case 1, the pressure difference between the water underneath and above the pencil is greater than in the case 2. Is the buoyant force different in these two cases?

Good question. +1

 

Think carefully about your definition of bouyancy force.

Edited January 28, 2023 by studiot

[Saber]

1 hour ago, Genady said:

To see if you have understood it right, think about the following question.

Take a pencil 20 cm long and 0.5 cm thick. Compare the buoyancy in these two cases:

1) you push it under water while holding it vertically,

2) you push it under water while holding it horizontally.

In the case 1, the pressure difference between the water underneath and above the pencil is greater than in the case 2. Is the buoyant force different in these two cases?

Can  you  read  minds  from  long  distances ?   Because i was   thinking about the  very  same  question  in my  mind  today    *  not  with pencil but with a wooden  bar
And  i  thought    no  .....the  buoyant  forces  must  be   the  same in  both  cases  right ?

In the vertical  mode  the  pressure difference is way  higher    but the  area that  the pressure is applied to  is less

 

In the horizontal mode  its  vise versa   meaning    pressure difference is lower but   area of  that the pressure app,lies to  is  more

 

 

[Lorentz Jr]

1 hour ago, Saber said:

In the vertical  mode  the  pressure difference is way  higher    but the  area that  the pressure is applied to  is less

In the horizontal mode  its  vise versa   meaning    pressure difference is lower but   area of  that the pressure app,lies to  is  more

Right. And in both cases the total downward force on the pencil is the pencil's weight minus the total weight of displaced fluids, including both air and water.

 

2 hours ago, studiot said:

Not quite, the hot air ballon is a special case that is more complicated.

Lorenz' analysis applies to rigid bodies. The hot air balloon is a deformable body.

The standard pressure analysis applies to any object once its size, shape, and mass have been established. An ordinary object's deformability only affects its shape and volume. In the case of a hot-air balloon, only its mass is affected (except to the extent that its fabric stretches), and the pressure analysis still applies to it.

Quote

Think carefully about your definition of bouyancy force.

The definition is simple: It's just the total force of the fluid on the object due to the fluid's weight, minus the object's weight, whatever that might be once any unrestrained hot air inside the object has equilibrated with the ambient pressure at the opening. Complications involving the object's internal mechanical properties aren't part of the definition.

2 hours ago, studiot said:

the pressure inside a hot air balloon must be greater than the pressure outside, except at one point.

True, but not exactly on topic, I think, and the final result is still determined by the pressure analysis (or the fluid-weight calculation, once you know that works).

Edited January 28, 2023 by Lorentz Jr

[Saber]

3 hours ago, studiot said:

Not quite, the hot air ballon is a special case that is more complicated.

Lorenz' analysis applies to rigid bodies. The hot air balloon is a deformable body.

I can explain it fully if you can do high school maths for science ?

But it is basically due to the fact that the pressure inside a hot air balloon must be greater than the pressure outside, except at one point.

Can you see why this is true ?

Not   sure ..........because  if the  out side pressure was  grater  the  balloon  would not  hold its  shape ?  and   deflate ?

[studiot]

36 minutes ago, Saber said:

Not   sure ..........because  if the  out side pressure was  grater  the  balloon  would not  hold its  shape ?  and   deflate ?

Well done you have the right of it. +1

A hot air balloon will only stay inflated of the internal pressure is greater than the external pressure, otherwise it will collapse.

 

1 hour ago, Lorentz Jr said:

The standard pressure analysis applies to any object once its size, shape, and mass have been established. An ordinary object's deformability only affects its shape and volume. In the case of a hot-air balloon, only its mass is affected (except to the extent that its fabric stretches), and the pressure analysis still applies to it.

I'm sory but this analysis is just plain inadequate.

 

Here is a standard analysis of the subject @Saber  please ask if you need anything further.

 

[MigL]

Bouyancy is what is called a 'residual' force, similar to the strong interaction keeping nucleons together being 'residual color force of the quark-gluon interaction.
Bouyancy is caused by gravity, the actual 'force', which causes the stratification of pressures and the tendency of heavier ( greater gravitational force ) to tend to a lower potential.

[TheVat]

The pressure of a hot air balloon overall is equalized with the outside.  The balloon rises due to buoyancy force only on the top hemispheric portion of the enclosure.  I.e. the pressure differential is all in that portion as heated air convects up there, IIRC.

With a standard teardrop balloon, the top hemispheric area is a cap that the hot gas pushes upwards against due to buoyancy, i.e. that inverted bowl of gas weighs less than the exterior gas being displaced.  The tapering fabric of the balloon below that hemisphere of taut material is cut to match how the ropes will hang down during flight. The fabric in that tapering part of the balloon is not under any force (the ropes are taking the force and transferring to the gondola) and is not billowed out or inflated.  At least this is what a balloonist in Albuquerque told me.  My observation of that type of balloon seems to fit with this account.  IOW, it ain't a party balloon.

Edited January 28, 2023 by TheVat
typeo

[Genady]

2 hours ago, Saber said:

Can  you  read  minds  from  long  distances ?   Because i was   thinking about the  very  same  question  in my  mind  today    *  not  with pencil but with a wooden  bar
And  i  thought    no  .....the  buoyant  forces  must  be   the  same in  both  cases  right ?

In the vertical  mode  the  pressure difference is way  higher    but the  area that  the pressure is applied to  is less

 

In the horizontal mode  its  vise versa   meaning    pressure difference is lower but   area of  that the pressure app,lies to  is  more

Yes to everything  

BTW, you did much better than ChatGPT. When I've asked ChatGPT the same question, its response was this:

[Lorentz Jr]

2 hours ago, studiot said:

I'm sory but this analysis is just plain inadequate.

Inadequate for what? The OP wants a beginner's introduction, not a PhD.

Quote

The lift of a balloon is mainly due to the weight of atmospheric air it displaces.
... its gross lift is equal to the weight of atmosphere it displaces.
... the pressure of the gas at the top of the column will be less than that at the base b an amount equal to the weight of the column of gas.

This text is very impressive and authoritative, but I don't see where it adds anything helpful to the conversation. It repeats the basic facts several times, expresses things mathematically, and adds lots of details about specific gasses and the nature of the atmosphere. It doesn't even mention hot-air balloons. 🙄

The things that uniquely affect a hot-air balloon are:

• The hot air has to be treated as part of the balloon (or at least it can be treated that way as an approximation), even though there's an opening at the bottom.
• The balloon keeps reducing its own buoyancy by heating up the surrounding air and simultaneously cooling off. (This decreases the volume of the air inside the balloon. Some of the outside air enters the balloon, so the mass of the inside air is higher).
• Someone in the basket periodically increases the buoyancy by heating the air with a torch. (This increases the volume of the hot air. Some of the air exits the balloon, so the mass of the remaining air is lower.)
• Of course, the balloon will collapse and fall if the supply of heat fails for any reason.

Edited January 28, 2023 by Lorentz Jr

[Genady]

Here is a suggestion to produce perpetual motion using buoyancy. Consider this kind of device submerged in water: 

It has two wheels with a belt, and cups attached to the belt. I drew two cups on each side, but the belt can be as long as needed and there can be as many cups attached as needed.

Each cup is covered with a flexible membrane with weight attached to the center of the membrane. When cup is on the right, the opening faces upward and the weight pushes the membrane inward. When cup is on the left, the opening faces downward and the weight pulls the membrane outward. 

Thus, the cups on the right have smaller volume than the cups on the left. Consequently, the buoyancy force on the left is greater than on the right, and the device starts rotating clockwise. Each time a cup crosses from left to right over the wheel on top, its membrane moves inward and its volume decreases, but at the same time another cup crosses from right to left under the wheel on bottom, its membrane moves outward and its volume increases. So, the motion continues.

We know that something is wrong here, but what?

[Lorentz Jr]

44 minutes ago, Genady said:

We know that something is wrong here, but what?

Nothing! The cups on the left are "inflated" more, so the belt will rotate clockwise until one of the cups reaches a wheel. 😎

Now someone else has to finish the problem. 😋

[studiot]

2 hours ago, Lorentz Jr said:

Inadequate for what? The OP wants a beginner's introduction, not a PhD.

I think the OP should be the judge of what they want or don't want, not you.

2 hours ago, Lorentz Jr said:

This text is very impressive and authoritative, but I don't see where it adds anything helpful to the conversation. It repeats the basic facts several times, expresses things mathematically, and adds lots of details about specific gasses and the nature of the atmosphere. It doesn't even mention hot-air balloons. 🙄

In fact this text contains nothing more than can be found on the lower secondary school syllabus (GCSE in the UK).

The reason that the pressure at the bottom equals atmospheric is that a hot air balloon is not sealed. There is a hole at the bottom so the pressure in the balloon must equal the pressure outside. This restriction is not necessary for a sealed balloon which can be at considerably higher pressure all round and considered as a rigid object for analysis purposes.

It does show (without PHD level stuff) that there is a lift  force pushing up on the inside of the upper part of the balloon.

It doesn't mention this in the article but this force is not applied at the 'centre of bouyancy' , which is where the bouyancy force acts and so is important in considering the stability of the system - something I chose not not mention before. The textbook deals with equilibrium and centre of bouyancy elsewhere and I thought that a subject beyond this thread.

[swansont]

4 hours ago, Genady said:

When I've asked ChatGPT the same question, its response was this:

!

Moderator Note

Please stop doing this. One might as well be asking the proverbial “man on the street”

It doesn’t belong in these discussions

 

[Lorentz Jr]

1 hour ago, studiot said:

I think the OP should be the judge of what they want or don't want, not you.

The OP already told us what they wanted to know: whether the buoyant forces on pieces of wood and hot-air balloons are of the "same type" and where they "come from".

Buoyancy comes from the force of a high-pressure area underneath an object, which is caused by the weight of the surrounding fluid, even if the object is a balloon. The only relevant difference between balloons and rigid objects is how the forces pushing them up from below are transmitted internally, and that's not what the OP asked about. Maybe they'll be interested in that, I don't know, but please introduce related topics like that as additional information instead of starting your comment with "Not quite", as though it's a correction.

 

 

[studiot]

56 minutes ago, Lorentz Jr said:

Buoyancy comes from the force of a high-pressure area underneath an object, which is caused by the weight of the surrounding fluid, even if the object is a balloon.

So what does the 'force of high pressure' act on considering the bottom of the hot air balloon is open  oh wise one ?

To make it quite plain it has no bottom.

 

[Lorentz Jr]

1 hour ago, studiot said:

So what does the 'force of high pressure' act on considering the bottom of the hot air balloon is open  oh wise one ?

It acts on the air at the opening (obviously), and it acts on the fabric in the region surrounding the opening. This is possible because the hot air in the balloon maintains a combination of high pressure and low density. I would imagine that may be one reason the lower conical part of a typical balloon is so long: The air inside it helps to insulate the hot air in the upper part from the cooler air below.

[studiot]

Just now, Lorentz Jr said:

It acts on the air at the opening (obviously), and it acts on the fabric in the region surrounding the opening. This is possible because the hot air in the balloon maintains a combination of high pressure and low density. I would imagine that may be one reason the lower conical part of a typical balloon is so long: The air inside it helps to insulate the hot air in the upper part from the cooler air below.

The Montgolfier shape is not the only possibility.

Cylindrical hot air balloons work perfectly well too.

What, by the way, is the point of pushing up on fabric at the bottom ?

It will simply buckle or rumple under even the slightest push.

It is vital to maintain tension in the skin of any balloon, open or closed.

There is even a discussion of this in the article I posted.

What a pity you don't like it because it is a nice piece of uncomplicated mechanics that is not often taught these days.

[Lorentz Jr]

33 minutes ago, studiot said:

What, by the way, is the point of pushing up on fabric at the bottom ?

It will simply buckle or rumple under even the slightest push.

The entire surface of the balloon is supported from the inside by whatever the pressure is at the opening (or at least it doesn't rise fall so much with height), which is higher than the outside pressure at higher elevations. So no buckling, but don't try using a hot-air balloon upside-down. 😁

Edited January 29, 2023 by Lorentz Jr

[studiot]

Just now, Lorentz Jr said:

The entire surface of the balloon is supported from the inside by whatever the pressure is at the opening, which is higher than the pressure at higher elevations. So no buckling, but don't try using a hot-air balloon upside-down. 

So you are claiming that a pure tension structure made of flexible fabric can support compression ?