Why Buoyancy is Imaginary

[Roger Long]

(Huge collective groan across cyberspace when people open the forum thread listing.)

I know this topic has been beaten to death in the long cabin fever threads below but I promised this explanation and I try to keep my promises. With a few notable exceptions, most of you have figured out the buoyancy thing pretty well but you might still enjoy reading this.

http://www.rogerlongboats.com/Buoyancy.htm

 

[Bill Roosa]

Wow Roger

I love the fog analogy.

 

[Ross]

(Huge collective groan across cyberspace when people open the forum thread listing.)

I know this topic has been beaten to death in the long cabin fever threads below but I promised this explanation and I try to keep my promises. With a few notable exceptions, most of you have figured out the buoyancy thing pretty well but you might still enjoy reading this.

http://www.rogerlongboats.com/Buoyancy.htm

Perfect! you can see what is happening but you can't see how it is happening.
For years people believed that rotting meat produced maggots and flies.

 

[CalebD]

Sooo, Roger, when are you going to go after all the scuba diving training organizations and equipment manufacturers who train people to use a BC or buoyancy compensator for swimming at various depths below the surface? Shouldn't they be calling this piece of equipment a 'gravity compensator' in your view? It does compensate for gravity below the sea surface but sadly will not work in the open air on the beach to elevate a person. For that you need a hot air balloon (another gravity compensator). Or am I just spewing a lot of hot air in the fog?
Nice explanation though.

 

[Hermit Scott]

Since this thread started I have been thinking about it alot. That is a great explination that you give with the balance beam.
I was thinking about how I saw bouyancy. IF water pressure was the same all around a submerged object, then the object would be neutrally bouyant at any depth and not push up in the water.
I have a new understanding of this. And my wife says I'm just wasting my time on here! HA

 

[Hermit Scott]

If you take a rigid cube and push it down in the water, then the force pushing up is constant no matter how deep you go?
I wondered what made bouyancy disappear as you went deeper. I guess it's just the air getting compressed until the weight of your body exceeds the weight of the water displaced by your body. I used to think that bouyancy worked less the deeper you go as well as the compression of the air in your body that made you sink.

 

[kloudie1]

Yip, the psi generated that holds up the floating thing is the same as the water displaced will produce if arranged in the same shape as the part of the floater that is submerged. WHEW.. I have played with this phenom a bunch in the fluidized beds of catalytic crackers at 1200F.. works the same.. amazing sometimes to hear lightweight concrete chunks bumping into things in there as they float about and circulate in the bed..
Good job generating so much discussion and showing so much insight, Roger.

 

[Roger Long]

Good job generating so much discussion and showing so much insight, Roger.

Thanks. I've enjoyed it enough that I'm going to expand it into a full presentation on my web site. The link will only be available here until it's finished so this group can be my test audience and point out anything that isn't clear.

You can see the start here:

http://www.rogerlongboats.com/Stability.htm

 

[Ross]

Roger, An excellant start. I ask for clarification in the third paragraph on center of gravity . "Put a screw eye in the exact center of a 2x4 and it will hang straight down" . Should that read, "put a screw eye in the exact center of the end of the 2x4"?

 

[Roger Long]

Should that read, "put a screw eye in the exact center of the end of the 2x4"?

Good catch. Thanks. Keep it up.

 

[alangbaker]

Good catch. Thanks. Keep it up.

In addition, you should change the phrase "centre of gravity" to "centre of mass", and yes, I realize it's a nit pick, but what you describe as unmoving in a rigid body is the centre of mass and not the centre of gravity.

The centre of gravity of a rigid body is the point where the sum of all the gravitational forces can be said to act and that *does* change a tiny bit with orientation.

 

[alangbaker]

If you take a rigid cube and push it down in the water, then the force pushing up is constant no matter how deep you go?

Yes, that's correct.

Staying with the one foot cube oriented such that the top face and bottom face are horizontal, then since pressure goes up linearly in a non-compressible fluid, the difference in pressure between the top and bottom faces stays constant and thus the net force upward stays constant.

 

[DanW9494]

Actually there is variation in water density due to temperature and salinity. I'm sure you've heard that submarines like to hide beneath thermoclines where the temperature difference at the interface can bend sound waves.

If you drop your cube to where the top is above and the bottom below a thermocline, the force pushing up will increase slightly since the water below is more dense, and the bouyant force would be slightly higher. Submarines compensate for this since they want to stay beneath that layer, and monitor temperature to be sure they are.

In the ocean the salinity on average is 35 parts per thousand, with a range of 32 to 37 ppt. The Black Sea has 16 ppt. Also, just above 32*F or 0*C the water density increases significantly from electrochemical alignment changes.There can be changes in salinity as you drop your cube that could change buoyancy very slightly as well.

From the Office of Naval Research: http://www.onr.navy.mil/Focus/ocean/water/density1.htm
there are three zones of water density in the ocean, the surface mixed which is 2%, the pycnocline zone which is 18%, and the deep zone has the remaining 80%.

So water pressure is not just due to gravity and depth, but also the density of water which can vary at different depths and locations. So water pressure can be off a little from what your calculator would result.

Most of the time people measure depth by measuring water pressure. It's close, but to be a lot closer you have to compensate for changes in temperature and salinity. And it's more difficult if there are layers of temperature and salinity above you that you cannot measure.

 

[Ross]

Let's not concern ourselves with the forest and trees syndrome and pay attention to the purpose of the discussion.

 

[DanW9494]

Ross,
If you do not want to know anything about what changes the density of water, then you do not want to know why a boat floats lower in fresh water than sea water, why the water pressure 1 foot down in freshwater is less than the water pressure 1 foot down in sea water, and why it's just a little bit higher in winter than in summer.
A very large ship's captain has to take into account the extra draft going into a Black Sea port, while your buoyancy loss isn't enough to worry about.

People want to think water pressure as the end all be all of buoyancy, fine. But I was trying to explain why water pressure varies with the density of that water, and the causes of that density change, as well as the depth.

Roger,
I think you had it right with the middle of the 2x4. A screw eye in the end is no different than a lump of lead. I've never seen a 2x4 vertical in the water, much less from something that light

 

[Ross]

Dan I know why sea water has a higher specific gravity than fresh water and I know why ice floats and if a 2x4 is ballasted on the end it will float vertically in the water because its CG is lower than its CB. Don't doubt my knowledge or my need for more knowledge.

 

[DanW9494]

Ross, I'm sorry that I've obviously offended you.

As a peace offering I have calculated for you the amount of ballast placed on one end that would be needed to get a standard 2x4 to float vertically. It has to be at least 10.9 ounces of "wet" weight for every foot of Douglas fir and at least 7.4 ounces for every foot of Southern yellow pine. We use Douglas fir out here so that would be at least 5 lbs. 8 ounces of wet ballast including the screw eye to vertically float a 8' stud. If measured dry, the ballast would need to be 6 lbs. 6 ounces if it was all steel like the screw eye.

This is based on a specific gravity of 31 lbs. per cubic foot for the fir and 38 for the pine. Obviously kiln drying can change specific gravity, but I understand that is an average. Also, you all probably know that they don't make 2" x 4" lumber anymore so I used a cross section of 5.9 square inches. And I'm floating it in seawater, so remove 2.5% of the ballast if you want to use freshwater. My opinion is that the end ballasted 2x4 will not float vertically until more than 50% of it is underwater for it's center of gravity to be exactly underneath it's center of buoyancy.

The reason I'm interested in this minutia is that the water pressure at the bottom of a vertical Douglas fir stud is exactly the same as the water pressure at the bottom of a vertical Southern yellow pine stud.
And the displacement of the two studs is exactly the same.

Yet the ballast weight is different, so the buoyancy force is different.

Some say displacement. Some say water pressure.
I'm saying that the underlying quality that explains and predicts it's displacement, water pressure exposure, and whether it is floating or sinking is it's density relative to the water's density. So I think relative density should be the center of any discussion on buoyancy force.

 

[Roger Long]

I have calculated for you the amount of ballast placed on one end that would be needed to get a standard 2x4 to float vertically.

Just to be clear, I wasn't intending to say anything on my web site about the 2 x 4 floating vertically. I was describing it hanging in air as a way to visualize where CG is. I'll take a look at making that clearer.

So I think relative density should be the center of any discussion on buoyancy force.

Water density is certainly important. In fact, when we (naval architects) do stability tests we take along an aquarium hydrometer to measure precisely the density and temperature of the water. For current discussions however, when many are just trying to get a handle on the basics, we can assume a nominal sewater density. The amount that even fresh and salt water vary isn't very siginficant unless you are trying to get a very exact measurement of stability.

Density of the floating object is irrelevant to a discussion of buoyancy. A cubic foot of lead has exactly the same buoyancy as a cubic foot of foam in water. The buoyancy is determined by the volume. Whether it sinks or floats depends on what is happening at the other end of the "scale" which is where the density of the floating object determines whether it floats or sinks.

 

[Roger Long]

In addition, you should change the phrase "centre of gravity" to "centre of mass", and yes, I realize it's a nit pick, but what you describe as unmoving in a rigid body is the centre of mass and not the centre of gravity..

The center of gravity of an object of uniform density is at the center of mass.

The centre of gravity of a rigid body is the point where the sum of all the gravitational forces can be said to act and that *does* change a tiny bit with orientation.

Please explain how and what you mean by "tiny". We aren't concerned with tiny effects here. If the sun is shining on one side of your boat, the structure will expand slightly. The increase buoyancy will cause a tiny heel. But, nobody could measure it so, so what?

 

[Ross]

Dan, For your calculations to be completely valid you must select your 2x4 from clear, straight grain wood, with no grain runout, with a uniform growth rate across its width. You did not specify the size of the screw eye and you didn't allow for water absorption in the submerged portion of the stick.

Oh! one other thing, Did you allow for the distribution of mass when you calculated the ballast?