The role of height in on required weight to reach neutral buoyancy

[EFX]

Here is another way to reason out the question starting with the buoyancy equation:

B = VD - W

where B = buoyant force: positive = float, negative = sink, 0 = neutral. V = volume of the water displaced by the diver, D = the density of the water, and W = the weight of the diver.

Can the height affect the buoyancy of a diver under water? It depends. The height is not part of the equation above. If the difference in height between two divers changes the difference in weight without changing the volume of water displaced then yes, the buoyancy will change. If we assume the two diver's weight is the same the buoyancy can still change but that only depends on the change of density between the two divers. Using an alternate form of the equation here is why:

B = VD - Vd

Here, d = the density of the diver. Vd = weight of the diver.

Since the weight can't change, the term Vd can't change. The only way that buoyancy can change is if we change the term VD. However, D, the density of water does not change between the two divers. Therefore, V must change. But if V changes we must change d to keep the weight the same. If we assume that a taller diver is leaner (more muscle mass) than our shorter "rounder" diver then the taller diver will have a larger density (muscle is more dense than fat). To keep the weight the same, V must be lower because d is higher. This lowers the term VD while keeping the term Vd the same. The result is that B becomes lower for the taller diver compared to the shorter diver. For this case the taller leaner diver is less buoyant than the shorter "rounder" diver even though their weights are the same.

 

[markmud]

1) As the specific weight of iron is 7.85, the volume of 1000 kg (1 ton) of iron is 1000/7.85=127.38 liters.
When the boat is floating, the weight of the displaced water must equal the weight of the iron boat, so the boat is displacing 1000 liters. When the boat is sunk, if no air is trapped inside its compartments, it will displace just the volume of iron, so 127.38 liters. Hence when the boat is sunk the waterline will go down, as the total volume of water+boat diminished by 1000-127.38 = 872.62 liters.
2) if the block is of iron, the water level will be the same as the sunk boat. If it is by concrete, or other material having smaller specific weight than iron, of course the level will be higher, but it will reach the level of the floating boat only if the block is made of a material with same specific weight as water (1), or smaller....
If the specific weight is smaller than that of water, despite the volume of the block will be larger than 1000 liters, it will displace always 1000 liters of water, and the excess volume will stay above the water line. Hence the waterline on the border of the pool remains the same as the floating boat when the block is also floating, having a specific weight smaller than water.

I love this answer! I never thought anyone would go into so much detail. Way to go!
Thanks for picking-up on my mistake. I did not describe the material of the one-ton block.

Here is another way to reason out the question starting with the buoyancy equation:

B = VD - W

where B = buoyant force: positive = float, negative = sink, 0 = neutral. V = volume of the water displaced by the diver, D = the density of the water, and W = the weight of the diver.

Can the height affect the buoyancy of a diver under water? It depends. The height is not part of the equation above. If the difference in height between two divers changes the difference in weight without changing the volume of water displaced then yes, the buoyancy will change. If we assume the two diver's weight is the same the buoyancy can still change but that only depends on the change of density between the two divers. Using an alternate form of the equation here is why:

B = VD - Vd

Here, d = the density of the diver. Vd = weight of the diver.

Since the weight can't change, the term Vd can't change. The only way that buoyancy can change is if we change the term VD. However, D, the density of water does not change between the two divers. Therefore, V must change. But if V changes we must change d to keep the weight the same. If we assume that a taller diver is leaner (more muscle mass) than our shorter "rounder" diver then the taller diver will have a larger density (muscle is more dense than fat). To keep the weight the same, V must be lower because d is higher. This lowers the term VD while keeping the term Vd the same. The result is that B becomes lower for the taller diver compared to the shorter diver. For this case the taller leaner diver is less buoyant than the shorter "rounder" diver even though their weights are the same.

Now that answers the OP's question in a way that I can even understand! Love'n it!


m

 

[Neilwood]

I love this answer! I never thought anyone would go into so much detail. Way to go!
Thanks for picking-up on my mistake. I did not describe the material of the one-ton block.



Now that answers the OP's question in a way that I can even understand! Love'n it!


m

And it is all pretty much irrelevant as they will still have to do a proper weight check.

 

[drk5036]

And it is all pretty much irrelevant as they will still have to do a proper weight check.

Just to reiterate, skipping a weight check was never the point, since they are simple and effective. I was more curious from an academic point of view whether height was a variable in proper buoyancy that was being overlooked.

 

[Angelo Farina]

Just to reiterate, skipping a weight check was never the point, since they are simple and effective. I was more curious from an academic point of view whether height was a variable in proper buoyancy that was being overlooked.

That's fine. I also wanted to always understand the reasons for everything.
Never been satisfied with oversimplified explanations!
Probably this is one of the reasons for which I decided to become an engineer...
And in scuba diving, understanding means acting consciously, and being more safe.
I would never make a life-threatening activity based on concepts given to me as unexplained rules, to be followed just by faith.

 

[CT-Rich]

I have not read every post in the thread, but being on the extreme end of the spectrum, I thought I would put in my 2 psi. At 6’7” and 240 lbs, I am tall and thin. I definitely use more wight than the average diver, and not by a little. With a Fusion Drysuit and 200 gram undergarments, I use 24 lbs on a harness and a additional 16 lbs plus a steel 120. Diving wet with 5mm full wetsuit I use 22 lbs. It sounds like a lot, but I will be a floater with an empty tank.

There is a big difference between someone like me a and a typical 5’10” male diver. Short and round is not the same as long and lean, I will let the rounder divers speak for themselves.

 

[markmud]

I have not read every post in the thread, but being on the extreme end of the spectrum, I thought I would put in my 2 psi. At 6’7” and 240 lbs, I am tall and thin. I definitely use more wight than the average diver, and not by a little. With a Fusion Drysuit and 200 gram undergarments, I use 24 lbs on a harness and a additional 16 lbs plus a steel 120. Diving wet with 5mm full wetsuit I use 22 lbs. It sounds like a lot, but I will be a floater with an empty tank.

There is a big difference between someone like me a and a typical 5’10” male diver. Short and round is not the same as long and lean, I will let the rounder divers speak for themselves.

Hi CT-Rich,

A little OT; a little humor here.

I am sure you use the same gas volume as the 135 lb. female does with a single AL80 on a tropical dive?

No, are you a gas hog? PADI has training that can fix that for you...

Sarc button now off.

m

 

[CT-Rich]

Hi CT-Rich,

A little OT; a little humor here.

I am sure you use the same gas volume as the 135 lb. female does with a single AL80 on a tropical dive?

No, are you a gas hog? PADI has training that can fix that for you...


Sarc button now off.

m

PADI has a class for everything. I am sure for a few dollars more they would happily lower my SAC and firm up my BMs. I think I could even get certified as a manicurist through them. I could proudly carry it with my boat diver cert, shore diver cert, night diver cert, drysuit cert, wetsuit cert, navigation cert, sock darning cert, left handed diving cert, nitrox cert, pool cleaning tech III cert, low vis cert, high vis cert, travel diver cert, stay at home diver cert, agnostic tech diver II cert, Hebrew diver I & II and sewer diver III.

 

[michael-fisch]

PADI had a class for everything. Since they climbed into bed with their favorite insurer they no longer offer Cave Diver Cards even though I saw someone with a PADI Cave Diver Instructor Card in Florida back in 1998.

Michael

 

[Ukmc]

I am an average height and weight (I guess obese by dr’s standards- 5’11” , 200lbs). I started diving with 12 lbs of weight in salt water and 6 lbs fresh water diving rash guard, AL80 and felt too heavy. I got it down to 8 lbs in salt water on the last open water dive and felt a lot better but still a little heavy. I know tried 500psi tank with no weights in a fresh water and still have to have air in BC to keep neutrally buoyant. Diving weight calculators suggest I should be diving with a lot more weight. I am not sure if my body is more dense or more round but I think I will go with 6lbs on my next salt water dive... which is about 10 lbs lighter than what calculators would suggest.