Displacement of Scooters at Depth - Spun off from the A&I Discussion about Nothernone

[BRT]

I see. So a cylinder filled with water displaces less water than a cylinder filled with mercury?

Yes, by the volume of the water in the cylinder. Very simple really. Put a cylinder without a valve into a tank of water and check how much the water level comes up. When the cylinder fills with water the rise in the tank level will be equal to the volume of material in the cylinder. Put an open tank full of mercury into a tank filled with water and the level will rise equal to the volume of the mercury and the volume of the metal in the tank. A real smart guy figured that out a few years back. Had a problem with gold and kings crowns if I recall.

 

[scubadada]

I've not taken physics for 47 years, I didn't like it then

Weight of a DPV at the surface - weight of water displaced = weight of the DPV underwater.

When the DPV integrity is breached, and it fills with water, it no longer displaces the same volume of water, and becomes heavier. The change in weight will be the decrease in the volume of water displaced. It's hard for me to understand how the weight in the water could ever equal or exceed the weight on land

 

[dmaziuk]

Yes, by the volume of the water in the cylinder. Very simple really. Put a cylinder without a valve into a tank of water and check how much the water level comes up. When the cylinder fills with water the rise in the tank level will be equal to the volume of material in the cylinder. Put an open tank full of mercury into a tank filled with water and the level will rise equal to the volume of the mercury and the volume of the metal in the tank.

OK so a ruptured tank would displace as much as its shell volume whereas a ruptured scooter would displace the volume of its batteries and motor and so on. So if you pack the empty spaces in the scooter full of foam, you could have a scooter that loses very little of its displacement. And if the foam was very light, it'd lose very little buoyancy too. I take it, that's not normally done?

I guess the foam'd have to be stiff enough to not compress...

 

[BRT]

OK so a ruptured tank would displace as much as its shell volume whereas a ruptured scooter would displace the volume of its batteries and motor and so on. So if you pack the empty spaces in the scooter full of foam, you could have a scooter that loses very little of its displacement. And if the foam was very light, it'd lose very little buoyancy too. I take it, that's not normally done?

I guess the foam'd have to be stiff enough to not compress...

Yes, and non compressible foam may be hard to come by and heavy. And it would almost have to be in pieces that could be removed for service, so there would still be some air spaces.

 

[Dan]

I don't "think" so. Im pretty darned certain. As you said, physics.

Well, do the following test. Get 2 Coca-Cola cans. Open one of them, drink it & crush it down to a wafer. May be even hammer it down as much as you can to get rid of any air space in it. Then throw both the crushed Coca-Cola cab together with the unopened one. Which one would sink faster?

If both cans have no air in them, I bet you they will sink about the same time.

 

[Akimbo]

I have never seen an imploded scuba tank.

Interesting sidebar: I had a friend that wanted to implode Scuba tanks in very deep water in order to inexpensively generate an acoustic signature for a research project. I did some FEA (Finite Element Analysis) on 3D solids models for him. I forget the exact numbers but Steel 80s collapsed in the 9,000 to 10,000' range. I thought it was a clever concept but he didn't get funding. I don't think he actually tested the computer model.

 

[Dan]

I have never seen an imploded scuba tank. I have never seen an imploded scooter. I don't know what it looks like when that happens.

I assume it would be deformed to some degree. If so, it all comes down to Archimedes' Principle. Because the volume of a flooded scuba tank or scooter does not change, the difference in buoyancy would be 100% due to the difference in weight between the water that entered that volume and the air it displaced. If the physical body is distorted, then the volume would change, and both would have to be considered. As anyone who has taken AOW should know, if you take an empty but capped water bottle to depth, it will implode, and its total volume will be far less than on the surface.

Let's say that instead of imploding, a cylinder has exploded. In that case, it would be wide open. The volume of the cylinder will have changed dramatically. In terms of volume, there is no longer an internal volume to consider, and for buoyancy, the only thing that would matter is the weight of the metal itself and the volume formed by the volume of the metal--the same as a lead weight.

When there is no air trapped in the scooter, regardless whether it is fully flooded scooter or imploded, should be about the same.

Archimedes principle includes the weight of the container, not just the weight of the water being displaced. Why do you think a full oil tanker float lower than the empty one?

 

[Dan]

As I wrote earlier, I have never seen an imploded scooter. It's a pretty rare event. If an imploded scooter and a flooded scooter have the same volume, then, yes, their buoyancy will be the same.

Volume has nothing to do with it. Trapped air does

 

[Joneill]

I wasn't asking about buoyancy, I was asking about displacement. Displacement is volume and an object filled with air displaces exactly as much as the same object filled with water. I honestly don't know what happens (EDIT) to displacement when the object is open to surrounding water, I'm pretty sure its volume doesn't change.

If a tank is open to it's surroundings, then only the actual volume of the metal the tank made of is displacing the surrounding water (as others have shown in their calculations). Since the seawater just fills the open space in the tank when the tank is not sealed, the interior volume of the tank no longer factors into displacement.

 

[Joneill]

What is "zero buoyancy"?

The object was neutrally buoyant because it weighed exactly the same as the volume of water it displaced. Once water was introduced into the cylinder instead of of air, the scooter became negatively buoyant because it now weighs more than the volume of water it displaces.That volume has not changed, though

Actually, assuming that the water enters the cylinder via a leak, the volume does change - it becomes smaller. An open cylinder will only displace the volume of the material is it made from - the water inside is not displacing anything on a flooded (unnsealed) cylinder.