Archimedes Schmarchimedes

[Kirstie]

I have to bite the bullet soon and sit my DM physics exam. Now, I'm not a stupid person (I like to think) but I cannot grasp the whole 'volume/displacement/air needed to lift' concept. I've had it explained to me by a Course Director and I'll ask Turbanator to go through it again (poor sod) so I'm not looking for a lesson here.

What I need are some examples to work through. I'll do the ones in the PADI DM workbook but are there any anywhere else that I can use?

I'm more of a language/arts/literature person (physics, maths and I have a very poor history), and I'm getting myself tied up in knots about this, so any help would be appreciated.

Thank you.

[Woz]

Right. It's dead simple. Immerse somethign in a liquid and you get an upthrust equal to the weight of liquid displaced.

So if you have a 10x10x10 cm cube of something and stick it in say water that has a density of 1 kg/litre then you'll get an upthrust of 1kg. Now- if your 10x10x10 cube weighs less than 1kg (say it's polystyrene which weighs sod all) then it will float as the 1kg upthrust is much bigger than its weight. If the 10x10x10 cube is heavier, say lead, then it will sink as 10x10x10 of lead weighs about 11kg. However it will still have the same 1kg of upthrust so it will actually "weigh" on the bottom of your sink 10kg.

For denser liquids the upthrust is greater- see Digger's post on filling the SETT with mercury.

[Finless]

Examples/schmegamples!

Volume Displacement

Volume Displacement. Archimedes was a Greek mathematician, inventor and physicist who lived from 287 - 212 B.C. A king once gave him a difficult task. ...
www.rit.edu/~vjrnts/courses/matter/labs/volume_displacement/ - 8k - Cached - Similar pages - Note this
Volume Displacement

Volume Displacement. Question: If you were in a boat in a small swimming pool (so that you could measure the water level) and there were rocks in the boat, ...
www.newton.dep.anl.gov/newton/askasci/1993/physics/PHY23.HTM - 16k - Cached - Similar pages - Note this
Volume Displacement Measurement

Examples such as this illustrate MicroXAM optical profiler's efficacy in providing failure analysis, wear analysis, and volume displacement. ...
www.phase-shift.com/products/volume-displacement-measurement.shtml - 14k - Cached - Similar pages - Note this
Analysis of volume displacement and length changes of the ...

The fraction of total rib cage volume displacement (delta Vrc) contributing to abdominal displacement is predicted from anatomic considerations and ...
jap.physiology.org/cgi/content/abstract/53/3/750 - Similar pages - Note this

[Finless]

So ....................... when you pass .......................... you'll be a dive mistress?

[chrisch]

The man himself sat in the bath. There's a good start. As you get in the water level goes up. If the bath is full the water comes over the side. If whatever is in the bath (you in this case) weighs less than the water that comes over the side it will float. If it weighs more (e.g. Turb's PSP) it will sink.

Chris

[Kirstie]

Originally Posted by Woz

Right. It's dead simple. Immerse somethign in a liquid and you get an upthrust equal to the weight of liquid displaced.

So if you have a 10x10x10 cm cube of something and stick it in say water that has a density of 1 kg/litre then you'll get an upthrust of 1kg. Now- if your 10x10x10 cube weighs less than 1kg (say it's polystyrene which weighs sod all) then it will float as the 1kg upthrust is much bigger than its weight. If the 10x10x10 cube is heavier, say lead, then it will sink as 10x10x10 of lead weighs about 11kg. However it will still have the same 1kg of upthrust so it will actually "weigh" on the bottom of your sink 10kg.

For denser liquids the upthrust is greater- see Digger's post on filling the SETT with mercury.

I think I understand that bit. It's the order of the calculations that throws me. You know, the multiplying by 1.03 for sea water and 1 for fresh water, the volume of the object minus the displacement, the age of Archimedes divided by the gross annual olive crop etc etc.

Surely, in the real world, if you have to lift an object from the seabed, you take down the biggest liftbag you have, fill it completely full of air and let it go? Do people really sit about calculating how much air they need to the nearest bar? Do they buggery!

[Finless]

Originally Posted by chrisch

The man himself sat in the bath. There's a good start. As you get in the water level goes up. If the bath is full the water comes over the side. If whatever is in the bath (you in this case) weighs less than the water that comes over the side it will float. If it weighs more (e.g. Turb's PSP) it will sink.

Chris

The "it" in your example being Kirstie?

And the rest of you can stop perving .......... I'm sure Kirstie is fully clad in the bath!!!

[Woz]

Originally Posted by Kirstie

I think I understand that bit. It's the order of the calculations that throws me. You know, the multiplying by 1.03 for sea water and 1 for fresh water, the volume of the object minus the displacement, the age of Archimedes divided by the gross annual olive crop etc etc.

Surely, in the real world, if you have to lift an object from the seabed, you take down the biggest liftbag you have, fill it completely full of air and let it go? Do people really sit about calculating how much air they need to the nearest bar? Do they buggery!

Teh problem with lifting stuff isn't getting it to the surface but overcoming the "sticktion" of the seabed.

Anyway. The upthrust of an object is it's volume x density of the liquid. Take that away from it's weight in air and you have the required upthrust you need to make it neutrally buoyant.

So- say you have a 10x10x10 cm lump of lead you want to lift. Weight in air = 11 kg. Upthrust in fresh water = 1 kg. Weight in water = 10 kg. Volume of air needed to make it neutral = 10/1 = 10 litres.

Or for seawater:
Weight in air = 11 kg
Upthrust = 1.03 kg
Weight in water = 9.97 kg
Volume of air needed to make it neutral = 9.97 / 1.03 = 9.67 litres.

[The Doctor]

The easy way 1KG =1liter so if you had to lift 1KG from 40m you would need 5 liters of gas.

[Woz]

Now let's be a bit silly and assume we are diving in pure alcohol.

10x10x10 cube of gold.

Weight in air = 19.3 kg
Upthrust in alcohol = 0.78 kg
Weight in alcohol = 18.52 kg
Volume of air needed to make neutral = 18.52/0.78 = 23.74 litres

So you need more air to lift in booze than in water as the upthrust is lower as the alcohol is not as dense.

BTW for you pedants out there I am assuming that the weight of air is negligible. We could be really silly and lift with argon or something which is a bit heavier so you would need more.