Archimedes

[Avocet]

Shouldn't make a difference. The pressure at the bottom of the tank is given by the density of the fluid in it multiplied by the acceleration due to gravity multiplied by the "head" - the height of the top surface of the fluid above the bottom of the tank.

 

[jimbaerselman]

Richard,

I'm now completely convinced that this was a very subtle and entertaining troll! Well done sir, for keeping us entertained through so many posts.

 

[boomerangben]

Pye_End,

Been thinking about this and come to the conclusion that the term "relative densities" is the one that irks me. Pressures and forces is how a scientist would explain the scenario and is the "proper" description.

However, as you rightly point out, it is not very user friendly when you are talking about anything other than a rectangular box. Hence Archimedes' Principle and it being a short cut. Naval Architects deal with volumes and use planometers or mathematics to determine water plane (or sectional) areas on drawings for a number of draughts (stations) to get a hull volume. In fact nowadays, you can get free hull generating software which determines volumes in real time.

Once the underwater volume has been determined and the density of the water at the chosen location is known, the mass supported at that draught can be calculated and compared with that required. Again using the area calculations, you can determine how much water is displaced by sinking the vessel another (say) cm and hence determine draughts for various displacements.

Relative densities don't really come into it, but volumes of the submerged part of the vessel and density of seawater does. But having said that, it would seem that I am very close to talking relative densities, ie I am using mass and volume, but never using them to determine a density as such.

I hope I have managed to explain it ok and if there are any practicing Naval Architects out there who can correct me if I am wrong, they are welcome. It is a long time since I studied it and not really used it much since.

 

[boomerangben]

Filling it up at all, even through a drinking straw would cause a leak. The only difference being the size of the wet patch.

 

[Pye_End]

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Pye_End,

Relative densities don't really come into it, but volumes of the submerged part of the vessel and density of seawater does. But having said that, it would seem that I am very close to talking relative densities, ie I am using mass and volume, but never using them to determine a density as such.



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Exactly my point - all to do with mass - volume - density - not to do with water pressure. Glad you agree.

 

[Stoaty]

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When the weight of water needed to fill the hole your boat leaves in the sea, is the same weight as your boat, you float.

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Your dead right. I knew that. I woke up this morning thinking. Damn I meant equal to.

 

[mel80]

Ok, I've done my best to explain it but I guess that I can't. The reason that you shouldn't explain buoyancy in terms of relative densities is because you can have differences in density without having buoyancy e.g. in the abscence of gravity. And, as I've said a few times before, you cannot explain a force (which buoyancy is) using density.

I'd better finish by saying that it is not just me that you disagree with, but also physicists at the university of Winnipeg (see here ), but I guess that you know best. Note that they describe how the relative density thing is a consequence of the way the physics works, but not the cause; that is is the important distinction.

 

[mel80]

Here's another web page that explains the physics, and how Archimedes principle arises from differences in fluid pressure. Again the web page is from a university physics department; notice a pattern emeging here?

 

[Pye_End]

Surely the water ball and the object on this webpage would rise because the upward arrow at the bottom is bigger than the downward arrow at the top?

If this is the case then the answer to my question yesterday (17.23 and 18.09) is wrong? An object with the same density as the fluid it is in will rise, as far as I remember from O level.

From my tennis ball question yesterday you also said that the medium pressure difference was the important factor - which is dependant on fluid density.

I have said that I agree that the forces can be resolved, but that it is not a useful thing to do - its not very easy to predict floating/sinking/waterline, but that the factors used in analysing the forces are far more useful. It reminds me a little of saying a cup sits on a table because the table pushes back. Has to really but does it really get you anywhere?

 

[Pye_End]

Your website link is interesting.

Buoyancy force = m times g time fluid density divided by object density.

Doesn't have pressure differential between top and bottom in it (even though they may be used to resolve the forces) - just shows that it is not a particularly useful way of applying buoyancy.

 

[boomerangben]

So what do you mean about relative densities? The term relative density implicitly implies there are two densities. But there is only one in Naval Architecture. The density of the ship does not come into it, and note how Archimedes Principle makes no mention of the density of the body you are trying to float.

I stand by pressures being the mechanics behind making something float. Archimedes gives us a short cut to make the maths easier, but it is volumes, not densities that matter (apart from of course the density of the water).

 

[mel80]

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Doesn't have pressure differential between top and bottom in it (even though they may be used to resolve the forces) - just shows that it is not a particularly useful way of applying buoyancy.

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That was pretty much my point! Maybe I wasn't explaining myself very well.

 

[duncanmack]

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So what do you mean about relative densities? The term relative density implicitly implies there are two densities. But there is only one in Naval Architecture. The density of the ship does not come into it, and note how Archimedes Principle makes no mention of the density of the body you are trying to float.

I stand by pressures being the mechanics behind making something float. Archimedes gives us a short cut to make the maths easier, but it is volumes, not densities that matter (apart from of course the density of the water).

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That's OK as far as it goes. However..

If a "vessel" is more dense than water then the "vessel" will not float.
If less dense then it will float.

A brick will not float but a hollow brick can be made to float (a hollow brick, btw, is less dense than a solid one /forums/images/graemlins/grin.gif).

Submarines - or more correctly submersibles have variable density. When on the surface they are less dense than the water, submerged they are the same density as the water. While submerging they are denser than the water.

Simple really...........

 

[Pye_End]

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So what do you mean about relative densities? The term relative density implicitly implies there are two densities.

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The two densities I refer are of that of the object and that of the fluid. In the case of a square barge in water then it will float if the average density of the barge is less than the density of the salty water it is sitting in - furthermore the density ratio will give you where the waterline will be (ie %volume above an below). This I think was the original question - at what point does an object float. The Newtonian / forces related explanation - how do you use this to give an indication of when the vessel floats without referring to weights and volumes (ie densities)?

In the case of a Naval architect working out where this will be then I would imagine they would use the weight of the vessel, and the volume of water (at whatever densities they work on) that it needs to displace - in other words when the weight / displaced water = density of the fluid. Not really the original question I would have thought but very much related.

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I stand by pressures being the mechanics behind making something float. Archimedes gives us a short cut to make the maths easier, but it is volumes, not densities that matter (apart from of course the density of the water).

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I am sure that you would also include wieght as one of the factors as well as volume - the two compnents of density?

I agree that you can resolve the forces for a floating object (I think it would be fairly serious if you couldn't!), but to calculate whether an object floats or not then you consider its weight and volume, and compare agains the density of the fluid - ie you compare their relative densities. Take an object - say a ball - and put it in the water - how would you work out whether it floated or sank? I would ask how much it weighed - work out the volume, and therefore the density, and then compare with the density of the water it was in. If it were more dense it will sink, if it were less dense it will float - and the ratio will tell me how well it floats. Can't see you getting to either of these answers using pressures/forces without resorting to these factors.

Suppose you could argue it is 'chicken and egg' - ie are you using forces to explain the calculations or visa versa, but I would argue that the crucial factor in whether an object floats is in its relative density. Tell me how you would use pressure/force argument in a practical way without referring to mass and volume?

 

[Pye_End]

Fair comment.

 

[Cruiser2B]

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Doesn't have pressure differential between top and bottom in it (even though they may be used to resolve the forces) - just shows that it is not a particularly useful way of applying buoyancy.

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That was pretty much my point! Maybe I wasn't explaining myself very well.

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Huh? Didn't you say "The reason that you shouldn't explain buoyancy in terms of relative densities is because you can have differences in density without having buoyancy e.g. in the abscence of gravity."?

Not to belabour it, I see your point, but the pressure discussion is really theoretical - the only practical way to look at buoyancy is as a factor of gravity and the densities of the object and the medium in which it's immersed (relative density). How about another conundrum? Take your cube and immerse it - there are six sides surrounded by water. The forces applied to the sides cancel each other out; there's a downforce above and a greater upforce below. If the resultant upforce is greater than the weight of the cube, it floats; if not, it sinks. What if the cube is on the bottom of the dock, or the sea-bed? There is no water creating a force on the bottom. The side forces still cancel each other out, and there is still a downforce, so does the cube lose all buoyancy? Imagine you put a styrofoam cube on the floor of the drydock, then flood it, will it not float?

 

[boomerangben]

"Ratio of densities..."

You can only use the ratio of densities for a slab sided vessel (the rectangular barge scenario). Almost all floating bodies have a water plane area that varies with draught meaning that you cannot use a linear relationship (a ratio) to determine the draught. In the case of a tennis ball, if its density is say 0.3 that of water, its draught will not be 0.3 the diameter of the ball.

As I have said before, a Naval Architect determines the volume of the vessel at various draughts. He selects a water density and that gives him the displacement and compares that with the weight of the ship. At no time does he need to calculate the density of the ship. If the ship turns out to be heavier than the mass of displaced water, then he needs to increase the submerged volume by increasing the draught. Yes all the components are there to calculate density, but it is never done. Why? because you cannot (except for the special case sited above) determine the new draught using relative densities because the volume of a ship does not increase by the same amount at all draughts.

The only time I have used relative densities is when designing SUBMERGED clump weights, ie when you need to generate a certain down force to hold something in place. (trained as a Naval Architect to make things float, spent a career making sure everything sank! - now I spend my life keeping aluminium flying - and that has absolutely nothing to do with relative densities!!!)

You can use relative densities to determine if something will float or sink, but not to determine its draught.

 

[boomerangben]

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Imagine you put a styrofoam cube on the floor of the drydock, then flood it, will it not float?

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Yes because the dock floor exerts a force on the polystyrene block before you start to flood (otherwise the polystyrene block would fall through the dock floor). When you start to flood the dock tiny amounts of water creep under the block, giving a pressure acting on the bottom of the block.....

If the joint between the polystyrene and dock bottom was perfect (ie there is no way for water to get under the block) it would stay on the bottom of the dock during flooding. Strange but true and this is part of the theory behind suction anchors - ones that can withstand a greater up force than their mass. (Although I would admit that suction anchors are held in place by friction more than by suction) However you do have to sink the anchor first so in practice it has to be negatively buoyant.

 

[Pye_End]

[ QUOTE ]
"Ratio of densities..."

You can only use the ratio of densities for a slab sided vessel (the rectangular barge scenario). Almost all floating bodies have a water plane area that varies with draught meaning that you cannot use a linear relationship (a ratio) to determine the draught. In the case of a tennis ball, if its density is say 0.3 that of water, its draught will not be 0.3 the diameter of the ball.

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As I said the ratio of densities will give you the VOLUME above and below the waterline - in the case of a ball it is easy, as is a pyramid etc. I agree that a ship with complex topsides it is probably harder to calculate, and I have always agreed - it is unlikely that this calculation is used in this way to calculate waterline! Although with the age of the computer, who knows, somebody may caome along and say that it is. Submarines may be a little more important to calculate correctly so it may be exactly how it is done. I know not.

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You can use relative densities to determine is something will float or sink, but not to determine its draught.

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Was this not roughly where we started? Exactly my point - relative densities will determine whether an object will float or sink. However, you CAN use it to determine draught, but for complex bodies, as you say, why bother.

 

[boomerangben]

I agree, densities can be used to determine IF things float or sink, but don't explain WHY things float and are not used to determine where the water line is (though I suppose you could if you wanted to make more work for yourself).

If I had said that right at the start, I wouldn't have wasted your or my time!!