Archimedes

[richardabeattie]

How do boats really float?

Scenario One: A squared sectioned barge with flat ends not unlike a long box gets dragged into a rectangular lock full of water. It floats by displacing the water that was in the lock.
Suppose the lock is only an inch bigger than the barge - length width and depth - the barge can still be dragged into it. (Let's forget the dynamics and surface tension issues and assume we are moving this barge very slowly with a rope so an inch of clearance all round is enough)

Now we shut the gates and the barge is still floating. Why? What water is it now displacing? How does the small amount of water left in the lock water know whether the lock gate is open so all the other water outside is helping it?

Scenario Two: We build a dry dock and in it we build a barge which is one inch smaller than the dock and supported one inch off the bottom. With the dock gates still shut we pour in enough water to fill the inch gap all round the barge. So now it's floating?

I did Latin and Greek and learned Morse so I ought to be able to work this out for myself but I can't.

 

[Aja]

Size has Nothing

to do with it.

It is the weight of the barge in both instances. The weight displaces the equivalent amount of water.

Donald

 

[Sailfree]

I think you may better understand it by considering your Senario 2 situation.

The ship is held off the bottom by 1" supports, the dry dock is slowly filled. At the point when the water reaches up the side of the boat such that the volume of water the boat displaces = the weight of the boat it starts floating. For every extra 1" height of water added into the dock the boat then floats 1" higher. It could just be 1mm of water around the boat or an ocean the principle is the same.


A lenght of string 12" long if formed into a cicle has a diameter of 12 divided by Pi approx 4". Its radius is therefore approx 2".

If you stretch a piece of string all the way round the world and then added 12" of string how much would it rise off the surface of the world? Its the same approx 2" , difficult to imagine but true.

I always like to visualise things but sometimes the results are initially surprising

 

[sarabande]

Enough of the British habit of estimates, please Sir !

Given a modal "string" circumference of the earth of 25000 miles, the radius is 252,229,299.363057 inches, and with the extra 12 inches added, the new radius will be 252,229,301.273885 inches. Tut !


What was it Gauss said concerning meaningless precision ?

(I must admit I did the calcs, cause I didn't believe you ! Ooops /forums/images/graemlins/blush.gif)

 

[mel80]

I dont think that anybody has ever suggested that it is the weight of the displaced water that causes objects to float; it is its buoyancy relative to its weight. Buoyancy is ultimately dependent on water pressure, and this is independent of volume.

The fact that a floating object displaces it's own weight of water is coincidental to this.

 

[gandy]

Visualise the water pressure pressing in on the hull from all directions. In the simple example of a vertical sided flat bottomed hull the pressures on each side cancels out, so the barge doesn't want to move sideways. The pressure on the underside acts upwards in opposition to gravity.

 

[dolphin]

Why ships float
Boats or ships made of steel are hollow. The total weight is less than the water it displaces, and thus the ship will float.

Different liquids can have different densities. For example, since a pint cooking oil is lighter in weight than the same volume of water, it is less dense than the water. Different gases can also have different densities. For example, helium is lighter than air, because it is less dense.

A ship will displace a volume of water that is equal to the weight of the ship. That is why a loaded cargo ship will sit lower in the water than an unloaded one. The difference would be equal to the weight of the load.

more info at
http://www.school-for-champions.com/science/fluidfloating.htm

 

[richardabeattie]

Gentlemen
None of you has answered the question.
When the barge is in the lock with the door shut the water has been displaced to outside the lock so what is holding the barge up other than the inch of water left rounfd it.

Aja: What water is displaced in theis scenario
Sailfree: You pour a small amount of water down a slot between th edry dock and the barge and it floats as soon as that small aount reaches the water line? I think not. Imagine the inch is now a milimetre! A few gallons would be enough to surround the barge!
Dolphin: You are copmpletely ignoring the constraint that in my close fitting dry dock there is no room for suffiecient weight of water to be enough to exceed the weight of th ebarge.
Gandy: How can so little water exert the pressure needed?

Come on chaps this is a serious question carefully set out. Even I know why steel boats float in the sea! But I want to know what happens when there ain't no large body of water being displaced and yet the barge gets into the dock and can be floated out once the gate is open.

 

[mel80]

Archemedes principle states that:

"The weight of fluid that a submerged object displaces is the same amount of buoyancy force applied to the submerged object."

Note that it does not state that the weight of the displaced fluid causes the buoyancy. It is the pressure difference in the water column that causes the buoyancy, and that is independent of how much water is left.

In other words, Archamedes principle is a useful tool, but it does not explain why things float.

 

[Pye_End]

To some extent they have answered the question - this displaced water does not cause the boat to float - displaced water is as a result of the barge floating. It is the relative densities that does it (not pressure).

What you have to ask your self is when you have closed the lock gate, why would it sink if the barge is lighter than the water?

 

[mel80]

[ QUOTE ]
is the relative densities that does it (not pressure).


[/ QUOTE ]

It is the pressure that causes buoyancy. e.g. a 1m cube of lead has exactly the same bouyancy as a 1m cube of polystyrene (when both are submerged) because the pressure difference between the top and bottom is the same (as are the surface areas) in each case.
The relative density is responsible only for determining whether the buoyancy can overcome the weight or not.

 

[boatmike]

This is the silliest thread I have read for a long time. It does not matter if there is one inch, one millimetre or one bleedin' mile of water around the vessel. Pressure only varies with vertical distance. The pressure at the bottom of a 1 metre column of water 1 inch diameter is exactly the same as the pressure at the bottom of a barrel 1 metre deep or the pressure you would experience diving one metre below the surface of the sea. The only slight variation is the salinity of the water. Salt water has a slightly different density than fresh so the pressure will vary. Float it in treacle and it will float higher. The only requirement in a lock is that there is sufficient volume of water to float the vessel and this volume will be very small if you only had 1 mm clearance all around it but provided that the depth is achieved the vessel will float.

 

[Spuddy]

Very enjoyable. As a side issue : the lock gate is closed and a dockyard matie pokes a pole into the water. This displaces some of the water in the dock and so the level rises; the rise is up the pole which then displaces more water - causing a further rise.......Eventually causing the dock to overflow. Last time I brought this up someone mentioned Hoffnung's builder's anecdote

 

[Pye_End]

Not sure I appreciate the nuancies of your argument.

It is the relative densities that determines whether an object floats or sinks.

Does your 'relative pressure' argument imply that an object may 'float' at 10m but not at 5m? It was drummed in at o-level that this was not the case - assuming I was well taught! Perhaps I mis-understand.

 

[cindersailor]

Nice question! Think of it in a slightly different way. The lock only 1" larger in all dimensions than the barge is full and the gates closed. The barge is lowered into the lock by crane and displaces the volume of water equivalent to its weight at which point it is floating. The water has overflowed over the lock gates. Are you suggesting that the barge is now not floating? The confusion arises because it is counterintuative that a heavy/large barge is floating in a very small volume of water which has much less weight than the barge. But there is no doubt that the barge has displaced the volume of water equivalent to its weight in being lowered into the lock - it is therefore floating. In effect the lock walls and gates are taking the place of the large body of water that normally surrounds a floating vessel.

If the barge is now craned out there will only be a small amount of water in the lock, if it is put back in it will float again as before, but this time it has not displaced any water from the lock! If the weight of water in the lock is less than the weight of the barge it cannot possibly displace its own weight in water as it is lowered in this time so how does it float?


Another question in the same vein which I was once asked at a job interview. You are in a smal boat on a reservior and have a brick which you throw overboard. What happens to the water level in the reservoir?

 

[mel80]

Yes, sorry, I was a bit caught up in my own argument.

You are right that is is the relative densities that determine whether somthing floats. My point was that it is water pressure, and more specifically the difference in pressure between the top and bottom of a submerged (or floating) object that causes buoyancy.

As to whether an object will float at 10m, but not at 5m: It depends on the object. Water is (to all intents and purposes) incompressible, so pressure will increase linearly with depth and an object of given size will always have the same buoyancy. However, some objects are compressible (like fish) so their volume (and thus their buoyancy) will change with depth. That is why many fish have swim bladders to enable them to maintain neutral buoyancy at a variety of depths.

 

[Pye_End]

So going back to the original question - which I think can be turned around a bit - if you have insufficient water to displace, but the vessel still floats, it appears that 'Archimedes was wrong'?

 

[mel80]

Archemedes principle was intended to be used as a tool; not an explanation. In other words, in was a neat trick of the physics involved that a floating object would create a hole in the water (or theoretical mass of water) that was precisely equal to the weight of the object, and this trick was useful for a number of practical purposes.

So he wasn't really wrong as such because he never proposed that it was displacement that caused things to float.

 

[cpedw]

I was going to describe the craning in/out illustration but cindersailor beat me to it. Does that help your understanding?
It's also interesting to consider the Falkirk wheel
(a canal boat lift if you're not familiar with it). It consists of 2 buckets, each of which can connect to canals at different heights. If the water depths in the 2 canals are the same, then each bucket contains the same amount of water and the wheel is nicely balanced and takes very little effort to turn it, as long as all the gates are closed and the water is retained in the buckets. But there's not very much call for moving water from one canal to another so often the buckets are filled with boats and just a bit of water. It doesn't matter how many boats are in each bucket, as long as they are all afloat and the water depths in the 2 canals are the same, then the 2 buckets still weigh the same and the force to turn the wheel stays small. Clever, isn't it?
Regards,
Derek

 

[gandy]

[ QUOTE ]
Gandy: How can so little water exert the pressure needed?

[/ QUOTE ] The pressure is generated by the height of water above the point where you're measuring the pressure. The volume doesn't matter, only the height. There's no paradox there.