If the Boat Sinks: Newsletter Challenge (03/21/06)

In order for an object to float, it must displace its weight in water. With a closed system, such as the lock, if a barge is displacing water, floating, when it entered the lock, and all of a sudden sank, or no longer displaced enough water to float, and did not run aground, then the water level in the lock will fall.

Once the barge sinks, don't you think the actual volume of the barge will displace more water, making the level in the lock increase?

Once the barge sinks, don't you think the actual volume of the barge will displace more water, making the level in the lock increase? Yes I do believe you are correct. If the water level is constant, the barge would displace the water and the only place the water could go is up.

No - the reasoning is as follows: For this to be true, the barge would need to be less dense than water; i.e occupy more space for the same mass. It would therefore be impossible to sink the barge !! Ah you say - what about the steel ? If you were to throw all the steel overboard first, it would now no longer displace water equal to its weight, only its volume. Since it is more dense than water, the level in the lock would fall.

The barge displaces its own mass of water in order for it to float. Displaced mass = volume of water x density of water = mass of loaded barge (Archemides wasn't it?). But air voids inside barge (& below water line at that) will fill with water when barge sinks. Overall density of barge will increase. The lock water line will go down by the volume of the air voids inside the barge.

No, I don't think so. If it sinks, the volume of the barge is full of water, and no longer displaces water. Granted, it would displace some water, but it would be the amount of water displaced by the steel as if it were melted down and formed a solid block, discounting any air pockets. I think it goes back to the shape of the barge in the first place. A solid block of steel will not float, or displace its weight in water, but if you reshape that same block of steel into the shape of a hull, then it will displace enough water to support the steel. The weight of the steel has not changed, and even the volume of steel has not changed, just the shape. Consider the following: In order for something to float it has to be shaped in such a manner as to displace a volume of water at least equal to its own weight. The lock is a closed system, a certain amount of water, none added, none taken away. The barge is loaded with steel when it enters the lock, none is added none is taken away. While it is floating in the lock, the barge is displacing its weight in water, plus the weight of its cargo. This displacement of water will be noted as a water level in the lock. If the barge sinks, then it no longer displaces enough water to support it and its cargos weight, or it displaces less than the volume of water equal to its weight, or a smaller volume of water than when it entered the lock, so the water level in the lock will fall.

The barge is not a submarine, mind you. The water in the lock is in the lock, no matter whether its in the lock itself, or in the barge in the lock. Closed system??? What about the miles above the lock water. It the sinking of the barge (if it could sink in a lock, which it can't), could cause the water level to rise at all, or drop...think of the ramifications that would have for physics in the world. When glacial icebergs break loose and fall in the ocean, the shore line levels would rise...even while they were being lowered by the melting caused by atmospheric warming. No more global warning crisis? This is really a very simple question. It's just hard to keep from getting hung up on trying to describe it.

The barge is not a submarine, mind you. The water in the lock is in the lock, no matter whether its in the lock itself, or in the barge in the lock. Closed system??? What about the miles above the lock water. It the sinking of the barge (if it could sink in a lock, which it can't), could cause the water level to rise at all, or drop...think of the ramifications that would have for physics in the world. This is really a very simple question. It's just hard to keep from getting hung up on trying to describe it.

I think your explanation is correct, if you assume that there is no large water-tight pockets of air on the barge (which is probably a valid assumption). However, if there were large air pockets, then the water level could rise. You have to consider weight per volume, not just weight. If the boat and cargo weigh 10 lbs. it will displace 10 lbs. of water to float. If the boat and cargo are mostly steel, then the volume of 10 lbs of steel is much less then 10 lbs of water, therefore the water level will drop when the boat sinks. However, if there are large, sealed air pockets on the boat, it is possible that the volume would be more then that of the displaced water and therefore the water level could rise. Imagine a balloon in a tub of water. It will barely diplace any water while floating. However, if you force it under water, the water level in the tub will rise. You can postulate the possibility of the boat even sinking under these circumstances, even if it took on water.

The key phrase is "For any reason" NB A floating bage displaces its own weight of water, a sunk barge displaces less than its own weight - that is why it sinks So if something holes the barge below the water line, water flows in and air flows out until it sinks the water level in the lock will fall slightly since less water is displaced. If the someone switches on an electromagnet, pulling the barge to the bottom with large pockets of air trapped inside the water level will rise because the barge is now displacing its own weight of water PLUS the volume of barge which was previously above the water line If someone loads the barge with an extra few tons of steel until it sinks, initially complete with air pockets the water level will initially rise by enough to balance the extra steel and then sink as water flows into the holds and air flows out There must be some scenario in which the water level remains the same but the only one I can think of right now is if the average density of the steel and wood combined averages out to 10lbs/gallon (8lbs/US gallon)

Once it has sunk, the weight is irrelevant. It displaces its VOLUME in the water. Therefore, the water level must rise.

Nay, nay and thrice nay !! The amount of water displaced by the floating barge is equal to weight of the barge plus its load. Think - if this were not so all steel ships would sink as steel is more dense than water. You need to make a conceptual leap here. For example Aluminium is denser than water, right. If you take a piece of aluminium foil and scrunch it up into a ball - it sinks; your theory looks safe so far... Now retrive the foil and shape it into a saucer shape - hey presto ! It floats. We have not added or taken away any mass, merely changed the shape so it displaces water in excess of its weight. This contradicts your hypothesis, which must therefore be false. Forget all this spurious rubbish about air pockets and the like - that's just engineers being deliberately obtuse - it adds nothing.

hahah potatoe

Is it a trick question? The water in the lock remains the same because it will be at the level of the water outside. Water will enter or leave the lock to accommodate any change of displacenment. If it is not a trick question, then when the boat sinks the water displacement will be equal to the volume of the steel - whereas the water displaced when afloat will be equal to the weight of the steel. As a ton of steel occupies much less room than a ton of water (about 13%) the water level will fall.

When the barge is floating x gallons of water is displaced. If the barge sank the water would fill the air space within the hull so I would say that the water level in the lock would drop.

The water level will fall. The buoyancy force is equal to the weight of the water displaced. When the boat and its load go under water, the only water displaced will be the volume held by the boat and load which will be less than the water displaced in order to keep the heavy load afloat.

The way I see it, the water level will fall while the barge is in the process of sinking, presuming that the load is all heavier than water. However, once the barge is fully submerged and additional air escapes from the hull the water level will fall even further, unless the lock is not locked from the influence of outside water. A different scenario emerges if, for some reason, there is no exchange of air and water involved, as is in the case of the barge just being too heavy to float in the first place. In that case the water will most definitely rise. The clue to this maybe is that the barge is being lowered into the lock.

The level will fall - but not necessarily because of the change in boyancy. If we consider boyant effects only, the level would fall if the vessel were punctured, but it could rise if it sank because of being overloaded - at least until sufficient air had escaped to cause the level to fall again. (The upward force on the barge is equal to the weight of water it displaces. For the barge to sink without changing its weight, the upward force on it would have to reduce, which means that the weight of water displaced would reduce). However, according to the question, the vessel is about to be lowered, in which case it must still be connected to the upper volume of water, whose height is constrained by a sluice. So the effect of the sinking will be to create a wave, which will cause a peak of water to flow over the sluice. So the level will fall until enough water flows to replace it - even if the barge is actually displacing a greater volume of water than before.

Doesn't matter whether or not the barge is in a lock or not (however, the water level is easier to see on the wall of a lock than the shore of a lake). If a boat is floating, it and its contents displace a volume of water equal to the weight of the boat and contents. All contents with a greater density than water will sink to the bottom and displace less water, so therefore, the water level will go down. Assuming that the boat can be sunk (e. g. not made of materials less dense than water), if it were to sink, it would displace less water than it did when floating, and the water level will go down further. If all other contents of the boat floats because they're less dense than water, then the water level will not change. If the less dense(than water) contents are forced to the bottom (as they would be if they were trapped by more dense stuff of sufficient weight to keep them under water), the water level will rise, but not to the level when everything was kept afloat.

You are giving me a headache. The answer is obvious the amount that is dispaced while afloat is equal, to the amount that is displaced when sunk, the volume of water stays the same. In a closed system you can test it for yourself...The water niether rises or lowers...test it...

A lock is not a closed system. Duh!!

Try this at home. Put a handfull of rocks in a bowl and float them in a pot of water deep enough to sink the bowl and rocks. Put enough rocks in the bowl to bring the water line half an inch from the bowl's top edge. Note the water level when the bowl and rocks are floating. Push the bowl of rocks under water and please let me and everyone else know whether or not the water level went up, down, or stayed the same. Thanks . . .

Ahhh . . . I just figured out why you're confused! The question is NOT about the VOLUME of water -- it's about the WATER LEVEL!

Sorry, but this would not be the case. The vessel relies on air to remain afloat. If you sink the ship you must remove the air inside the hull. Where does the air go? it sits above the water inside the lock. The water level in the lock that was displaced by the air inside the hull will cause the water level to drop.

See my neutron star example further down the replies for the answer.

Since a vessel displaces its weight below the water (hence the reason for a boot stripe or plimsoll mark) it leaves the part of the vessel above the waterline (freeboard) virtualy weightless and void. when the barge sinks water will fill this void and the water level in the lock will fall. Test: fill a 1gal. container two thirds full and float a glass then record the water level. Sink the glass and ta-daaa challenge solved. Anyway; a good lockmaster will close the gates and pump water out until the barge rests easily on the bottom the boat crew in the meantime will undo any moorings to the barge so as not to take the boat down also then wait for salvage.

Sorry . . . I didn't see your response until after I posted a challenge to zzzgrinch to do the experiment.

Think of it this way. Imagine a vessel that has as its cargo a 1 cm cube which contains the equivalent volume (1 cubic centimeter) of neutron star material (imagine that the material can be contained and would not expand). Imagine the vessel floating in a huge container (the lock).

The weight of the 1 cm cube would be 8E13 to 2E15 grams or a hell of a lot if you please.

In order to float that on water, which has a density of approximately 1 (depending on the water's salt content) you need to have a vessel displacement volume which has a net density less than one.

Let's assume that the vessel has no mass or its mass is negligible compared to the 1 cm cube's and its hull wall volume is zero. How big a volume would you need for the ship? It must be larger than the equivalent weight of water of the same volume or 2E15 grams of water. One milliliter of water = 1 gram, so the volume that the vessel displaces must be 2E15 milliliters! The rest is air. That air is below the hull's water line.

Now pull the plug in the hull and let the ship sink. What happens? We said for this thought experiment that the hull volume is dimensionless, so all we have is the 1 cm cube. The air that was inside the vessel will rise above the lock's water line, but the cube sinks. The lock's water level drops a lot! The exact amount of the drop is equivalent to removing 2E15 - 1 milliliters of water from the lock!!!

It is easier to see this with the above example, but the same principle applies to the steel in the ship of the original question. Steel, while not as dense as my imaginary neutron star sampler kit, is significantly denser than water and if the ship sinks, the water level must also drop!

Any vessel that floats and utilizes air inside the hull to float the vessel, when sunk, will displace less water when submerged than when floating. However a submarine violates this rule. How? the air used for buoyancy in the ballast tanks is compressed into a volume where the density of that ballast air is higher than water and the ballast tank is filled with water.

Haven't we had this question in the last month or so? The battleship in the bath....

Collectively we've learnt something, as the regulars are all agreed the water level will drop.

I'm still wondering what's unusual about the Severn-Trent Canal locks...I'm sure they're the same as other locks in the UK ;o)

First, I would have to tell her that whoever put her up to asking the question forgot to also tell her that the barge could never sink, as she imagines it, in the lock because the distance from the barge's bottom to the lock's bottom is, in all probability, shorter than the barge's freeboard. After explaining the meaning of freeboard to her, I would then go on to tell her...'but let's imagine that lock really is very very deep...that the water goes down as far, say, as that gantry there goes up...that the barge really could sink; then maybe we can figure this out?" When she said, "Mmm, okay," I would continue: "Okay, why don't we play a little make-believe? Let's all imagine that you and your brothers and sisters and I each have an imaginary bucket...no wait...let's imagine that we are going up to the top of that great big gantry there; and when we get to the top, we're going to lower that great big bucket down into the lock to get a bucket full of water. Okay, now we've hoisted a bucket full of water out of the lock. Now, look at the water line on the sides of the lock. Do you see? It's gone down, right?" "It sure has! Is that how much water we took out?" "You got it. What a clever child you are! Now, let's move the big bucket over and drop the bucket of water into the barge. Careful now, don't let it splash out! Okay, now the water that was in the lock is in the barge, right?" "Right." "Now, child, look at the sides of the lock again. Where is the water now? "Hey, it's back up to where it was before!" "Right. So couldn't we say that the water we took out of the lock and put into the barge made the water in the lock go back to where it was?" "I t h i n k so." "Couldn't we also say that when we put the water into the barge--and the barge is in the lock--isn't that just like as if we put the water back into the lock?" "Mmmm." "Okay, wanna try another bucket full?.... "Same thing this time, too? Right?" "Yeah!" "So it's like: when we put the water from the lock into the barge, the barge keeps the water from 'spreading out' the way it could when it was actually in the lock. And, if it can't spread out, it all just goes to the bottom of the barge, right?" "Right." "Now look over at the sides of the barge. See there where it's painted different colors, one above the other to make a line that's even with the water? See how the water in the lock is just below that line?" "Yeah?" "Okay, why don't we put another bucket full from the lock into the barge and see what happens?" "Hey, the water went down again and came back up just like before!" "Right. And look at the side of the barge now; the water's up higher now; see? You can't even see the line any more. Where did it go?" "The water came up the side of the barge and covered it up." "Right! So what happened to the barge? Did it go up? Or down?" "Huh?" "Quiet boys!" Okay, honey, the water on the side of the lock went down and came back up to where it was when we took water out and put it in the barge; but it only came up on the side of the barge. Wouldn't that mean that the barge went down in the water?" "O-h-h. Y-e-a-h." "So it's like...the extra water in the barge is making the barge push down into the water. And when it—when the barge--pushes down on the water below the barge, that water is pushed out from under the barge and over to the sides of the lock?" "Yeah!" "And when the water gets to the sides of the lock, it has no where else to go but up; can you see?" "Right." "Okay. So, if every time we lift out a bucket full, the water in the lock goes down so far; and then every time we put the water in the barge, it comes back up in the lock the same distance....couldn't we say that the distance that the water went down in the lock--which is the same distance the barge pushing down made it come back up when we put the water into the barge that's in the lock--couldn't we say that that distance between the lock's water when it's low and when it's back where it was...that that distance tells us how much water is in the bucket?" "Yeah!" "Right. That, darling children, is what's known as displacement. The amount of water in the bucket tells us how far down—when we count the buckets full—how far down we can make the barge push into the water, and how far up the side of the lock we can make the water go back up." "Displacement?" "Right. And if we talk about some kinds of ships, about the size of the bucket—how far a bucket full can make the water move up in the lock--how many buckets we could put in them and they still float…we would call that the ships' tonnage." "T-t-onnage." So, do we know the answer to your question, daughter? Will the water keep staying where it was on the lock sides if the barge sinks?" "Sure. It will." "Wait. Not so fast. Why don't we try something just to be sure? What do you say we go on and keep filling the barge with water until it j-u-u-st begins to sink, but doesn't really sink; it only stays barely floating…. "….Okay, now let's climb back down to the platform from this gantry and take a closer look. Here we go…. "Now then, we saw that taking buckets-full out of the lock and putting them in the barge is just like putting them back into the lock; the water stays the same on the side of the lock….Now, if the barge was to keep going down into the water by itself, with the water pouring into it from the lock all by itself….what do you think? Won't that water just be going back into the lock, too? Won't the water level on the side of the lock still stay the same even though we aren't picking up and dropping buckets full?" "It should." "Okay then. Take your imaginary hand bucket there. Now, dip it in the lock..that's right…and get a bucket of water. Now, throw your bucket of water into the barge. It's okay, go on… "…Oops! There goes the barge. But look now. Where's the water on the side of the lock?" "Hey! Right where it was! It's in the same place where we said it would be!" "Right…and there's your answer. But tell me. Is that a good thing or a bad thing?" "Wh-u-u-t??" "Is it good, bad, or just okay, that the water doesn't go up or down after the barge sinks?" "….???" "Okay, Daddy will tell you. It's good; and it's bad, both." "I don't want to know and I don't care." "Well, you can be that way, but do you remember about our house back home on the beach…and about global warming? Remember we were talking about, if the icebergs and ice caps all melt, then one day our house on the beach might disappear under the ocean?" "Yeah? But…" "Well, would that be good or bad?" "Whew! Bad. Gheez!" "Well then…if sinking the barge could make the water in the lock go up or down, that would mean we could save our house on the beach wouldn't it?" "….???" "Sure it would. All we'd have to do is take land and dump it in the ocean; or dredge the bottom of the ocean and put the earth from there back up on the land. Whichever way would lower the ocean…because we'd be sinking something…just like sinking a barge; that way we could keep our house above the water. Isn't that right, silly person with silly questions?" "Daddy, you're silly." "Anyone wanna go for a swim?

Same as antecedant post. Resubmitted in text format to restore format...ease of reading
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First, I would have to tell her that whoever put her up to asking the question forgot to also tell her that the barge could never sink, as she imagines it, in the lock because the distance from the barge's bottom to the lock's bottom is, in all probability, shorter than the barge's freeboard.

After explaining the meaning of freeboard to her, I would then go on to tell her...'but let's imagine that lock really is very very deep...that the water goes down as far, say, as that gantry there goes up...that the barge really could sink; then maybe we can figure this out?"

When she said, "Mmm, okay," I would continue: "Okay, why don't we play a little make-believe? Let's all imagine that you and your brothers and sisters and I each have an imaginary bucket...no wait...let's imagine that we are going up to the top of that great big gantry there; and when we get to the top, we're going to lower that great big bucket down into the lock to get a bucket full of water. Okay, now we've hoisted a bucket full of water out of the lock. Now, look at the water line on the sides of the lock. Do you see? It's gone down, right?"

"It sure has! Is that how much water we took out?"

"You got it. What a clever child you are! Now, let's move the big bucket over and drop the bucket of water into the barge. Careful now, don't let it splash out! Okay, now the water that was in the lock is in the barge, right?"

"Right."

"Now, child, look at the sides of the lock again. Where is the water now?

"Hey, it's back up to where it was before!"

"Right. So couldn't we say that the water we took out of the lock and put into the barge made the water in the lock go back to where it was?"

"I t h i n k so."

"Couldn't we also say that when we put the water into the barge--and the barge is in the lock--isn't that just like as if we put the water back into the lock?"

"Mmmm."

"Okay, wanna try another bucket full?....

"Same thing this time, too? Right?"

"Yeah!"

"So it's like: when we put the water from the lock into the barge, the barge keeps the water from 'spreading out' the way it could when it was actually in the lock. And, if it can't spread out, it all just goes to the bottom of the barge, right?"

"Right."

"Now look over at the sides of the barge. See there where it's painted different colors, one above the other to make a line that's even with the water? See how the water in the lock is just below that line?"

"Yeah?"

"Okay, why don't we put another bucket full from the lock into the barge and see what happens?"

"Hey, the water went down again and came back up just like before!"

"Right. And look at the side of the barge now; the water's up higher now; see? You can't even see the line any more. Where did it go?"

"The water came up the side of the barge and covered it up."

"Right! So what happened to the barge? Did it go up? Or down?"

"Huh?"

"Quiet boys!" Okay, honey, the water on the side of the lock went down and came back up to where it was when we took water out and put it in the barge; but it only came up on the side of the barge. Wouldn't that mean that the barge went down in the water?"

"O-h-h. Y-e-a-h."

"So it's like...the extra water in the barge is making the barge push down into the water. And when it—when the barge--pushes down on the water below the barge, that water is pushed out from under the barge and over to the sides of the lock?"

"Yeah!"

"And when the water gets to the sides of the lock, it has no where else to go but up; can you see?"

"Right."

"Okay. So, if every time we lift out a bucket full, the water in the lock goes down so far; and then every time we put the water in the barge, it comes back up in the lock the same distance....couldn't we say that the distance that the water went down in the lock--which is the same distance the barge pushing down made it come back up when we put the water into the barge that's in the lock--couldn't we say that that distance between the lock's water when it's low and when it's back where it was...that that distance tells us how much water is in the bucket?"

"Yeah!"

"Right. That, darling children, is what's known as displacement. The amount of water in the bucket tells us how far down—when we count the buckets full—how far down we can make the barge push into the water, and how far up the side of the lock we can make the water go back up."

"Displacement?"

"Right. And if we talk about some kinds of ships, about the size of the bucket—how far a bucket full can make the water move up in the lock--how many buckets we could put in them and they still float…we would call that the ships' tonnage."

"T-t-onnage."

So, do we know the answer to your question, daughter? Will the water keep staying where it was on the lock sides if the barge sinks?"

"Sure. It will."

"Wait. Not so fast. Why don't we try something just to be sure? What do you say we go on and keep filling the barge with water until it j-u-u-st begins to sink, but doesn't really sink; it only stays barely floating….

"….Okay, now let's climb back down to the platform from this gantry and take a closer look. Here we go….

"Now then, we saw that taking buckets-full out of the lock and putting them in the barge is just like putting them back into the lock; the water stays the same on the side of the lock….Now, if the barge was to keep going down into the water by itself, with the water pouring into it from the lock all by itself….what do you think? Won't that water just be going back into the lock, too? Won't the water level on the side of the lock still stay the same even though we aren't picking up and dropping buckets full?"

"It should."

"Okay then. Take your imaginary hand bucket there. Now, dip it in the lock..that's right…and get a bucket of water. Now, throw your bucket of water into the barge. It's okay, go on…

"…Oops! There goes the barge. But look now. Where's the water on the side of the lock?"

"Hey! Right where it was! It's in the same place where we said it would be!"

"Right…and there's your answer. But tell me. Is that a good thing or a bad thing?"

"Wh-u-u-t??"

"Is it good, bad, or just okay, that the water doesn't go up or down after the barge sinks?"

"….???"

"Okay, Daddy will tell you. It's good; and it's bad, both."

"I don't want to know and I don't care."

"Well, you can be that way, but do you remember about our house back home on the beach…and about global warming? Remember we were talking about, if the icebergs and ice caps all melt, then one day our house on the beach might disappear under the ocean?"

"Yeah? But…"

"Well, would that be good or bad?"

"Whew! Bad. Gheez!"

"Well then…if sinking the barge could make the water in the lock go up or down, that would mean we could save our house on the beach wouldn't it?"

"….???"

"Sure it would. All we'd have to do is take land and dump it in the ocean; or dredge the bottom of the ocean and put the earth from there back up on the land. Whichever way would lower the ocean…because we'd be sinking something…just like sinking a barge; that way we could keep our house above the water. Isn't that right, silly person with silly questions?"

"Daddy, you're silly."

"Anyone wanna go for a swim?

Nice job and a nice story! However, you missed a critical element in your story.

Imagine you fill your bathtub and put a bucket in the tub. Now place one or more bricks into the bucket at let it float in the tub. Next, mark the water level inside the tub.

Let's say the bucket floats such that it is half submerged. If you remove one cup of water from the tub and pour it into the bucket, the bucket sinks a little and the water level in the tube remains unchanged.

However, compare the water level inside the bucket to the water level outside the bucket. The water inside the bucket is below the water level outside the bucket. It has to be or the bucket would not float! If you keep pouring water from the tub into the bucket at some point the bucket will drop down into the tub such that the water outside the bucket is even with the lip of the bucket. As you correctly noted in your story, the water level on the tub wall is still unchanged. However, the water level inside the bucket is still below the water level in the tub. The difference between the two levels is composed of air.

Now take a teaspoon of water from the tub and pour into the bucket. The equilibrium is now disturbed and the bucket begins to drop enough so the water outside the bucket begins to pour over the bucket's rim and down into the inside of the bucket, filling the remaining volume of air inside the bucket. When this happens, the bucket, with its bricks, submerges and the bath water level will be lower than the original level just prior to the bucket's sinking. The amount that the tub's water level drops is equal to the volume of air that was in the bucket just before it sank.

Try it for yourself, but do it when your wife is out and do not use permanent marker to mark the tub!

Anonymous,

Thanks for your very kind—your undeservedly kind—reply. How humiliating. To make matters worse, it now occurs to me that I've encountered this particular challenge—about sinking vessels--in one form or another—before, even decades before. I would surmise that is has come up many times even, in the centuries before that. Anyway, you are exactly correct in not overlooking the requirement for freeboard, and for excess inboard capacity, in order to float any vessel heavier than water: which would include even a floatable raft—until it became water logged. Anyway, I have revised my story accordingly and reposted it I think it only fitting to post it in your name—because I wouldn't want to get points for your correct solution. However, if the system will not permit me to do so, then please accept any points as your own. Okay?

By the way…about your bucket in the tub experiment. I found that a soup bowl and pressure cooker pressure/steam release cap, in a sink of dirty dish water, and with a thumb pressed against the sink at the water level, will work quite as well.

Thanks again.

Cow Anon

Correction credits: Anonymous Coward.
Barge story, rev. 1

First, I would have to tell her that whoever put her up to asking the question forgot to also tell her that the barge could never sink, as she imagines it, in the lock because the distance from the barge's bottom to the lock's bottom is, in all probability, shorter than the barge's freeboard. After explaining the meaning of freeboard to her, I would then go on to tell her...'but let's imagine that lock really is very very deep...that the water goes down as far, say, as that gantry there goes up...that the barge really could sink; then maybe we can figure this out?" When she said, "Mmm, okay," I would continue: "Okay, why don't we play a little make-believe? Let's all imagine that you and your brothers and sisters and I each have an imaginary bucket...no wait...let's imagine that we are going up to the top of that great big gantry there; and when we get to the top, we're going to lower that great big bucket down into the lock to get a bucket full of water. Okay, now we've hoisted a bucket full of water out of the lock. Now, look at the water line on the sides of the lock. Do you see? It's gone down, right?"

"It sure has! Is that how much water we took out?"

"You got it. What a clever child you are! Now, let's move the big bucket over and drop the bucket of water into the barge. Careful now, don't let it splash out! Okay, now the water that was in the lock is in the barge, right?"

"Right."

"Now, child, look at the sides of the lock again. Where is the water now?

"Hey, it's back up to where it was before!"

"Right. So couldn't we say that the water we took out of the lock and put into the barge made the water in the lock go back to where it was?"

"I t h i n k so."

"Couldn't we also say that when we put the water into the barge--and the barge is in the lock--isn't that just like as if we put the water back into the lock?"

"Mmmm."

"Okay, wanna try another bucket full?....

"Same thing this time, too? Right?"

"Yeah!"

"So it's like: when we put the water from the lock into the barge, the barge keeps the water from 'spreading out' the way it could when it was actually in the lock. And, if it can't spread out, it all just goes to the bottom of the barge, right?"

"Right."

"Now look over at the sides of the barge. See there where it's painted different colors, one above the other to make a line that's even with the water? See how the water in the lock is just below that line?"

"Yeah?"

"Okay, why don't we put another bucket full from the lock into the barge and see what happens?"

"Hey, the water went down again and came back up just like before!"

"Right. And look at the side of the barge now; the water's up higher now; see? You can't even see the line any more. Where did it go?"

"The water came up the side of the barge and covered it up."

"Right! So what happened to the barge? Did it go up? Or down?"

"Huh?"

"Quiet boys!" Okay, honey, the water on the side of the lock went down and came back up to where it was when we took water out and put it in the barge; but it only came up on the side of the barge. Wouldn't that mean that the barge went down in the water?"

"O-h-h. Y-e-a-h."

"So it's like...the extra water in the barge is making the barge push down into the water. And when it—when the barge--pushes down on the water below the barge, that water is pushed out from under the barge and over to the sides of the lock?"

"Yeah!"

"And when the water gets to the sides of the lock, it has no where else to go but up; can you see?"

"Right."

"Okay. So, if every time we lift out a bucket full, the water in the lock goes down so far; and then every time we put the water in the barge, it comes back up in the lock the same distance....couldn't we say that the distance that the water went down in the lock--which is the same distance the barge pushing down made it come back up when we put the water into the barge that's in the lock--couldn't we say that that distance between the lock's water when it's low and when it's back where it was...that that distance tells us how much water is in the bucket?"

"Yeah!"

"Right. That, darling children, is what's known as displacement. The amount of water in the bucket tells us how far down—when we count the buckets full—how far down we can make the barge push into the water, and how far up the side of the lock we can make the water go back up."

"Displacement?"

"Right. And if we talk about some kinds of ships, about the size of the bucket—how far a bucket full can make the water move up in the lock--how many buckets we could put in them and they still float…we would call that the ships' tonnage."

"T-t-onnage."

So, do we know the answer to your question, daughter? Will the water keep staying where it was on the lock sides if the barge sinks?"

"Sure. It will."

"Wait. Not so fast. Why don't we try something just to be sure? What do you say we go on and keep filling the barge with water until it j-u-u-st begins to sink, but doesn't really sink; it only stays barely floating….

"….Okay, now let's climb back down to the platform from this gantry and take a closer look. Here we go….

"Now then, we saw that taking buckets-full out of the lock and putting them in the barge is just like putting them back into the lock; the water stays the same on the side of the lock….Now, if the barge was to keep going down into the water by itself, with the water pouring into it from the lock all by itself….what do you think? Won't that water just be going back into the lock, too? Won't the water level on the side of the lock still stay the same even though we aren't picking up and dropping buckets full?"

"It should."

"Okay then. Take your imaginary hand bucket there. Now, dip it in the lock..that's right…and get a bucket of water. Now, throw your bucket of water into the barge. It's okay, go on…."

"Wait!" "Wait" "Hold it." "Don't." "Daddy!" "Not yet!" "No." "…."

"What is it kids? Hold on. Not all at once. What is it, Son?"

"What about the freeboard?"

"Freeboard?"

"Yeah, don't you remember? The freeboard."

"Hmm. Oh yeah, but what about it?"

"Well, look! It's all gone! There's no freeboard anymore!"

"So, what do you think that means?"

"Well, you said that if the distance from the bottom of the barge to the bottom of the lock was not more than the freeboard, then the barge cannot sink. It can only be swamped and rest on the bottom of the lock."

"Right."

"Then what if the barge is resting, right now, on the bottom of the lock."

"But we said the barge would be deeper than that."

"Yeah, I know. But, we could still pretend it's on the bottom, right now, when the freeboard's all gone."

"And the point would be?"

"If we put any more water from the lock into the barge, the barge cannot push down and move…what was it?...oh yeah, cannot displace…any more water out from under it."

"Go on."

"So now, it we put any more water from the lock into the barge, it will only pile up in the barge; but the barge can't displace the water in the lock if it's on the bottom already! And if we can't displace more lock water—because the barge is into the lockwater as far as it can go—the water level in the barge can't be pushed back up. Now, we would be just taking water out of the lock but we wouldn't be putting it back; we'd only be putting it in the barge's extra inside space…"

"Inboard space."

"…huh, right, inboard space. But it won't be free space--free to put anything into--because there isn't any freeboard any more."

"Extra space?"

"Sure. The tonnage thing. Because there has to be enough space—enough displacement—by the barge so that the water displacement—the displacement in the lock—weighs as much as the barge and whatever's in the barge: the steel, the water now, and the air."

"Well, I think we don't have to count the air…"

"No? Uhh…"

"…because the weight of the air on the lock and on the barge is the same."

"Oh, right. But, anyway, now that the barge doesn't have any freeboard, but it's still floating, there has to be extra space or otherwise it would not be floating…if it is floating."

"Hmm. Interesting point. What do you say, kids? Daughter?"

"I don't like this. We said that the barge was deep. Now you want to say it's not. That doesn't seem fair."

"Now see what you've done, Son? How do you answer that? If the lock's deep like we said before?"

"Huh…oh, I was looking at the barge. See there, there really is extra space…inboard space."

"What do you say if the barge is deep…like when we started out?"

"Er, well…well I don't think that would make any difference. If the barge goes under, the water just runs into the extra space; the space that was above the water, in the freeboard, before we started, would still be there; only it would be under the water. The water would run into it just like it was running out of the lock through a drain. Only, the drain's not at the bottom of the lock; it's at the top. It would be just like when we scooped water with the big bucket, but before we put it back."

"Well, only one way to be sure. Daughter! Ready with your bucket? Oh, yes! Whoever wins buys the ice cream. Agreed?

"Yeah!" "Yeah." "Yeah!" "Yeah." "Yeah!"

"Agreed, Son?"

"Ohh, alright…and whoever loses jumps off this platform and into the water."

"Fair enough. Okay, throw your bucket into the barge, girl…..

"…Oops! There goes the barge. But look now. Where's the water on the side of the lock, daughter?"

"Hey! The water went down, just like we said it would!"

"Just like I said it would. What's this we stuff?

"Looks like he's got us there, Daughter. But, there's your answer. The water drains into the barge's extra space which has been pushed below the lock's water level, and lowers the water in the lock. Now then, I'm ready for that ice cream. Who else?

"Now, I'm ready to see Daddy…go jump in the lock! Who else?

"Anyone wanna go for a swim? But no diving, Okay Son? No telling where that barge is…and we don't want to miss our ice cream on account of something like a cracked head."

"Oh yes, one more thing."

"What is it daughter?"

"…about that global warming, and our house on the beach….I think now that it's a bad thing, no matter what."

"What global warning? What are you talking about?"

"You remember. The last time we were here? The icebergs and stuff?"

"Oh yeah. What about it?"

"I'm afraid we won't be able to save our house, no matter how much dirt we sink."

"No? Why not?"

"We wouldn't have any freeboard."

"Touche! …unless we put the beach house up on a barge."

"Daddy, you're not only silly, you're insufferable.

I would think, that if the barge sinks, the crew controlling the lock system would empty out the lock, so the barge would not be lost, therefore the water level would decrease.

"I think if it was a witch, it would sink and if it floats, like wood, we should burn it." (taken from history of the world in paraphrase) You guys crack me up, really funny stuff, original and thought provoking. Kind of like mythbusters and cudlow and kramer combined into one web site. It can be gravity or anti gravity - time or lost time, mind benders or puns. Maybe they can tie this web site into a TV cable show for the few who appreciate and question our universe from the very large billions of stars in the cosmos to the sub atomic energy that makes it all possible. Only think is I cannot watch cable TV while at work ! I must admit I am addicted to this site.