# Goofy question for you guys

## Main Question or Discussion Point

Very slow day at work, and the mind has been wandering and wondering...

Imagine that you have a semi truck that, in lieu of a trailer full of goods behind it, it has an open-top swimming pool, the length, depth, and width of the trailer. (cool, eh?)

Now, imagine that someone is treading water in the center (assuming the trailer is 40 feet long, that would put them 20 feet behind the cab). The truck is moving at, say, 40 miles an hour and hits a concrete wall head-on, bringing it to an instant halt.

How badly injured, at all, will the swimmer be? What do you expect would happen?

Assume the frame of the truck and trailer is intact.

I know that the body of water will continue to move forward and splash over the top of the trailer, probably taking the swimmer with it. But my real question is, will there be any compression of the water? Will the swimmer feel any shock of the impact or will the rapid change of the shape of the water as it swells over the lip be the first indication that something is wrong?

What if there is a lid on the trailer, and the swimmer is suspended in the center of the body of water, wearing scuba gear?

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Danger
Gold Member
I'm just going to take a stab at this, since I really don't know. It seems to me that the swimmer would be the analogue of a fighter pilot. He's pretty well constricted as to his movement (as if strapped in), but his internal organs would still suffer trauma from being flung about within his body. That's just an educated guess, though.

mgb_phys
Homework Helper
Assuming the water doesn't just slosh over the cab - suppose it is a sealed tank and the swimmer has scuba gear!
The water isn't very compressible and would pretty much stop instantly (again assuming you hit a sufficently massive object) the swimmer would then be forced forewards through the water at 40mph until they hit the front wall or the water resistance slowed them down enough.
It's exactly equivalent of being in the water and someone giving you a 40mph push in the back.

russ_watters
Mentor
I don't see why the swimmer would be forced forward in that scenario, mgb- he's just another part of the water, so if it stops almost instantly, so does he.

What you would get is the water hammer effect, since the entire body of water can't stop all at once, it actually does pile up at the front even though it is mostly incompressible. The water in the middle only "knows" the truck has crashed when a pressure wave moves from the front of the pool towards the back. This pressure wave is what would stop the person as well (and inflict the trauma that danger was talking about).
http://en.wikipedia.org/wiki/Water_hammer

Water hammer (or, more generally, fluid hammer) is a pressure surge or wave caused by the kinetic energy of a fluid in motion when it is forced to stop or change direction suddenly. It depends on the fluid compressibility where there are sudden changes in pressure. For example, if a valve is closed suddenly at an end of a pipeline system a water hammer wave propagates in the pipe.

Any guesses as to how much pressure would be exerted? Let's go with the closed top/underwater diver scenario.

And what would be more destructive to the diver: having a 2-foot air gap between the water level and ceiling, or no gap at all (tank completely full)?

How compressible is the water, anyway? How much of a 'cushioning' effect will the water have if any?

Seems to me that due to the fact that a human is much more compressible than water, he'd be somewhat flattened due to the momentum of a few tons of water smashing him from both sides.

Interesting question . IMO, the fluid would move towards the truck and so would the swimmer. If there is something that stop the water from splashing all over, then the water stops nearly instantly since it is pretty incompressible. The pressure gradient generated across the water body will give the swimmer some interesting force of buoyancy-kind, but in the horizontal direction. This force should be small, since this depends on the deceleration which is not pretty much. Moreover, this pressure gradient vanishes quickly after the crush. I agree with mgb_phys that the main force stopping the swimmer should be the resistance and drag force. This is generated by the relative velocity between the swimmer and the water.

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I think it's hard to give a good answer to this question without specifying at least a very short deceleration time for the truck when it hits the wall. Since you're assuming it is rigid, then you're implying an infinite acceleration, which means an infinite force, thanks to F=ma.

Of course, there will be some finite time before the tank comes completely to rest, but you're still suggesting a very high acceleration. This is important, because - thanks to Prof. Einstein - we know that the inertial reaction forces we feel when under the influence of a constant acceleration act just like gravitational forces. Therefore, if you calculate the real acceleration that is required to bring this tank to a halt, and then convert that to g's, you can imagine this guy in a tank of water under that many g's of gravitational acceleration. That can lead to very large pressures, as you know if you've ever dived more than a few meters below the surface.

I didn't mean to imply that the halt would be instant. I threw in the bit about the rigidity of the truck only to eliminate questions about damage done to the tank.

So, my mobile swimming pool fantasy maybe isn't such a good idea? :)

Thanks for the responses so far.

agree with that, belliott4488, the time is also important. after some thought, it seems possible to view the problem in this way:- Suppose the swimmer (whose float in water) is a 'bag of water' (hmmm... a strange thought i know), since this generated pressure gradient can stop the whole water body instantly, it seems reasonable that it can also stop this 'water bag'. Now let us suppose the horizontal buoyancy is sufficient to stop the bag full of water.

It suddently occurs to me that the density gradient in the swimmer human body is also important. What will happen to the 'bag' when it is holding somethings both very heavy and very light, and with an average density equal to water? The heavy components inside the bag should rush towards the truck.

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DaveC426913
Gold Member
Note that, since the water is virtually incompressible, one important effect is that the tank would explode. mostly out of the back. (Same reason a pickle jar will explode if you bang on its lid, or why the safe door exploded in http://www.imdb.com/title/tt0227445/" [Broken])

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mgb_phys
Homework Helper
I don't see why the swimmer would be forced forward in that scenario, mgb- he's just another part of the water, so if it stops almost instantly, so does he.
Good point I was picturing the swimmer as a solid object on a friction-free surface.
But if you think of them as just another bag of water surrounded by water.

DaveC426913
Gold Member
So, the swimmer would be killed, right? From stopping instantly?

russ_watters
Mentor
Well, someone asked above how big the pressure wave is. I don't know, but I suspect it might be enough to kill him. It's basically the same effect as a supersonic plane flying over you at low altitude. Those can knock you down and blow out your eardrumbs at the very least. The wik link I posted has pictures of pipes that have been destroyed by this effect: http://en.wikipedia.org/wiki/Image:Blown_expansion_joint.jpg

Regarding whether the swimmer would move - it matters if the swimmer is floating, sitting on the bottom, or hovering neutrally buoyant. If he's sitting on the bottom (and heavier than the water), he'll move forward after the water hammer passes him, if he's floating at the top, he'll move backwards, and if he's hovering neutrally buoyant, he'll stay where he was. This effect is noticeable if you are driving in your car on a cold day and suddenly stop. You get a blast of cold air from the back of your car as it displaces the warm air from your recently warmed-up heater.

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water hammer is truely very strong. the picture stunned me well. A compressible object in the water, say an empty can of air, probably cannot survive the pressure waves. The moment the wave passes the can, the great pressure difference between the two sides promptly destroys the can. I think the swimmer's lung will be compressed and his life may be risked, it depends on the deceleration time.

russ_watters
Mentor
Yes, you're right - even if the swimmer is neutrally buoyant, there are pockets of air and denser things like bones. The pressure wave would wreak havok on his insides.

Inside a sealed vessel full of air that was on the back of the truck the person would go splat against the front of the vessel.
If you increase the density of the medium from air to something say half the density of the human like some kind of dense foam the humans velocity would slow more gradually. With water the cussioning effect of the water would be much less (close to the same density as the person) and the human would be more likely to sustain injury because of the sudden stop.
Closer to being in a sealed container full of gravel.

If there was a lid on top of the water and the swimmer was in the middle. The swimmers brain (actually floating in fluid inside the scull) would due to inertia keep moving and crash with the inside of the scull. This is the same reason somewone can get braindamedge when you hit them hard in the face with your fist without doing any damadge to the scullbones. The human bodys density is very close to the waters, so I guess the human body wouldnnt moove to much in relation to the watertanc. If the body weight less then water it would moove away from the trucks direction before the crash i guess. But than again the air in the lungs would rather be blown out or something. Pressurewaves moves very effectively in water so the mans body would be
destroyd. If we really shall get into guessing - mine is that the difference in pressure inside the head and outside would make the water brake in through his ears or nose etc and the lungs would get damadged in someway. What of the three things that would kill him first I dear not guess.

Thanks for all the interesting responses!