Hypothetical water pressure question

I had a bizarre thought while contemplating Copernicus in my math class today.

Say, hypothetically, there was a planet made out of water, or some other liquid with similar properties. I’m fairly certain that there are about eight million reasons why this couldn’t occur, but let’s pretend that it can. So we have a massive sphere of water floating around in space.

What would happen, theoretically, if someone dove in and somehow got to the center of it? There’d be a few miles of water on top of him, so one would think taht the pressure would be ‘squish and die’ in intensity. But, if there’s equal pressure coming from all directions (since our brave diver is in teh middle of a sphere), would that still happen? Would tossing in a few floating islands on the surface of the water effect things?

I consider this question extremely important for my future, as I am considering a career in the illustrious field of ‘fictional water planet diving’.

Firstly: Very good work by GoogleBot on selecting ads for this thread.

Secondly: are you referring to a solid sphere of water/other liquid, or a planetary body with a core?

In any case the amount of pressure exerted would depend on the gravitational strength of this body; if it were a floating ball of liquid, there might be little to no pressure. Of course, I would assume that any body of liquid that size would necessarily have a strong gravitational field of some kind.
Sorry, planetary-scale deep sea diving is not my specialty.

Water pressure isn’t directional. You’d get crushed, but you’d feel weightless (because there is no gravity at the center of the planet)

There would be no net force on him, since the forces would cancel out. But then, if you stick your head in a vice and tighten it, there’s no net force on your head, either. Either way, you’d get squished.

What is meant by “No net force?”
This is a question of statics and/or hydraulics not dynamics,

You don’t have any force (well, it’s inadequate) inside you pushing back out, so, yeah, you’d still be crushed.

That’s still a valid observation. I think the point Chronos was trying to illustrate is that all external forces would be in balance; however, internal pressure would (presumably) be less than the hydrostatic pressure and thus would (for a body the size of our hypothetical water planetoid) crush a person. The pressure (assuming for hypothetical purposes that this is a homogeneous spherical body of pure water) is only a function of the distance from the center and the total mass of the body.

We can dive to limited depths by equalizing the pressure of our internal cavities with that of the ambient water pressure by breathing a pressurized breathing gas, but that only takes you down a couple of thousand feet (neglecting the biomechanical and neurological effects of breathing highly compressed gases which limit you to a few hundred feet). If you’re breathing a liquid breathing fluid (a la the oxygenated fluorocarbon solution as portrayed in The Abyss you can dive several thousands of feet, and your tissues, being flexible and filled with fluid that is mostly water, are sufficiently resilient to resist catastrophic collapse. However, at some point the pressure will be great enough to crush or shear the protein cell membranes, compress nerves, and cause interior non-equalized cavities (like the interior of bones) to collapse.

A few other points to consider:
[li]The enormous pressure would probably result in very high temperatures in the interior of your wateroid. The pressure would keep the water in a liquid state, but it may be well above boiling; in other words, it would be a celestial pressure cooker. Ugh.[/li][li]Temperature variations and the Newtonian fluid behavior would probably result in massive convection currents between the surface and the interior layers. Good luck trying to swim against the tide.[/li][li]Even if it didn’t crush you instantaneously, the pressure would certainly deform your eyeballs–you wouldn’t be able to see anything down there–and the force of transmitted pressure waves in the hypercompressed water would make your hearing useless at best. The pressure would squeeze tactile nerve endings flat. So, you’ll be blind, deaf, and senseless, which is probably for the best as you are being simultaneously crushed and boiled. [/li][/ul]

Happy diving, and remember; don’t dive in an unfamiliar lake headfirst. :wink:


[QUOTE=Stranger On A Train]
[li]The enormous pressure would probably result in very high temperatures in the interior of your wateroid. The pressure would keep the water in a liquid state, but it may be well above boiling; in other words, it would be a celestial pressure cooker. Ugh.[/li][/QUOTE]

Your points are all very interesting, but I’m wondering about this one. Why or how would pressure result in very high temperatures?

I’m curious.

If the radius of the planet is only a few miles, then the pressure at the center is not going to be anything amazing.

A blob of water that small is likely to evaporate into space, but if we ignore that and do some quick calculations (assuming a radius of, say, 5km) we’re dealing with a total mass of around 5.24x10[sup]15[/sup] kg - not quite one billionth of the earth’s mass. So I question the assumption of enormous pressures and temperatures.

I was assuming something more the size of the Earth.
Thats a lotta water!

Why the dichotomy? Of course it’s a question of dynamics. It happens to also be in that special-case subset of dynamics known as statics. The reason we know it’s statics is that the net force is zero.

Ever heard of the equation PV=nRt? If not, that equation tells us several things, the relevant one here being that an increase in pressure causes an increase in temperature. I know it applies to gasses, but I suppose it applies to liquids too? Maybe I’m thinking of the wrong thing, but I think this link will put you on the right track at least:

This is an interesting question. What would the dynamics of a water world be? If we assumed one Earth diameter and gave it a similar spin at the same distance from a similar sun, but with no axial tilt? I can envision that convection and coriolis forces would give it some truly extreme ocean currents and likely the mother of all weather systems, like two bands of permanent hurricanes. It’s not going to rate very highly as a vacation destination.

However, NinjaChick’s question asked about conditions at the center of the planet. If her Kevin Costner were to descend in God’s own bathyscaphe or teleported directly to the center, what would he find there? It seems to me that the pressure at the center would be zero. Since P = ρgh and g (gravity) is zero at the center of a planetary body (because there is an equal amount of mass on all sides). Or am I missing something here?

Also, since the gravitational forces decrease as you move toward the center, there would be a zone of maximum pressure somewhere between the surface and the center. Would this zone be occupied by a shell of pressure ice or would compression heating keep it liquid?

As I said, an interesting question. If only Hal Clement had written a book about this place!

A blob of water the size of the earth would weigh approximately 1.1x10^21 metric tons. Given that our earth weighs ~6x10^21 metric tons, the gravitational attraction would have to be about 1/6 that of earth, meaning you could dive six times farther than on Earth (accounting for pressure only; don’t know much about the details of scuba diving).

Still, I’d have to imagine the cold of space would cause the world to form a thck crust of ice quickly, while pressure at the center gave it a hollow, water-vapor core. Sort of like a giant casaba melon:-).

Well, we can get down what? About 5 miles in the deep parts. So, what is the normal temp. at that depth?

Shirley there is a formula for determining the max gravitational pressure in a gas or liquid that could be used on Earth or Jupiter? And at what % of depth it would be located at…

Pressure would be greatest at the center because in any direction you have one radius depth of water pressing down on you. Of course net gravity is zero at the center so as you increase in depth the pressure increase won’t be linear as divers on earth experience but it will be at its maximum.

What, exactly, is causing the water to press down? It is being equally attracted in all directions. Also, in zero G, which direction is “down”?

The only net force I can see is that of surface tension, and that’s not very much when you spread it over an entire planet.

What would a planet made mostly of water (H2O) be like?

Rhubarb – Don’t start by thinking about the center. Start by thinking about the very outer layer of water. Gravity from all the other layers pulls the top layer down. What is counteracting that gravitational force? The pressure of the second layer. So we know what the second layer’s pressure is: enough to hold up the top layer.

Now the second layer is being attracted by gravity to the third and lower layers. So there’s a little less force than the top layer, but it’s still there. Now what is holding the second layer up? The difference between the pressure of the third layer and the pressure of the second layer. So the pressure in the third layer is higher than in the second layer.

Same thing all the way down – the pressure keeps increasing as you go down, it just doesn’t increase as fast as it does at the top. So the center has a very high pressure, because it has to hold up all the other layers. Even though holding up the second to last layer doesn’t take much force, it still has to hold up all the other layers.

Does that help?

Chronos used a vice as an analogy, which I think would be helpful here. Imagine a small sphere at the center of the water world. Now for some tiny area on the surface of this small sphere, there is a column of water (more like a skinny cone) leading toward the surface. There is also an equal column on the antipode point (e.g. a column running to the north pole would have an equal column at its antipode running to the south pole). These two columns are gravitationally attracted to each other, producing a crushing force on the tiny sphere. This is occurring in all directions around the tiny sphere, so the sphere will be crushed on all sides. This despite the fact the net gravitational attraction (and the net force applied to the sphere) is zero.