Camping with the guys last weekend, the following thought experiment was most heatedly discussed and there is still no agreement (though I a confident I know the answer).
Suppose you drill a large diameter hole all the way through the (center of the) earth and hit the bottom of the indian ocean. Once you pierce the bottom of the ocean floor, the seawater begins rushing down the hole (pulled by gravity) accellerating toward the center of the earth. The column of water hits the center of the earth, it begins climbing up the hole toward the other side of the earth. The question is, ... Where does the water stop? Does it just come to the surface on the other side, or does it come squirting out of the hole like a geyser?
For the purposes of this experiment, assume the pipe is a large-diameter, frictionless pipe. Assume sea-level evevations at both sides of the earth and assume the pipe is insulated so the high temperatures in the earth's core don't turn the water to steam.
Assuming that the hole passes through the earth's center of mass, the acceleration will go to zero, and the flow will stop. I think.
I agree with Jim, it would have to stop at the center of gravity, very near the center if the earth.
> Assuming that the hole passes through the earth's center of mass, the acceleration will go to zero, and the flow will stop. I think.
Since the column of water is incompressible, the acceleration will never go to zero until the entire hole is totally full. Until this point the velocity of the water column will keep on acelerating.
> I agree with Jim, it would have to stop at the center of gravity, very near the center if the earth.
It certainly would not stop at the center of the earth. This is the point where the force (and acceleration) if the water is the greatest. All the gravatational force is in the same direction.
Okay, it stops at the equal gravity point on our side, about sea level. Like any other two bodies of water that are connected.
These are just quick of the top of my head. 😀
I think the pipe would equalize the pressure (same geoid elevation on both ends - elevation of Indian Ocean surface).
As I mentioned before, when the flow starts, the water column begins accelleration (velocity increasing). The column of water will continue to accellerate all the way through the earth. Even when the water column is heading upwards and has reached within 100 feet of the surface, it still continues to accelerate since there is more water pushing down from the Indian ocean than there is in the rising column. Only when the column reaches the surface does the aceleration go to zero and at this point the water column is at it's highest speed since the water started flowing. What force would suddenly make this large mass of water stop flowing at the surface?
Now here is a very important issue!
Keith
> Now here is a very important issue!
Personally I find discussions like this much more interesting than talking about watching overpaid, grown men playing games on TV, but that's just me.
> I think the pipe would equalize the pressure (same geoid elevation on both ends - elevation of Indian Ocean surface).
Eventually, I believe it would.
Pretty interesting idea. I think the gravity on our side would offset the gravity on the other side, thereby causing it to slow down and not spew out our side.
I think it would be possible to experiment with it by taking a large container of water and putting a tube in the bottom with a valve of some type or just by clamping the tube. Curve the tube into a u-shape and cut it off at the elevation of the top of the container, much like a water level. This would recreate the situation, except the center of gravity would be at the base of the "u" instead of the center of the earth. You could suddenly release the valve and see what the water does.
Just my thoughts, but I might be missing something.
Perry
Perry, you are right about that one!
And who are these men?
> Pretty interesting idea. I think the gravity on our side would offset the gravity on the other side, thereby causing it to slow down and not spew out our side.
>
> I think it would be possible to experiment with it by taking a large container of water and putting a tube in the bottom with a valve of some type or just by clamping the tube. Curve the tube into a u-shape and cut it off at the elevation of the top of the container, much like a water level. This would recreate the situation, except the center of gravity would be at the base of the "u" instead of the center of the earth. You could suddenly release the valve and see what the water does.
>
> Just my thoughts, but I might be missing something.
Yes, I had this exact idea. I may have to construct the apparatus just to proove that the water will come squirting out like a geyser and collect my bet money.
You might be right. If you do it, please let us know.
> Pretty interesting idea. I think the gravity on our side would offset the gravity on the other side, thereby causing it to slow down and not spew out our side.
>
> .
The gravity on our side eventally offsets the gravity on the other side but not until the entire column is full. At this point the water has been accelerating the whole way and is at it's maximum velocity. The momemtum of water is unstoppable at this point.
> Suppose you drill a large diameter hole all the way through the (center of the) earth and hit the bottom of the Indian Ocean. Once you pierce the bottom of the ocean floor, the seawater begins rushing down the hole (pulled by gravity) accelerating toward the center of the earth. The column of water hits the center of the earth, it begins climbing up the hole toward the other side of the earth. The question is, ... Where does the water stop? Does it just come to the surface on the other side, or does it come squirting out of the hole like a geyser?
Perry, while it didn't make the newspapers, we actually did just this when I worked for the Hughes Corporation in the late 1960's and early 70's. The cover story was that we were trying to raise a Soviet submarine, but really we were interested in deciding who had won a bar bet that Howard Hughes had made with Jayne Mansfield.
She claimed that the problem was a simple physics problem that could be solved from the consideration of the balance of forces acting upon the masses. This was after all the same approach that had enabled the structural design of her undergarments. Hughes, on the other hand, had claimed that gravity was vastly overrated and thought that the result would depend mainly upon factors outside those given.
My only way to answer that question is to go back to the universally accepted Newton's Law of Gravitation. If mass of water reaches the center of earth then the distance between their centers of gravity collapses to zero thus leaving the universal formula with zero value denominator. In such a case, force of gravitation reaches infinity.
Install a hook on the ceiling of a room (high ceiling is most impressive) at the centerline of the room. Then install a frictionless cable to the frictionless hook. On the other end of the cable, attach a bowling ball. Do so such that the cable and ball system will just touch your nose as you stand with your back against one wall. Stand there perfectly still, holding the bowling ball to your nose with the cable being taut. Then release your grip. Do not push the ball. Merely let it go. The bowling ball will not strike the opposite wall. On it's return swing, stay motionless as the ball nears your nose, but does not touch it.
In your hypothetical situation, the quantity of water entering from one side will be offset by the increasing quantity on the other side of "center". While the theoretical pipe is frictionless, the mass of air that must be pushed out of the pipe to be replaced by water will dictate a loss of energy such that the water will not reach the surface on the far side.
Put me on the list that says water hammer (velocity) will cause the water to spew out the other side. But you do realize that if you started out drilling vertical, your drill hole will have to be curved to hit the center of the earth, not straight.:-)
James