Free Fall Scenario: 100kg Piston Kinetic Energy After 20m Drop

[beckerman]

Lets say you have a piston falling in a long cylinder. The piston weighs 100kg but only weighs 1kg under water. The cylinder is filled with water, but there is plumbing going from the bottom of the cylinder to the top. As the piston falls the water can move in a continuous loop, from the bottom of the piston to the top. Taking the waters momentum into account, and assuming 100% efficiency what would the kinetic energy of the piston be after a 20m freefall?

 

[Hootenanny]

What are your thoughts on the matter?

 

[beckerman]

I must warn you I am not a scientist, and am pretty ignorant when it comes to physics. My thoughts are the 1kg of mass we have would set the water into motion. Gravity would cause the piston to continue to accelerate. The initial resistance of the water would keep the piston from accelerating at 9.8mpss initially, but once the water was flowing it would accelerate at or near this speed. I think once everything was moving, you would have the kinetic energy of a 100kg object even though it is submerged and weighs only 1kg underwater. I also think that since joules are a measurement that pertains to energy required to stop a moving object, the fact that the water is moving with the piston, and also would need to stop, would have to be figured into the equation.

 

[Chronos]

The weight of the piston is irrelevant, only the mass is of any real consequence.

 

[beckerman]

Could you elaborate please.

 

[DaveC426913]

I'm thinking it would get nowhere near anything like terminal velocity. The biggest factor would be the diameter of the plumbing and resultant flow rate.

(Or, more accurately, the flow rate through the plumbing would define the terminal velocity.)

 

[beckerman]

Lets say the plumbing is very large, larger in area than the cylinder. If the water can flow very freely than what would prevent the piston from accelerating at 9.8mpss?

 

[rcgldr]

Lets say the plumbing is very large, larger in area than the cylinder. If the water can flow very freely than what would prevent the piston from accelerating at 9.8mpss?

The problem is water doesn't flow very freely. The piston is doing work on the water, accelerating the water downwards, and the fluidic drag (did I just invent a term?) is very large.

If it were a tight cylinder, then you'd have the force of gravity accelerating the piston and all the water being circulated by the piston. The density of the piston, the path the water flows, and the viscosity of the water would determine the terminal velocity.

 

[Danger]

Lets say the plumbing is very large, larger in area than the cylinder. If the water can flow very freely than what would prevent the piston from accelerating at 9.8mpss?

You have another problem with that. If the plumbing is of higher capacity than the cylinder, you wouldn't be able to force it all the way back to the top.

 

[beckerman]

You would never have to "force anything back to the top" because the cylinder and the plumbing would be completely filled with water. The inlet for the plumbing would be above where the top of the piston is at the beginning of the descent. This way the piston never has to work against gravity to raise a water level. I think Jeff Ried is on the right track. We can assume a density since we know mass in and out of water. Our piston has a mass of 100kg but displaces 99kg of water when submerged. So we could say the piston has a volume of 9900cc. How to calculate the effect of the water viscocity is beyond me. It would seem to me that there would be a figure for this that could be plugged into a formula as a value for resistance.

 

[Danger]

Okay. I was thinking of the plumbing being empty to start with. That was a bit dumb on my part. Something about the wording of your original post gave me that impression.

 

[Gelsamel Epsilon]

Assuming 100% efficiency then I think it will accelerate at normal g (not factoring in friction, but does 100% efficiency include nil-friction?).

 

[DaveC426913]

1] A rate-limiting factor will be the bottleneck between the piston and the plumbing. Unless the plumbing is the same X-sectional area as the piston - which means the device is simply a hollow, fluid-filled doughnut.

2] Friction is a huge factor.

3] I think the terminal velocity of the falling piston will be limited to however fast the piston would sink in a swimming pool. (In fact, much slower, but that's an upper limit.) Especially considering the initial condition that the piston is very nearly neutrally buoyant. This will dramatically slow the process.

 

[beckerman]

As far as friction is concerned, I was thinking of a piston with a little bit of clearance so there would be a thin layer of water that would travel with the piston, between its outer wall and the inner wall of the cylinder. In comparison to an object sinking in a swimming pool I think in this situation the object would have to descend much more quickly. The mass is near neutral at the very beginning of the descent, but as the water moves from beneath the piston it would change. In a pool the effect the water would have on the mass would remain constant. I see the effect of the piston has on the water as being similar to hooking the suction and pressure lines together on a water pump. Initially there would be energy used to set the water into motion. Once it was moving the amount of energyy required would decrease. Once the piston establishes momentum with the water the amount of work required to keep it moving would be minimal. As the work requirement decreases the piston would then be able to accelerate. As this occurs and the water and piston are moving, we really cannot say we have an object that is near neutral bouyancy either since an object will not float in a water column that is moving straight down.

 

[rcgldr]

Initially there would be energy used to set the water into motion. Once it was moving the amount of energy required would decrease.

The water would be accelerating just as fast as the piston, and due to visocity, the amount of engery required to maintain a constant acceleration would increase. Since the force is fixed, the piston and water would reach a terminal velocity if the cylinder is tall enough.

 

[beckerman]

But would the velocity over a 20m freefall be the same as it would be if falling through the air? Or would the object reach terminal velocity at a low speed and in a short distance?

 

[rcgldr]

But would the velocity over a 20m freefall be the same as it would be if falling through the air? Or would the object reach terminal velocity at a low speed and in a short distance?

No, the only way to get true free fall is in a vacuum with no air. The air provides resistance, and water provides much more resistance than air.

 

[Danger]

No, the only wall to get true free fall is in a vacuum with no air.

Might I assume that you meant 'way'? That would maintain my respect for you.

 

[Chronos]

Turbulence is the keyword. Think about it.

 

[rcgldr]

Might I assume that you meant 'way'?

Oops, editted the post. Was listening to something while typing, apparenly my multiplexing paths got crossed.

 

[beckerman]

No, the only way to get true free fall is in a vacuum with no air. The air provides resistance, and water provides much more resistance than air.

I understand water provides more resistance than air, but we are not falling through water. Not in the same sense that we would be falling through air if something fell out of a tree for instance. When an object falls through a stationary fluid it has to push the stationary molecules of that fluid out of the way to move. As the object moves past these molecules frictional forces present themselves to all sides of the object creating drag. In this case rather than pushing past any molecules the piston is pushing the molecules through the plumbing. The water moves with the piston as opposed to around the piston. I guess my question is if the water presents so much resistance to allowing the piston to descend in this scenario then why? The only possibility I see is friction between the water molecules and the walls of the piston.

 

[Danger]

Was listening to something while typing, apparenly my multiplexing paths got crossed.

Pink Floyd is a valid excuse. Carry on.

 

[DaveC426913]

The only possibility I see is friction between the water molecules and the walls of the piston.

Friction between the water and the walls of the entire construct. Realize that ALL the water is moving. Also turbulence, since the construct has twists and bends.


Really, you seem to be imagining that it will fall as if in air. I think it will fall as if in water. Slowly.

 

[Danger]

Yeah... it's not going to hit anything like the terminal speed that it would have in air. I've tried looking at it in reverse, as well. If there's a rope attached to the top of the piston, you're not going to be able to pull it back up as quickly as you could in air.

 

[beckerman]

I agree that it would not move as fast as in air, I also believe the terminal velocity would be slower than it would be in air. I do not agree the descent would be "slow" as it would be in water. Lifting the piston is an interesting way to look at this. The thing that I think is important to remember is that the weight of an object depends on where it is. An object can weigh one amount on Earth and a different amount on the moon for instance. This object weighs 1kg under water. If you were lifting the piston and let go of the rope, would you say it weighed 1kg during the period where the waters momentum was still carrying it upwards? I think the opposite is true also. The piston weighs 1kg in still water, not in water that is moving in the same direction that gravity is pulling it anyway. Hence I think the force we have to overcome effects like turbulence and friction (which I think could be minimized quite a bit in the design of the device anyway) would be similar to a 100kg object not a 1kg object. Either object is going to accelerate to Earth at the same velocity, however the heavy object will be affected less by the drag of the water.

 

[Danger]

By that same reasoning, the oxygen and nitrogen bubbles in the water are more affected by the 'drag' of the water; they do not, however, travel downward at the same acceleration as the other things. In fact, they don't travel down at all.

 

[beckerman]

Oxygen and nitrogen bubbles float. An object that weighs 1kg under water sinks. I do not really understand your comment. Maybe I am missing something.

 

[Danger]

Merely pointing out that the following is a self-contradicting statement.

Either object is going to accelerate to Earth at the same velocity, however the heavy object will be affected less by the drag of the water.

They won't accelerate at the same velocity because the drag gives each a different interaction. Also, things don't accelerate at a velocity; they accelerate at a rate of velocity change.

 

[NoTime]

I see the effect of the piston has on the water as being similar to hooking the suction and pressure lines together on a water pump. Initially there would be energy used to set the water into motion. Once it was moving the amount of energyy required would decrease.

Seems to me, if you totally neglected friction, that you could treat this as an unbalanced wheel.
However, friction/turbulance between the walls of the tube and the water are going to have a major impact.
OTOH I suppose you could freeze the water, get rid of the tube, and mount it on a low friction bearing

 

[DaveC426913]

Seems to me, if you totally neglected friction, that you could treat this as an unbalanced wheel.

I was thinking along the same lines when I was moving toward a "hollow donut" idea.

Perhaps this should be addressed to the OP. A device operating on an "unbalanced wheel principle" cannot be used as a power source, because you expend as much energy lifting the weight back to the top.

Even though OP's idea is somewhat far from an unbalanced wheel, the principle still applies. He's still simply "storing" the energy as potential energy. Drop the weight to convert it into useful energy.

But it's still nothing more than a storage device, one that has to be "recharged".