# Free fall scenario

1. Aug 30, 2006

### 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?

2. Aug 30, 2006

### Hootenanny

Staff Emeritus
What are your thoughts on the matter?

3. Aug 30, 2006

### 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.

4. Aug 30, 2006

### Chronos

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

5. Aug 31, 2006

### beckerman

6. Aug 31, 2006

### 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.)

7. Aug 31, 2006

### 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?

8. Aug 31, 2006

### rcgldr

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.

9. Aug 31, 2006

### Danger

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.

10. Sep 1, 2006

### 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.

11. Sep 1, 2006

### 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.

12. Sep 1, 2006

### 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?).

13. Sep 1, 2006

### 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.

Last edited: Sep 1, 2006
14. Sep 1, 2006

### 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.

15. Sep 1, 2006

### rcgldr

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.

16. Sep 1, 2006

### 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?

17. Sep 1, 2006

### rcgldr

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.

Last edited: Sep 2, 2006
18. Sep 1, 2006

### Danger

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

19. Sep 1, 2006

### Chronos

Turbulence is the keyword. Think about it.

20. Sep 2, 2006

### rcgldr

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