Calculating work in a body of water

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Discussion Overview

The discussion revolves around calculating the work required to move a volume of water at a significant depth, specifically in the context of a submarine extending an arm into the water. Participants explore the effects of pressure at depth on the work done, considering both theoretical and practical implications.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks to understand how to calculate the work needed to move water at a depth of 300 meters, questioning how pressure affects this calculation.
  • Another participant clarifies that the arm extends from an air-filled compartment, indicating that the pressure inside the submarine is not the same as the external water pressure.
  • Some participants propose that if the arm extends slowly enough to avoid drag, the work done can be calculated as force times distance, with force being the pressure difference times the cross-sectional area.
  • There is a challenge regarding whether the work required to push an object out of the submarine is the same at depth as it would be above water, with some asserting that increased hydrostatic pressure at depth necessitates more work.
  • One participant acknowledges the clarification provided by another, indicating a better understanding of the pressure considerations involved.

Areas of Agreement / Disagreement

Participants express differing views on the impact of hydrostatic pressure on the work required to extend an arm from a submarine. While some agree that increased pressure at depth requires more work, others question the specifics of how this is calculated, leading to an unresolved discussion.

Contextual Notes

Participants do not fully resolve the mathematical implications of pressure differences and how they factor into the work calculation, leaving some assumptions and definitions open to interpretation.

gloo
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I want to know how much work it is to move a certain volume of water at a certain depth.
For instance, take a submarine at 300 meters depth and I want to have the submarine extend out an arm from inside. the Arm is 1 meter by 1 meter by 5 meters long. Thus the volume of water displaced is 5 meters cubed. At 300 meters the pressure of water is about 3750 Kilopascals. Since we have the formulas:

p=f/a
W=f * d

the mass of the water is 5000kg and the force is then 5000*9.81 =49050 Newtons?

but how do i incoporate the pressure at this depth? Certainly pushing this mass 1 meter over is easier on land then in such a high pressure?
 
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I am not pushing this arm in open water all isolated. It is coming from inside an air filled compartment inside a submarine. The pressure inside there is not 3750Kpa. So the 5 cubic meter arm comes out and displaces 5 cubic meters of water out of the way. How do i calculate the work. It takes more force to move it a cubic meter of water at 300 meters than if the sumarine was just sitting on land no?
 
If the arm extends like a telescoping antenna and does so slowly enough that drag isn't an issue, the work done is simply force times distance. The force is just the pressure [difference] times the cross sectional area.
 
russ_watters said:
If the arm extends like a telescoping antenna and does so slowly enough that drag isn't an issue, the work done is simply force times distance. The force is just the pressure [difference] times the cross sectional area.

So Russ, if I am in a submarine, and i have to push out some object from the inside where the air pressure is 101Kpa, and push a pole out through the wall of the submarine (assume there is an o ring to keep the water out but allows the pole to move), it would be the same work at 370 meters of water as if the sub was above the surface and I am pushing it out into air?
 
gloo said:
So Russ, if I am in a submarine, and i have to push out some object from the inside where the air pressure is 101Kpa, and push a pole out through the wall of the submarine (assume there is an o ring to keep the water out but allows the pole to move), it would be the same work at 370 meters of water as if the sub was above the surface and I am pushing it out into air?

No.

As Russ indicated, the force is equal to the cross-sectional area of the object times the pressure applied to that area. As you go deeper in the water the hydrostatic pressure will increase thus requiring a larger force and more work.

CS
 
Ahh, thanks guys. I didnt' read Russ' comment in detail. That totally makes sense.
 

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