# Calculating work in a body of water

1. Jan 19, 2010

### gloo

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?

2. Jan 19, 2010

### gloo

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?

3. Jan 19, 2010

### Staff: Mentor

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.

4. Jan 20, 2010

### gloo

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?

5. Jan 20, 2010

### stewartcs

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

6. Jan 20, 2010

### gloo

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