Which is the most efficient way to dive?

[Juanmdq]

Hi Everybody!

Lets say I have a sphere or an elipsoid of 10m3 full of air so it floats. I then open a valve that let's water in. At some point it will start to sink to the bottom. Let's say 100m deep.

Once its down there I would like to refloat it. Which should be the most efficient method (less energy required) to make that happen? Should I pump air in? Use a hidraulic piston with a sealed plate to push the water out from the inside out?

If your figured it out.. can you estimate the amount of energy required to do that?

Would love to hear some creative answers!

Thanks!

 

[Andrew Mason]

The most efficient way to float the ball is to pump air from just above the surface into the ball to force the water out. If you pump the water out without replacing it with air you will be continually increasing the pressure difference: each successive unit of volume of water that you pump out will require more pressure than the previous unit. P x V = Energy/work. If you know the amount of water in the ball the amount of work required to remove it will be $\int P dV$ where P is the difference between the air pressure and the water pressure. That is the amount of energy you will use. Each 10.0325 m of water depth is one atmosphere or 100325 Pa. So the pressure at the bottom is about 10 atmospheres.

AM

 

[Juanmdq]

Thanks Andrew! Great response! Do you mind a follow up question? Let's say I start pumping air from the surface to the bottom 100m deep. Does the force I need to send it down will increase with depth? Also once I start filling the ball , since it would be open at the bottom to let the water out, the air would be inmediatly compressed to 10 atm right? So I would have to pump 8 or 9 times the volume of the ball to change it bouyancy? Thanks again!

 

[Andrew Mason]

Thanks Andrew! Great response! Do you mind a follow up question? Let's say I start pumping air from the surface to the bottom 100m deep. Does the force I need to send it down will increase with depth? Also once I start filling the ball , since it would be open at the bottom to let the water out, the air would be inmediatly compressed to 10 atm right? So I would have to pump 8 or 9 times the volume of the ball to change it bouyancy? Thanks again!

In order to gain positive buoyancy you would have to pump out just enough water so that the mass/volume of the ball was just less than the density of the surrounding water. At that point, the pressure difference between the top and bottom of the ball is enough to overcome gravity and the ball will start to rise. So, the amount you have to pump out depends on the mass of the ball (without water) and its volume and how much water is inside it at the bottom.

Submarines control buoyancy by controlling the amount of water in its ballast tanks. It carries tanks of compressed air to replace the water.

AM

 

[Rive]

I then open a valve that let's water in.

This is the part what makes it difficult and inefficient. This way, the air inside will be compressed according to the pressure at the bottom, so the volume remaining would be ~ 1/8 of the volume required to refloat. You have to replace all the missing volume of air from the surface by pumping, and that is a lot of work.

Use a hidraulic piston with a sealed plate to push the water out from the inside out?

The most efficient way is if that piston alone could be used to make the device both sink and then refloat.

 

[russ_watters]

Lets say I start pumping air from the surface to the bottom 100m deep. Does the force I need to send it down will increase with depth? Also once I start filling the ball , since it would be open at the bottom to let the water out, the air would be immediately compressed to 10 atm right? So I would have to pump 8 or 9 times the volume of the ball to change it bouyancy?

Yes. And you'd have to compress it -- it doesn't compress itself.

 

[Juanmdq]

Thank you all for taking the time to answer! I really do appreciate it!

 

[Juanmdq]

The most efficient way is if that piston alone could be used to make the device both sink and then refloat.[/QUOTE]

Im not sure what do you mean but it sounds intersting. I thought to use a piston that would push the water out while at the same time let air in from the surface with a hose in a container with a cylinder shape. When the piston is contracted the cylinder would be filled with water, when the piston is extened it would push the water out and suck air in from the surface.

My point being. What is more energy demanding? compressing air to pump it into the container or pushing the water out and letting air in from the surface?

Thanks again!

 

[russ_watters]

My point being. What is more energy demanding? compressing air to pump it into the container or pushing the water out and letting air in from the surface?

Ideally, each method can be 100% efficient. Are you looking to design something to do this in reality or is this a theoretical exercise?

 

[Rive]

When the piston is contracted the cylinder would be filled with water, when the piston is extened it would push the water out and suck air in from the surface.

Not from the surface, but from the interior of the device. So when the piston is 'contracted' the sum volume of the device would be reduced by the volume of the cylinder, while the mass would remain the same. So it could dive. When the piston 'extends' the volume would be increased by the volume of the cylinder, so the device could float again.
The energy requirement would be related to the pressure at the bottom and the volume of the cylinder instead of the volume of the whole device.

Submarines are based on a similar idea, it is just that big piston is not practical, so compressed air is used instead of piston to push out of the water from the tanks (what replaces the cylinder).

 

[Juanmdq]

Thanks Rive!

 

[LURCH]

There is an autonomous sub used for research that uses this method, and it is extremely efficient.

https://www.whoi.edu/main/slocum-glider

As you will see, they also use their vertical motion to propel themselves. These vehicles travel slowly, but can go for weeks on a charge of four lithium ion batteries. There is even one version that can get enough energy to power itself by harvesting the temperature gradient between deep water and the surface.

 

[Baluncore]

Lets say I have a sphere or an elipsoid of 10m3 full of air so it floats. I then open a valve that let's water in. At some point it will start to sink to the bottom. Let's say 100m deep.

The fundamental problem here is that a gas filled submarine that regulates depth by buoyancy is inherently unstable. Any 10 metre rise or fall creates a change in hydrostatic pressure of one bar, which amplifies the cause. That is why any implosion of a submarine structure causes it to plunge to greater depths which induces further collapses, until it collides at speed with the seafloor. The same is true for ships that sink, as the air within them is compressed they accelerate towards the bottom.

Accurate depth regulation is usually done with vertical axis propellers, or by keeping moving which drives water past hydroplane control surfaces to provide a lift or down-force.

A tube open at the surface may be crushed by the hydrostatic water pressure at depth. If the tube contains gas under pressure it will require a very significant investment in stored energy. If a snorkel or hose to the surface is permitted then you only need to replace it with a cable and a surface float to regulate depth. That system design migrates to become a winch on a raft, with the submarine becoming a diving bell.

The real design challenges begin when you insist on having people in the submarine. If you can remove humans and air from a submarine, you can fill the submarine with a light oil that will protect the electrical and hydraulic control systems, while neutralising the buoyancy. That also eliminates the requirement for a pressure hull, so the envelope can be made from a softer plastic material which reduces the mass and volume required for neutral buoyancy operation. Submarine design then migrates towards that of an oily fish, with flatter faced liquid filled optical systems.

Understanding the chemical and physical mechanisms that allow whales with lungs to hunt squid at depths greater than 2km, where hydrostatic pressures are over 200 bar, should be more enlightening than designing a massive submarine in which humans must open a tin of sardines for their lunch.

 

[hutchphd]

As usual I am confused.
Water is approximately incompressible so its density is constant with depth.
If the object in question is a rigid pressure vessel its buoyancy therefore does not change with depth. To change from marginally sinking to marginally buoyant requires an infinitesimal increase in airspace using an infinitesimal amount of work (either by active injection of air or active removal of water). This is a submarine.
If the object is not rigid then the situation is more complicated as the object loses buoyancy with depth ( anyone who has worn neoprene knows this...) and the process of regaining the surface will require air at bottom pressure sufficient to make up the lost air volume (and an energy cost = pressure x .volume) or equivalent mechanical work. If you are very clever I believe you can recover half that energy on the way up to the surface..