Buoyancy and gravity

[TheOldDog]

TL;DR

What are the effects of varying gravity on buoyancy?
Does the draft of a boat change with gravity?

Fairly simple - I think - but I may have missed something; HS physics was decades ago.

If a boat in a body of water on Earth has a draft of 1m, will the draft of the boat in a similar body of water on, say, Mars have the same draft? (Assume the same temperature of water.) I figured the change in water density would be minimal on the surface, even if it's an ocean we're considering.

This originally came up while reading a SciFi book where the 'artificial' gravity was changing but it got me thinking. After reviewing basic buoyancy I don't recall where gravity really played a role. Buoyancy is dependent on the mass of displacement and the mass of the object, right? I don't see where gravity enters into it - assuming there is *some* gravity (not 'weightless').

Any thoughts? Please let me know ...

 

[haruspex]

TL;DR: What are the effects of varying gravity on buoyancy?
Does the draft of a boat change with gravity?

Buoyancy is dependent on the mass of displacement and the mass of the object, right?

Archimedes' principle is usually expressed in terms of force and weight, not mass, but since the weight of the vessel and weight of the fluid displaced are both proportional gravity…

 

[Demystifier]

The pressure of the water is $p = \rho g h$, so gravity enters through the $g$. But the force of the water $pA$ (where $A$ is the area) acting upwards has to be balanced by the gravitational force $mg$ acting downwards, so the $g$'s cancel, i.e. the draft does not depend on gravity.

 

[Andy Resnick]

The pressure of the water is $p = \rho g h$, so gravity enters through the $g$. But the force of the water $pA$ (where $A$ is the area) acting upwards has to be balanced by the gravitational force $mg$ acting downwards, so the $g$'s cancel, i.e. the draft does not depend on gravity.

What do you mean? there is essentially no bouyancy in microgravity.

 

[Lnewqban]

Any thoughts? Please let me know ...

Buoyancy is about the weight of the displaced liquid respect to the weight of the boat.
At half gravity intensity, both weights would be cut in half alike.
At increased gravity by artificial means, both weights would be increased at the same rate.
The line of flotation of the boat should remain the same in both scenarios (unless I am wrong).

 

[Ibix]

I mostly agree with the above responses, but I think there are some caveats.

First, is the hull of the boat rigid? The pressure applied by the water will depend on the gravitational field strength, so a flexible hull may change shape when the local $g$ changes. That would change the volume of water displaced, so would affect the draft. (This is actually a plot point in Hal Clements' novel Mission of Gravity.)

Second, does $g$ vary significantly over the scale of the boat? With centrifugal gravity this will happen within a few boat-heights of the spin axis. The different mass distributions of the boat and water it displaces could lead to different drafts then.

 

[TheOldDog]

I mostly agree with the above responses, but I think there are some caveats.

First, is the hull of the boat rigid? The pressure applied by the water will depend on the gravitational field strength, so a flexible hull may change shape when the local $g$ changes. That would change the volume of water displaced, so would affect the draft. (This is actually a plot point in Hal Clements' novel Mission of Gravity.)

Second, does $g$ vary significantly over the scale of the boat? With centrifugal gravity this will happen within a few boat-heights of the spin axis. The different mass distributions of the boat and water it displaces could lead to different drafts then.

I love Mission of Gravity! There was nothing in there that seemed odd at all.
(I thought the use of a bowl instead of the outer surface of a sphere for a map was genius!)

In the SciFi novel I was reading the hull is rigid and the artificial gravity did not vary over the positions covered in the story.
An anti-gravity generator was decreasing the local planet-sized moon's gravity and was supposed to be fixed. A natural disaster was causing many problems, including disrupting the generators, causing the gravity to vary (a little) randomly over time. In the book, the vessel is changing draft as the gravity changes, which just didn't sit right with me when I read it.
So, either I misunderstood something in the story (that I also missed the second time through) or the author needs a review of basic physics. lol

 

[TheOldDog]

Archimedes' principle is usually expressed in terms of force and weight, not mass, but since the weight of the vessel and weight of the fluid displaced are both proportional gravity…

Exactly my thought at the time. *thumbsup*
(My brain was thinking in weights, which is how I learned it, but when I posted I went to metrics because I know a LOT of science is in metrics these days - much more so than when I was in school back in the stone age.)