How do boats float?

Factual Questions
1

I figured I would start a new thread since the zombie thread didn’t really answer the question I thought it would.

Anyway, the general idea is what tastycorm said:

My question is why does this matter? What’s so great about the weight of water the boat displaces that keeps a boat on the surface of the water? How does the water “know,” so to speak, that enough of it has been displaced and that it should start holding up the boat?
(How do boats float? - Factual Questions - Straight Dope Message Board)

2

The surrounding water was originally supporting a volume of water (i.e. exerting enough buoyant force on that water to keep it from falling) equal in weight to the boat. We just took that water away and replaced it with something that weighs the exact same amount (the boat) and takes takes up the exact same volume (the part of the boat that is below the surface of the water).

The surrounding water doesn’t know whether it’s pushing up on a 1000-pound boat-shaped chunk of water or a 1000-pound boat; it just knows it’s pushing up 1000 pounds. If you add a couple hundred pounds of cargo to the boat, it’s gonna move lower in the water until it’s displaced a volume equal to 1200 pounds of water; at that point, the surrounding water is pushing upwards with a total of 1200 pounds of buoyant force.

3

Say you’ve got a boat in the water. The water is pushing at the curved sides of the boat, trying to occupy that space, pushing the boat up. Meanwhile, the contents of the boat, and the weight of the boat itself, are pushing down. Which wins the pushing match depends on which push has more weight behind it.

4

Imagine a rectangular boat where the bottom surface has an area A and when floating the boat submerges to a depth h. The net force from the water pressure on the front and back surfaces of the boat will cancel out, as well as the right and left sides. As such, the net buoyant force on the boat will be due to the pressure on the bottom surface.

The pressure, P, at a depth of h is equal to the density of the water, d, times the depth, h, times gravitational acceleration, g, or P = hdg.

The buoyant force, F, will be the pressure time the area or F = PA = AHdg.

The weight of the water displaced, W, is volume displaced, A*h, times the density times g or W = AHdg.

So we see that the buoyant force F equals W, the weight of the water displaced.

5

Essentially, what matters is the water pressure at differing depths.

Water pressure increases as you descend, due the force of gravity acting on the water above.

If you put an object into water and submerge it to a depth of 1 foot, the total force on the object can be found by summing the the surface area of the submerged portions of the object at each depth, times the pressure on that depth. Using calculus, this is an integral over the submerged surface of the object.

If this force (the buoyant force) is equal to the force of gravity on the object (the object’s weight), the object will float at a depth of 1 foot.

If this force is less than the force of gravity, the object will sink. As more of the object is submerged, the buoyancy force increases because the submerged surface area increases, along with the pressure experienced by the lowest surfaces of the object. If the forces reach equilibrium before the object is totally submerged, it will stop sinking and float at the new depth.

If the buoyancy force is more than the force of gravity, the object will rise until the forces are in equilibrium, and then float at that depth.

If you work out the math, it turns out that the buoyant force is always equal to the weight of the water displaced. Intuitively, this makes sense, as the volume of water that would otherwise be in the place of the floating object would itself float, neither rising nor sinking.

6

Try looking at it this way. Take a toy boat into the bathtub, to keep things nice and small.

Start by holding the boat just touching the water. Right now, the boat and the water aren’t interacting, aren’t applying forces to each other.

Now, let gravity pull the boat down a little. The boat pushes against the water, causing the water to displace. The displaced water has to go up, because it’s confined in the tub. The displaced water wants to go back down because of gravity, so it pushes down against the rest of the water, which is turn pushes up against the boat. The amount of force pushing against the boat is equal to the weight of the displaced water. (Weight IS force, so this makes sense)

Now let go of the boat completely. As gravity pulls it down, more and more water gets displaced. The more water gets displaced, the more it pushes against the boat. So the farther down the boat goes, the greater the force pushing up on it.

On the other hand, the force pushing down on the boat, gravity, doesn’t change (significantly) as the boat moves. Eventually, the force of the water pushing up on the boat will exactly equal the force of gravity pulling it down, for a net force of 0, and that’s the depth the boat will float at.
The fun thing is, that’s not the only explanation of what’s going on. Here’s another that’s also valid. If you submerge an item in water, the water will press on it in all directions. That should be obvious to anyone that has put their hand in water. The amount of pressure depends on how deeply submerged the item is. That makes sense, too, the deeper you are, the more water over your position there is to push down.

So, you put a boat in the water. The water pressure pushes against the boat in all directions. All of the horizontal pushes just cancel out, because every bit of water pushing the boat to the left is countered by water on the other side pushing it just as hard to the right. But the water at the bottom of the boat is pushing up harder than the water at the surface is pushing down, because the bottom of the boat is deeper. And lo and behold, if you do all the math, it turns out the difference in force is exactly equal to the weight of displaced water, so long as the boat wasn’t completely submerged!

7

I think it is easier to envision if you think even smaller. Imagine a glass of water, partially full. If you stick your fingers down into the water the water level must rise. The force required to lift the water is the same as the force of your fingers pushing down into the water. You can think of the two as being on a balance scale. Fingers on one side, water on the other. Water up, fingers down/ fingers up, water down. If the force required to raise the water is more than the weight of the object, the object will float.

8

So, if I’m thinking about this right, the flotation has to do with water being a liquid. (As it obviously is). And, so, I’m thinking about what would happen if you had a boat floating away and then somehow instantaneously removed it from the water. It just disappears. So, there would be a hull shaped “hole” in the water. But obviously, this can’t happen, because the water would immediately start to level itself out. Is it this “level-itself-outness” of the water what causes the boat to float? Or at the very least, does it have something to do with it? Because the force that was moving all the water out of the way is gone, and so the water wants to move down due to gravity.

So, when you have a boat in the water, you have water that wants to be as close to the center of the earth as possible, but you have a boat in the way, so some water can’t be where the boat is, so it goes somewhere else. But, only so much of it can go somewhere else. The rest is basically stuck, and thus the boat can’t sink.

9

If you get a bucket of water and a basketball, then push the ball down into the water, it becomes very apparent that displacement is the same as lifting - a boat floats because when it pushes down into the water, that water is effectively being lifted out of the way - when the weight of water being lifted equals the weight of the boat, the system is in balance and the boat stops moving downwards.

10

Actually, the link you posted was to *this *thread.

Here is the old thread:

11

Here’s a better explanation of the “water presure pushing up”.
Take a pipe or a straw and put it into the water. As you immerse the straw, the water comes up the center of it to keep the same level.
Put your finger over the end - then push the straw into the water. What do you get- if it’s deep enough, you will feel the air pressure against your finger tip. Let it leak and the water fills the straw, again to the same level as outside the straw.
Basically, with the straw at 6 inches deep, the water at 6-inches deep is pushing up with pressure X. (see math in other posts…) This is balanced by 6 inches of water above, normally. If instead there is an object that weighs les than that, the water will push it up. If it weighs more, it will push the water down. The happy medium is reached when the item is deep enough to just balance the forces from water below…

12

Maybe a dumb question but here goes:

A giant ship like an aircraft carrier weighs less than the water it displaces? The ship is made of steel which is very dense so that does not make sense to me.

13

It’s hollow.
A solid steel aircraft carrier would sink like a… well, like a Lead balloon.

14

No, it weighs the same.

It’s not solid steel. It is, in fact, mostly air.

15

Look at the total volume of the aircraft carrier. It’s mostly hollow, meaning that the average density of the entire space it occupies is much less than that of water.

I Am Not a Physicist, but I think that’s roughly correct.

16

Unless, of course, water gets inside the ship. But then the thread becomes about how ships sink.

17

This is what happens when explosives detonate underwater, actually. The explosion pushes the liquid out, then when the blast wave dissipates all of the water rushes back in all at once, in order to become a stable system again (the “level-itself-outness” factor).

What happens is a big splash of water on the surface (no matter how deep the explosion was), because the walls of water rushing into the now entirely empty sphere cleared by the detonation accelerate, gather momentum, and that momentum has to go somewhere. That somewhere is the path of least resistance, or straight up, because it’s much easier to displace air than it is to displace more water.

18

The carrier is not 100% hollow , it has a lot of heavy stuff in it like planes, jet fuel, bombs, etc. But I guess that does not matter.

19

It does, to a point. Imagine you have A - A real aircraft carrier, loaded as usual. B- A solid sphere of steel weighing the same as the aircraft carrier A. A will float merrily, B will not.

This is what they meant above (mostly) about displacement. It’s not totally a function of weight, depends on size and shape as well.

20

Picture the inside of an aircraft carrier. Most of the space in an aircraft carrier (or any other boat not in the process of sinking) is just empty space. Only a tiny fraction of the space is taken up by anything other than air.