# Bouyancy

## Bouyancy in fluids

Bouyancy means the tendency of an object immersed in a fluid to float. Boats float in water and balloons float in air due to bouyancy. Everything pretty much has bouyant forces. The Battleship Arizona on the bottom of Pearl Harbor won't float but bouyant forces make it lighter. You weigh less because of the bouyant force of air.

Bouyancy was known to the most primitive people who saw logs floating. Dugout canoes, birch bark canoes, Men-of-War, Esther Williams and the Love Boat quickly followed. Building a boat and understanding how it works are not the same. Bouyancy was not understood until recently as measured in the history of man.

## Bouyancy in water

What happens when something is immersed in water? First, we know that the object displaces its volume of water. Fill a bowl with water and set it in a sink. Next place an object such as a ball into the water. Water will overflow the bowl and that volume will the same as the volume of the ball. This was discovered nearly 3000 years ago by Archimedes the Greek. (I think it was in Eureka, California)

Anyway, if we immerse a cube of lead that is 10 cm on each side it will settle and displace 1000 cc or 1 liter of water. Previously that 1 liter of water was resting on the bottom and not going anywhere. The heavier lead forced it upward to raise the level of the water by an amount equal to the volume of lead.

Let's look at what forces are on that liter of Plumbous (lead). The pressure all around the lead is the pressure of the height of the water to the surface. That pressure acts on the top surface of the lead. The pressure at the bottom of the lead is 10 cm of water weight greater than at the top of the cube. But 10 cm of lead is heavier than 10 cm of water so the lead stays on the bottom although it is lighter than when it was in the air. This same force acted on the liter of water that had previously been on the bottom and was displaced. But that water didn't move until the lead arrived. The water didn't move because 10 cm of water in the cube weighs the same as 10 cm of water pressure.

One liter of water weighs 1000 grams. Ten cm of water pressure on 100 sq cm of lead or water is a force of 1000 grams. Newton's law says that an object will continue at rest or in motion unless a force acts upon the object. A 1000 grams force on a 1000 gram weight will not move the weight. A liter of lead weighs 11,000 grams. A 1000 gram force acting on the lead will not move it but when immersed in water a liter of lead will need only 10,000 grams of force to lift it. The lead is bouyant by 1000 grams, the same weight as the displaced water.

Prove bouyant (upward) force is equal to weight of fluid displaced.

Upward force = difference in pressure force on bottom surface from top surface
F = A dp
dp = density x height of fluid (h) displaced
F = A x density x h
A x h = Volume
F = density x Volume
density x V = weight of fluid
F = weight of fluid QED

What if a cube made with lead plates one and one half cm thick is placed in water?. Such a cube would weigh 1000 grams. It will stay in place supported by the pressure of the surrounding water. None of it will be above water. If pushed to a lower level in the water it will remain there. It will act as a submarine.

What if the lead plates on the cube were only one cm thick? If the cube would become submerged it would have a weight of 600 grams supported by 1000 grams of water weight pushing up. The cube would rise until 4 cm is out of the water. With only 60% submerged the upward force of the water would suspend the cube as if it were a ship.

What can we conclude?

• A volume immersed in a fluid displaces its own volume of the fluid
• A volume will rise, fall or stay in place until it displaces a weight of fluid equal to its own weight.

This is all there is to bouyancy. A steel (or even a lead) ship can float because it displaces its weight of water. As cargo is added a ship will settle deeper into the water. A submarine will float the same way but it can vary its weight by filling tanks with water so that it submerges. It can adjust its depth by adding water or ejecting water with compressed air.

A human will float but can submerge by wearing a belt of lead. A human can submerge or rise by propelling himself with his feet or arms.

### A Bouyancy experiment

Obtain an emply soft drink bottle with top cut off so it is a cylinder with a bottom

Obtain full soft drink cans - one regular and one sugar free.

Obtain various materials that won't be damaged in water such as a wooden block, different plastic blocks and metal objects.

Cut top off the soft drink bottle so it is a cylinder with a bottom

Place soft drink can standing up in bottom of open topped soft drink bottle and mark outside a circle at the height of the soft drink can. This is the minimum fill line to immerse a soft drink can.

Remove soft drink can and fill with water to an inch or two above mark.

Immerse full soft drink can of regular soda. What happens?

Immerse full soft drink can of sugar free soda. What happens?

Can you explain the results?

The sugar free soda will float but the regular soda will not. Artificial sweeteners have less weight than sugar for the same sweetness. This difference in weight allows the sugar free soda to float.

Aluminum, used to make soft drink cans, is almost three times as dense as water. How can a dense can filled with water float in water?

There is a pocket of gas in the can plus gas disolved in the water. The bouyancy of this gas ofsets the excess weight of can

Place various objects of different materials that won't be damaged into the water. Observe what happens. Which sink, which float? Do any go below the surface but not settle to the bottom? Do hollow objects behave differently than solid?

### A Cartesian Diver experiment

This is a simple but classic little project. Fill a large empty plastic soda bottle to the brim with water. A one liter size clear soda bottle works best.

Use either a ball point pen cap, small vial or test tube, or the rubber bulb from an eyedropperfor the diver. Weigh the open end using modeling clay, wire, or whatever you can get to work so that the diver just floats in the water (it needs to have a little bubble of air in the top). It should be just on the verge of sinking. Paper clips (two small ones) work well with plastic pen caps.

Make certain that the bottle is filled to almost overflowing and screw on the cap. When the bottle is squeezed, the diver should descend. You can alternately use a large, wide mouth glass jar with a piece of thin rubber sheet secured tightly over the mouth. It will also work with a bottle and cork, although this is more difficult to operate.

What makes the diver move up and down?

When the bottle is squeezed, the water is forced into the diver, the only place it can go. The tiny bit of air in the diver is compressed, and the overall density of the diver increases, causing it to sink.

Obtain a two liter green plastic soda bottle, a plastic bag from the grocery, a drinking straw, tape and coins.

Cut a few (3-4) holes along opposite sides of the bottle. Gather the end of the plastic bag around the straw and tape it on tightly. Stuff the bag through the bottle's neck until it hangs loosely inside the bottle. Stuff straws end-to-end and tape them to make a really long straw. Tape enough coins along the sides of the bottle away from the holes so the bottle will sink entirely and levelly to the bottom of a bathtub or bucket. Leave one end of the straws above water.

Blow air gently into the straw and the "Submarine" will rise to the surface. When you suck the air out it will submerge.

### Bouyant objects experiment

A truly silly trick if you happen to have extra mothballs. Mostly fill a glass jar with water. Add a little vinegar - 1/4 to 1/3 cup (60 ml) - and 2 tsp. (10 ml) of baking soda. Stir gently. Add a few mothballs. As long as their surfaces stay fairly rough, they should begin to bounce up and down. This will also work quite well using clear soda water or alka seltzer with the mothballs. Raisins may be used instead of Moth balls.

This is different than the Cartesian Diver. What makes the object (mothball) move up and down?

The irregular surfaces on the mothballs or raisins hold some carbon dioxide bubbles. When enough bubbles accumulate to lift the weight of the mothball (or raisin), it rises to the surface. There, some of the bubbles of air escape into the atmosphere, and the mothball/raisin, which is denser than the water or soda, sinks to the bottom to start the cycle over again.

The effect will last longer if the container is sealed, as less carbon dioxide will be able to escape.

There are quite a few other small objects that will work. An oscillating couscous grain in seltzer water! The key is that they are able to trap air bubbles on their surface, that they are light enough to be buoyed to the surface by the bubbles, and that they won't dissolve in the liquid.

Fun with champagne or whatever

If you happen to be drinking any clear bubbly drink such as 7 Up, seltzer, champagne or a sparkling wine, raisins will bounce in the glass for a very long time. Of course, very few of those who enjoy a glass of champagne will have the patience or willpower to not drink the experiment.

Even more fun with gelatin

Pour your favorite clear lemon-lime soda into a clear glass cup, add some salt to the soda and put some Jell-O into the cup. After a while the Jell-O will bounce up and down inside of the cup as air bubbles accumulate and come off of the Jell-O.

As a high schoolstudent who was both a chemist and a history buff, I read that on board U.S. Navy ships some sailors made alcohol by fermenting raisens in a sugar solution. I set up this experiment in the kitchen using a gallon bottle with a water seal to let Carbon Dioxide (The result of fermentation along with alcohol) escape but not let Oxygen in to spoil the solution.

I was surprised to see the raisens bob up and down as the bubbles formed.

My Mother was surprised when the Minister paid a call one day and visited her in the Kitchen. She said he eyed the experiment all through the visit but never asked a question.

My parents were wonderful and allowed me to do experiments all the time as long as I explained what I was doing, why, and what I expected to happen. I hope your parents are as great.

## Bouyancy in other fluids

The same principles apply to fluids such as air. Air is much less dense than water and the density changes dramatically with height. In the upper atmosphere there is little fluid to displace.

Few natural things float in air. For things to float in air, the hollow portion is nearly always filled with gases lighter than air. Balloons filled with hot air, helium or hydrogen do float in air. Hydrogen is the lightest gas and is therefore the most efficient for floating but hydrogen mixed with air will explode so helium is usually used. The Goodyear Blimp is filled with helium. Hot air is the cheapest but not very efficient.

Problem: Show how you can determine the density (weight per unit volume) by weighing a solid in air and then weighing it when immersed in water.

Last Updated 7/15/98