School Science Lessons
11. Density of solids, liquids, and gases, relative density, r.d., hydrometers, buoyancy, flotation, Archimedes' principle
2011-12-25
Please send comments to: J.Elfick@uq.edu.au
Table of contents
11.0.0 Density
4.12.0 Density experiments, UNESCO
11.4.0 Buoyancy, flotation, Archimedes' principle
20.0.6 Density of gases
11.2.0 Density of liquids
11.1.0 Density of solids
11.3.2 Hydrometers, relative density
11.4.0 Buoyancy, flotation, Archimedes' principle
11.4.01 Buoyancy
4.200 Buoyancy, flotation experiments, UNESCO
12.3.3 Air has mass, air has weight
11.4.8 Archimedes' principle
11.4.9 Archimedes' principle, bucket and cylinder experiment
11.4.13 Board and weights float
11.4.2 Buoyancy of air
4.200 Buoyancy of water
11.4.1 Buoyancy of water
12.3.3.1 Carbon dioxide has mass
4.201 Cartesian diver
11.4.24 Centre of buoyancy and centre of gravity of a boat
4.118 Cold air is heavier than warm air
11.4.6.2 Density of different liquids
4.202 Density of irregular solid, overflow can
11.4.6.4 Equidensity drops
11.4.11 Estimate the load of a boat
11.4.17 Finger in beaker
11.4.19 Float a battleship in a cup of water
4.204 Float a lighted candle
4.211 Float a metal boat, Plimsoll line
4.213 Float a needle on water
4.206 Float an egg in tap water and salt water
11.4.1.1 Float an ice cube
4.205 Float different kinds of wood
4.207 Float grapes at different levels in water
11.4.02 Flotation
6.12 Floating and sinking (Primary)
19.1.0 Floating and sinking
11.4.6 Floating in different liquids
4.209 Floating in different density liquids
11.4.3 Floating, sinking and rising under liquid
11.4.18 Floating square bar
11.4.6.1 Liquids float on liquids, miscible and immiscible liquids
11.4.10 Measure buoyancy using method of weighing in water
11.4.21 Measure specific gravity of fluids
4.210 Model diving bell
11.4.7 Model diving bell, model submarine, diving bottle
11.4.12 Plimsoll line, load lines
11.4.20 Reaction balance
11.4.23 Rice grains rising and falling in aerated water
11.4.22 Spherical oil drop
4.203 Weight of a floating body
20.0.6 Density of gases
20.0.6 Density of gases
12.3.20 Density of air with a balloon
1.0.0 Density of gases, SVP, Saturation Vapour Pressure
12.3.19 Density of hot air and cold air
11.2.0 Density of liquids, relative density
11.2.0 Density of liquids, relative density
4.13 Density of a liquid, relative density
11.4.6.3 Density ball
11.4.6.2 Density of different liquids
11.2.1 Density of liquids using mass and volume
11.1.1 Density of liquids with U-tube and liquid of known density, balancing columns
11.2.3 Density of ice
11.4.6.4 Equidensity drops
11.2.2 Maximum density of water, negative expansion coefficient of water
3.26 Separate immiscible liquids of different density
4.31 Temperature of water at maximum density, 4oC
11.1.0 Density of solids
11.1.0 Density of solids
4.12 Density of a solid
11.1.4 Density of beans
11.1.5 Density of boy
11.1.3 Density of irregular solid, not using volume
11.1.2 Density of irregular solid, using mass and volume
4.202 Density of irregular solids, overflow can
35.11 Density (relative density of minerals) (Geology)
3.27 Separate solids using density differences
11.3.2 Hydrometers, relative density
11.3.2 Hydrometers, relative density, r.d. (formerly specific gravity, S.G.)
23.2.8 Coefficient of expansion of oil
4.208 Drinking straw hydrometer
16.2.1.11 Elevator paradox
32.5.3.2 Lead acid battery secondary cell
8.6 Prepare electrolyte for a lead accumulator cell
11.3.0 Relative density, r.d., Specific gravity, S.G.
35.11 Relative density, r.d. (Geology)
11.3.1 Relative density of liquids, using a relative density bottle
11.3.3 Triple scale wine hydrometer
11.4.0 Buoyancy, flotation, Archimedes' principle, density of fluids, pressure in fluids
11.4.0 Buoyancy, flotation, Archimedes' principle, density of fluids, pressure in fluids
11.4.01 Buoyancy
11.4.02 Flotation
11.4.03 Fluid density
11.4.04 Fluid pressure
4.200 Buoyancy of water
See diagram 11.200.1: Archimedes' principle
1. According to Archimedes' principle, (Archimedes of Syracuse 287 - 212 B.C.), an object wholly or partly immersed in a fluid will be subjected to an upward force, upthrust, equal to the weight of the fluid it has displaced. If the density of the object is greater than the density of the fluid, its weight will be greater than the upthrust and it will sink. If the density of the object is less than the density of the fluid, the upthrust will be the greater than its weight and the object will be pushed upwards towards the surface. As the object raises above the surface, how much fluid it displaces decreases. Also, the upthrust decreases until the upthrust acting on the submerged part of the object equals the weight of the object and the object floats.
Let v = submerged volume of floating regular solid, and V = volume of whole solid. Let d = density of floating solid, and D = density of liquid
Weight of floating solid = upthrust (weight of liquid displaced)
d = m / v, so m = v X d
V X d = v X D, so v / V = d / D
d / D is the relative density of the solid compared with the liquid and v / V is the fraction submerged
So fraction submerged = density ratio
If the floating solid has uniform cross-section area, v/V = submerged length / total length
So relative density of liquid = submerged length of floating solid / total length of floating solid.
Buoyancy does not increase with depth.
See diagram 11.279: Buoyancy of water
2. Use a metal container with a tightly fitting cover, e.g. a treacle tin. With the cover on, push the container into a bucket of water, with the cover end down, and quickly let go of it. Note the upthrust on the container. Put some water in the container and repeat the experiment. Keep adding water until the container can no longer float. Fill the container can with water and put the cover on. Put a double loop of string around the side of the container and then attach a large rubber band to the other end of the string. Lift the container by holding the rubber band and note how much the band stretches. Lower the container into a bucket of water and note the stretch in the rubber band. The buoyant force a fluid exerts on a submerged object is equal to the weight of the volume of fluid displaced.
3. Float a small wooden boat carrying a heavy piece of lead in a bucket of water. Note the level of the water at the side of the bucket. Remove the piece of lead and drop it into the water. Again note the level of the water at the side of the bucket. The water level has fallen because when in the boat the piece of lead displaces its weight of water. However when at the bottom of the bucket of water, the piece of lead displaces its volume.
4.201 Cartesian diver
See diagram 11.280: Cartesian diver | Order online: Cartesian Diver
1. Wrap copper wire around the narrow part of the rubber bulb from a medicine dropper to make a rubber diver. Fill a tall plastic container with water. Put enough water in the rubber diver so that it only just floats in the container of water. Most of the rubber will be under water. Adjust how much the rubber diver floats by pinching the bulb to remove air. Cover the container with a sheet of plastic and fix it tightly around the rim of the container with string or rubber bands. Press on the tight plastic cover to make the diver sink. Stop pressing on the tight plastic cover to make the diver rise.
2. Repeat the experiment using a very small glass tube to make a diver. Add ink to the water to help you see the water level in the glass tube. Note that when the cover is pressed down, the pressure is transmitted through the water to decrease the volume of the air bubble in the glass diver. So the water level rises in the tube. When the volume of the air bubble is too small to hold up the glass diver by displacement of water the glass diver will sink. When you stop pressing on the cover, the decrease in pressure is transmitted to the air bubble that expands so the water level in the glass diver decreases. The increased volume of the air bubble in the glass diver displaces enough water to provide an upward force by displacement of water to allow the glass diver to float again.
3. Push a wooden match stick into a hollow plastic ball. The plastic ball by itself just sinks in water but the match gives it enough buoyancy to just float. Shorten the match so that its end floats level to the surface of water in a plastic drink bottle. Close the bottle with a plastic cap. The pressure of the fingers on the walls of the plastic bottle is transmitted to compress the air in the plastic ball and it sinks.
4. Cut a fresh piece of orange peel in the shape of a submarine. Make portholes in the side with the end of a ball point pen. Put the orange peel submarine in a container of water sealed with a plastic cap. Bubbles in the orange peel allow the submarine to float. Pressure on the plastic cap is transmitted to decrease the size of the bubbles and the submarine sinks.
5. Use a plastic ball point pen top with a pocket clip. If air can pass through the upper end seal it with Plasticine (modelling clay). Attach a chain of paper-clips to the pocket clip so that the pen top can float near the surface of water with the paper-clips hanging down. Almost fill a large plastic drink bottle with water. Hold the pen top vertically over the bottle with the paper-clips hanging down then gently lower it into the water. Screw the drink bottle cap on tightly. Squeeze the sides of the plastic drink bottle with your thumbs to make the pen top sink. The pen top contains an air bubble. When you squeeze the sides of the drink bottle, you also squeeze the air bubble, so more water enters the pen top and it sinks because the air bubble displaces less water.
6. For a diver use a plastic sachet of sauce, mayonnaise or butter. The type you see used in airlines. The sachet contains some air. When you put the sachet in a plastic bottle full of water and squeeze the bottle, some the air is compressed, the volume of the sachet decreases and it sinks.
7. Use a tall wide mouth container or a plastic drink bottle. Wrap copper wire around the narrow part of the rubber bulb from a medicine dropper to make a rubber diver. Fill the container with water. Put enough water in the rubber diver so that it only just floats in the container of water. Most of the rubber will be under water. You can adjust how much the rubber diver floats by pinching the bulb to remove air. Cover the container with a sheet of rubber or plastic sheet and tie it to the sides of the container. If you press on the tight cover, the rubber diver will sink. If you stop pressing on the tight cover, the rubber diver will rise. Repeat the experiment using a very small glass tube of a medicine vial instead of the rubber bulb to make a glass diver. Add a small amount of ink to the water so you can see the level of water in the glass diver. Note that when the cover is pressed down, the pressure is transmitted through the water to decrease the volume of the air bubble in the glass diver so the water level rises in the tube. When the volume of the air bubble is too small to hold up the glass diver by displacement of water the glass diver will sink. When you stop pressing on the cover, the decrease in pressure is transmitted to the air bubble that expands so the water level in the glass dive decreases. The increased volume of the air bubble in the glass diver displaces enough water to provide an upward force by displacement of water to allow the glass diver to float again.
8. Use a big bottle of water and an inverted open vial or small test-tube as a diver. Slightly inflate a rubber balloon by lowing in it and attach it to the mouth of the bottle. Squeeze the balloon and diver sinks.
9. Use a big plastic drink bottle as a submarine. Pierce a hole in the cap and in the bottom of the drink bottle. Push a plastic tube through the hole in the lid. Fill the drink bottle with water and let it sink to the bottom of a big tub of water. Blow into the plastic tube and the submarine rises to the surface.
4.202 Density of irregular solid, overflow can
See diagram 11.281: Overflow can
Use an overflow can, a stone, and a catch bucket. Fill the overflow can with water to the level of the spout. Attach a string to the stone and weigh it with a spring balance. Weigh the catch bucket and put it underneath the spout of the overflow can so that it catches the water displaced when you put the stone in the water. Immerse the stone in the water and record its weight. It weighs less than in the air. Find the weight of the displaced water by subtracting the weight of the bucket from the weight of the bucket and water. The loss of weight of the object in water is equal to the weight of the water displaced by the object.
4.203 Weight of a floating body
Fill an overflow can with water and let it run out until the surface is level with the spout. Select a piece of wood that floats half or more submerged in the overflow can. Weigh the piece of wood with a spring balance. Weigh the catch bucket. Put the catch bucket under the spout. Put the wood block in the overflow can and note the balance reading. Find the weight of the displaced water by subtracting the weight of the catch bucket from the total weight of catch bucket and water. The weight of the water displaced is equal to the weight of the object.
4.204 Float a lighted candle
Push nails or pins in the lower end of a candle so that the candle floats vertically with its top a little above the surface of the water. Light the candle and watch it burn. The candle constantly loses mass as it burns. The candle continues to float if it displaces a mass of water greater than its own mass.
4.205 Float different kinds of wood
See diagram 11.284: Floating wood
1. Put pieces of wood and cork with the same dimensions in a pan of water and note how each piece of wood floats. Measure the ratios of lengths above and below water.
2. Place lengths of wood with equal dimensions in a graduated cylinder containing water. Insert a drawing pin (thumb tack) up into the bottom of the lengths of wood to make them float upright. Measure the ratios of whole length to length below water.
4.206 Float an egg in tap water and salt water
See diagram 11.285: Floating egg
After the egg is laid and it starts to cool, the air cell forms. In a fresh egg the air cell is quite small and the egg sinks to the bottom of a container of clean water. A fresh egg has a thick white that does nor spread out far in the pan and the yolk stands up. As the egg gets older it loses water by evaporation. The water is replaced by air so the egg decreases in weight and starts to stand up, smaller end down. Later the egg starts to rise to the surface of the water. A floating egg may not be bad but it should be opened in a separate container and discarded if any bad smell can be detected. The bad smell comes from hydrogen sulfide (rotten egg gas) produced by the decomposition of proteins in a rotten egg. Such an egg may contain the dangerous Salmonella bacteria that can cause sickness and death. A fresh egg can be made to float if you add cooking salt to the water to increase the relative density of the water. Ships float higher in salt water than in fresh water because salt water is more dense than fresh water.
4.207 Float grapes at different levels in water
Be careful! Do NOT taste chemicals in the laboratory.
Prepare 4 beakers of water. Put a grape in beaker 1 then fill the beaker with tap water. Put a grape in beaker 2, add some tap water then add sugar until the grape floats on the surface of the water. Prepare beaker 3 in the same way as for beaker 2 then pour out half the water. Wait until the solution in beaker 3 is still, then very slowly add tap water until the beaker is full. The grape now floats between the lower sugar in water and the upper pure tap water. Carefully increase the concentration of sugar in the water, while stirring, until the grape floats at the same level as in beaker 3. To investigate why the grapes float at different levels, taste the water in each beaker by touching the surface. You can taste the difference between beaker 1 and beaker 2, but beaker 3 tastes the same as beaker 1, and beaker 2 tastes the same as beaker 4.
4.208 Drinking straw hydrometer
Seal one end of a drinking straw. Put some sand in it until it floats in water in a vertical position. Put a rubber band round the stem so that you can slide it up and down as a marker. Mark the drinking straw at water level. Measure the length from the bottom end of the drinking straw to the water level mark, X cm. Assume the relative density of water = 1, and assume that the drinking straw has a uniform cross-section area. Mark the drinking straw for different relative densities, e.g. from 0.6 to 1.2. Check the accuracy of your drinking straw hydrometers with a glass hydrometer.
4.209 Floating in different density liquids
See diagram 11.287: Floating in different density liquids
A measuring cylinder contains 4 liquids of different densities. The density of liquid D > liquid C > liquid B > liquid A. Solids A, B, C < have different densities and float at different levels in the measuring cylinder. For example where kerosene floats over water, a piece of heavy wood may float in the water but below the kerosene but a cork may float on the kerosene.
4.210 Model diving bell
See diagram 11.288: Model diving bell
1. Use a small wide mouth bottle with a two-holes stopper. Put some stones or metal washers in the bottle so it floats in an upright position. Insert one arm of a U-tube through the stopper so that it extends to the bottom of the bottle. Insert a short length of glass tubing through the other hole and attach a long rubber tube. Put the bottle in water. Suck on the rubber tube. Water enters the bottle through the U-tube until the bottle sinks. You can make the bottle rise by blowing through the rubber tube. This model illustrates the principle of the tanks or pontoons used to lift sunken ships. Fasten a weight to the bottle, sink both in water and lift the weight by blowing air into the bottle.
4.211 Float a metal boat, Plimsoll line
See diagram 11.211: Plimsoll line
1. Shape a piece of aluminium foil into the form of a little boat. Float the boat on water. A floating boat displaces the volume of the boat under water. This volume is greater than the volume of the ball of metal foil. The weight of this volume of water displaced is equal to the weight of the boat, so the boat floats.
2. Squeeze the boat into a ball. Try to float the ball on water. The ball sinks. Buoyancy force = weight of water displaced. The ball of aluminium foil displaces its own volume of water. The ball is heavier than its own volume of water, so it sinks.
3. Plimsoll line, Plimsoll mark, load lines
Plimsoll lines (Samuel Plimsoll 1824-1898) are lines painted on both sides of a ship to show the minimum freeboard, load line, allowed in different parts of the world and at different seasons to prevent dangerous overloading of the ship. If you live near a sea port, look for the Plimsoll lines on the sides of the big boats.
4.223 Plastic syringes and air pressure
See diagram 12.301: Syringes and air pressure
[Some school systems do not allow the use of syringes in the classroom.]
1. With the tip sealed, use a syringe to compress air or to produce a partial vacuum. Attach a small piece of plastic tubing to let you seal the tip with a pinch clamp or seal the syringe by pushing the tip into a wooden block drilled to the appropriate size. With this base as a platform, use the syringe in a vertical position as a balance for measuring weight by air compression. You can quantify all the following experiments because syringes are already graduated.
2. Fill the syringe with a small amount of air and hang it inverted to serve as a "spring type" balance.
3. Compress moist air within a syringe to cause water condensation and make "artificial rain".
4. Attach a length piece of plastic tubing to make a simple syringe pump.
5. Put water in the tube to make an air thermometer or use 12 m of tubing to make a water barometer.
6. Couple two syringes with a piece of tubing to show pressure changes within closed systems.
Order online: Vacuum stopper, creates near vacuum in a plastic syringe
11.1.0 Density of solids
Density of a regular solid, irregular solid, liquid, gas
Density, rho or d, definition and units. Density is the ratio of mass to volume of a substance. The symbol is the Greek letter rho. However this document uses "d". Some authorities use "d" for relative density. This document used "r.d." for relative density, and s.g. for specific gravity, Density = Mass / Volume, d = m / V kg / m3. The density of air at sea level is about 1 / 800 the density of water. The density of a solid is the ratio of mass to volume. Use a balance to measure the mass. If the solid is insoluble in water, measure the volume from how much water it displaces, whatever the shape of the solid. Half fill a graduated cylinder with water. Note the reading. Immerse the solid in the water and note the reading again. The difference in the two readings is the volume of the solid. Examples of substances and their densities in g cm-3 which can be of interest to the chemist are as follows: sulfur: 2.0, quartz: 2.6, calcite: 2.7, copper: 8.9, lead: 11.4. Ores such as malachite, cassiterite and cerussite are not uniform in density as they contain variable quantities of quartz, feldspar and other minerals.
As the density of a solid is the ratio of mass to volume (mass per unit volume). Use a balance to measure the mass. If the solid is insoluble in water, measure the volume by displacement of water. Half fill a graduated cylinder with water. Note the reading. Immerse the solid in the water and note the reading again. The volume of the solid is the difference in the two readings. Examples of the densities of elements, in g cm-3, are as follows: aluminium: 4.70, carbon (graphite): 4.25, carbon (diamond): 3.51, copper: 8.92, gold: 19.30, helium: 0.147, hydrogen gas: 0.070, iron: 7.86. lead: 11.30, magnesium: 1.74, mercury: 13.60, nickel: 8.90, platinum: 21.40, silver: 10.50, uranium: 19.10, zinc 7.14. In SI units, measure density in kg m-3, e.g. density of dry air at sea level = 1.29 kg / m3.
Measure the density of examples of different metals then decide whether they are pure substances.
Material Water Air Aluminium, Iron Mercury Gold
Density kg / m3 1.00 × 103 kg / m3 1.29 kg / m3 2.7 × 103 kg / m3 7.9 × 103 kg / m3 13.6 × 103 kg / m3 19.3 × 103 kg / m3
11.1.1 Density of liquids with U-tube and liquid of known density, balancing columns
See diagram 11.1.1: U-tube
Clamp an U-tube in an upright position. Pour in some liquid of greater density to about the depth shown in the diagram. With the aid of the glass rod, introduce a quantity of the less dense liquid. using a 50 cm ruler and a set square, measure the heights h1 and h2 of the free surfaces of the liquids above the surface of separation. Calculate the density of the unknown liquid. The pressures at any two points in the same horizontal line in a liquid at rest are the same. Pressure depends on depth. Po + d1gh1 = Po + d2gh2, where Po is atmospheric pressure, d1 is the density of one liquid, d2 is the density of the other of the liquid. Then d1h1 = d2h2. So the density of the unknown liquid, d2= d1h1 / h2. Repeat the experiment for different values of h1 and h2 by using a less dense liquid and then calculate the density.
An U-tube contains mercury. Water, relative density 1, is poured into one arm of the U-tube and oil, relative density 0.8, is poured into the other arm until the mercury columns in the arms of the U-tube are level. If the height of the water is 15 cm, the height of the oil is 18.8 cm.
11.1.2 Density of irregular solid, using mass and volume
Use a beam balance to weigh mass of an irregular solid. Record the mass, m. Pour water to about half depth of a measuring cylinder. Record the volume, V1. Put the solid into water in the cylinder. Read the scale and record the volume, V2. Calculate the density of the irregular solid.
Volume of the solid = (V2 - V1). The irregular solid's density = mass / volume. So the density of the irregular solid, d = m / (V2 - V1) Repeat the above steps then calculate the average density.
11.1.3 Density of irregular solid, not using volume
See diagram 11.1.3: Density of irregular solid
Tie around an irregular solid a thin and strong string and tie a loop at the other end of the string. Use the loop to weigh the irregular solid with a spring balance. Read the scale and record the weight, w1. Immerse the irregular solid in a breaker of water and weigh again using the spring balance. Record weight, w2. To calculate the density of the irregular solid:
The buoyant force on the solid = mass of water displaced x gravitation acceleration, i.e. (Fb = mwater g = rwater x Vwater x g)
However buoyant force also equals the difference between the two weights measured, i.e. (Fb = w1 - w2)
Therefore w1 - w2 = (rwater x Vwater x g)
Vwater = Vsolid.
Vsolid = msolid / rsolid
So (w1 - w2) = (rwater x msolid / solid x g)
msolid x g = w1,
So (w1 - w2) = (rwater x w1 / rsolid) Density water = 1 kgm-3, then rsolid = w1 / (w1 - w2)
11.1.4 Density of beans
Use beam balance to weigh a dry, empty bottle with a stopper. Record the mass of the empty bottle, m1. Pour in the beans to about one third depth of the bottle and weigh again. Record the mass of the bottle with beans, m2. Fill the remaining space in the bottle with water. To prevent the beans from absorbing water and expanding, use cold water and work as quickly as possible. Shake gently to remove air bubbles. Plug the stopper. Wipe away excess water and then weigh again. Record the mass of the bottle with beans and water, m3. Empty the bottle and then clean it with water. Fill the bottle with water, plug the stopper, wipe dry and then weigh again. Record the mass of the bottle with water, m4. Calculate the relative density of beans. Mass of beans = m2 - m1, mass of water filling bottle = (m4- m1), mass of water filling the space left by the beans = (m3- m2), mass of water equal volume to the beans = (m4- m1) - (m3 - m2) Relative density of beans = (m2 - m1) / ([m4 - m1] - [m3 - m2]), i.e. the mass of the beans divided by the mass of an equal volume of water.
11.1.5 Density of boy
Weigh a boy. Half fill a tub with a known volume of water. Mark the level of water in the tab, level 1. Put the boy in the tub and press him under the water with a thin stick. When the boy stops moving under water, mark the level of the water in the tub, level 2. Let the boy leave the tub slowly to catch any drips. Note whether the level has water in the tub has returned to level, if not fill the tub to level 1. Add a measured volume of water to the tub until it reaches level 2. The volume of the boy = (level 2 - level 1). The density of the boy = weight of the boy / (level 2 - level 1)
11.2.0 Density of liquid, relative density
Weigh a small container with the liquid inside. Pour the liquid into a graduated cylinder to find the volume of the liquid. Use a balance to find the mass of the container and the mass of liquid transferred to the measuring cylinder. Obtain the density by dividing the mass of the liquid by the volume. The density of water is close to 1 g per cc, cm3, so you can compare the density of substance with the density of water as relative density. Relative density (formerly specific gravity), is the ratio of mass of a volume of a substance to the mass of an equal volume of water, at 4oC. Relative density has no units because it is a ratio, e.g. petrol r.d. 0.70, ethanol r.d. 0.79, ice r.d. 0.90, olive oil r.d. 0.92, water r.d. 1.00, sea water r.d. 1.03, glass r.d. 4.50, mercury r.d. 13.60, gold r.d. 19.30. A special bottle, a density bottle, gives an accurate measure of relative density. Let mass of empty density bottle = A, mass of bottle + liquid = B, mass of liquid = (B - A), mass of bottle + water = C, and mass of water = (C - A). Relative density = (B - A / C - A). Use a small bottle to measure the density of different liquids. A more convenient way to measure the density of a liquid is to use a hydrometer.
Find the density of a cola drink in an aluminium drink-can. Weigh the full aluminium can. Open the aluminium can and drink the cola. The weight of the aluminium can is approximately 13 g. The volume of the cola is written on the side of the aluminium can, e.g. 375 mL or 355 mL (12 oz). Calculate the density of the cola. Weight of aluminium can = 13 g / volume of cola. Repeat the experiment with "diet" cola where sugar is substituted by a chemical sweetener, e.g. phenylalanine, aspartame.
11.2.1 Density of liquid using mass and volume Weigh a small container with the liquid inside. Pour the liquid into a graduated cylinder to find the volume of the liquid. It will not matter if any of the liquid sticks to the side of the container. Use a balance to find the mass of the container and find the mass of liquid transferred to the measuring cylinder. Obtain the density by dividing the mass of the liquid by the volume.
11.2.2 Maximum density of water, negative expansion coefficient of water
See diagram 11.2.2: Density of ice and water depends on temperature
Ice has a larger volme than the original volume of water before it freezes. Water has a maximum density at 4oC. When water cools from room temperature to 4oC, it is contracting in volume. Most solids are denser than their liquids, but when water is cooled from 4oC to 0oC, its volume expands. At 4oC the density of water is 1000 kg m-3. At 0oC the density of water is 999.87 kg m-3 and the density of ice is 918 kg m-3. The lower density of ice is caused by the formation of a hydrogen bonded tetrahedral network of water molecules. The temperature of water decreases with salinity. A freezing mixture of ice and sodium chloride drops to -20oC.
In freshwater lakes, during the summer the upper levels are heated by the sun to form a less dense layer called the epilimnion above the cooler more dense layer, the hypolimnion, where anaerobic conditions may occur. In autumn the epilimnion cools and mixes with the hypolimnion causing overturn and churning up of nutrients towards the surface. Algae may use these nutrients to cause algal blooms. If you bore a hole through the surface ice of a frozen river and catch a fish through the hole, the fish will freeze to death when you pull it up became it has been living at a temperature between 0oC and 4oC.  During freeze-thaw erosion of rocks, water enters cracks in the surface of rocks, freezes in cold weather, then expand in warmer weather and splits off a piece of the rock. Incountries where milk is delivered to front door steps overnight on very cold nights the metal foil top of the milk bottle may lift up and the bottle may even shatter. In very cold weathe water can exand in water pipes and burst them.
1. Use a flask with a narrow stem to show volume changes and a thermocouple to show temperature changes when water is allowed to warm from 0oC. Immerse a water thermometer in an ice bath. Water at the bottom of a cylinder remains at 4oC when surrounded by ice at the middle.
2. Find the temperature at which water attains its maximum density. Fix two thermometers so that they measure the temperatures near the top and the bottom of a large beaker of water. Put a large block of ice into the beaker. The ice floats on the water as the density of ice is 0.91 kg / m3, i.e. less than the density of water. Note any changes in temperature of water until the temperature of water at the bottom remains constant. At first, the water near the floating ice is cooled by it and sinks towards the bottom of the beaker until the temperature of water at the bottom reaches 4oC. The water at the bottom will stay at this temperature for a long time with water colder 4oC remaining higher up near the ice because water at 4oC. than the temperature of melting ice at 0oC. This unique behaviour of water explains why a pond or river freezes from the surface downwards while the water at the bottom seldom falls below 4oC.
3. Put a large piece of ice into a glass of water. Arrange two thermometers so that they measure the temperatures near the top and the bottom of the water. The water cooled by the ice falls to the bottom. This fall continues until the water at the bottom of the glass reaches a temperature of 4oC. The water stays at this temperature for a long time, the colder water remaining higher up near the ice. So water at 4oC is denser than the water at 0oC. This curious behaviour of water is of great practical significance in nature, and explains why a pond freezes from the surface downwards while the bottom seldom falls below 4oC. So the floating ice insulates the water below from very cold atmospheric temperatures.
4. Add tap water to a cylindrical cup until the water surface is above the rim of the cup and the water will almost flow out. Measure the vertical height from the bottom of the cup to the surface of the water in the cup and measure the temperature of the water. Put the cylindrical cup in the freezer compartment of a refrigerator and leave it there for a few days. Take the cup out of the freezer compartment and measure the vertical height from the bottom of the cup to the surface of the water in the cup. Also, you may note the temperature in the freezer if you have a refrigerator thermometer. The ice surface is higher than the original water surface at the rim of the bottle. Water at 4oC has its highest density, 1g / cm3. When the water cools to the temperature of 4oC, the density of the water increases, so that the volume of the water decreases. When water cools from 4oC to 0oC, the intermolecular distance elongates so the volume of the water expands. The density of water at 0oC is 0.99987 g / cm3. In winter, water pipes may burst when the temperature of water in a full pipe lowers from 4oC to 0oC.
5. To study the expansion of freezing water, use identical drinking cups. Put a tray into the freezing compartment of a refrigerator. Fill a cup with tap water at room temperature so that the water heaps up to form a meniscus. Put the cup in the tray in the freezing compartment of the refrigerator. Add some extra water to the cup to get the highest possible meniscus. When the water in the cup is frozen, fill an identical cup with water at room temperature. Compare the meniscus of the frozen water with the meniscus at room temperature. The frozen water heaped up because it had expanded. Some people claim that the heaping up is in a north south direction due to Coriolis effect!  If a glass bottle with a screw cap is filled to the top with water then wrapped in a plastic bag before being put in the freezer compartment the glass bottle may shatter - a dangerous experiment. 
6. Examine the water in deep ponds may remain unfrozen throughout winter when the air temperature is below 0oC. Water has a maximum density at 4oC. When water is cooled, the temperature being above 4oC the density increases as the temperature is lowered. However, but at 4oC. water has its maximum density, and when cooled further the water expands instead  of contracting, and so the density decreases. At 0oC water freezes to ice and expands on solidifying, so that ice is less dense than water, and therefore floats on water. The pond is cooled from above, so as the temperature falls the water at the top becomes denser than the water below, and so falls, so that the warmer water  rises to the top, is cooled, and falls in its turn, thus convection currents are set up, and the temperature of the pond is kept sensibly uniform. However, at 4oC water has its maximum density and so on further cooling a decrease in density occurs and the water at the top becoming less dense than that below, convection currents cease. As the temperature of the air falls, the temperature of the surface falls also, until at 0oC. ice forms. Ice and water are bad conductors of heat, and so the temperature of the water deep down in the pond is higher than that of the surface layer, and even when the surface has been cooled well below 0oC, the bulk of the water in the pond will be at a temperature above 0oC.
11.2.3 Density of ice
Prepare ice cubes, some with food colouring, e.g. cochineal. The ice cubes must be completely frozen and not have unfrozen water trapped inside. Put equal volumes of water and vegetable oil in a measuring cylinder, the water in first. Check that the two layers of water and oil are completely separated. Carefully lower an ice cube into the oil and watch it float in the oil. As the ice cube melts, the melt water trickles down the side of the ice cube, sinks through the oil and joins the water layer below. Repeat the experiment with an ice cube stained with food colouring. Watch the movement of the coloured water droplets and note whether the coloured water merges with the water below or makes a separate coloured water layer below the water. The density of ice is slightly below 0.92 g per cm2 and the density of a vegetable oils is slightly above this value. The density of water is about 1 g per cm2.
11.3.0 Relative density, r.d. (formerly specific gravity, S.G.)
1. Relative density, r.d., relative density bottle, hydrometer, r.d. water and ice, specific gravity
Relative density, r.d., is the ratio of the mass of a volume of a substance with the mass of an equal volume of water at a temperature of 4oC. It is a physics quantity of no dimension. For convenience, use this ratio instead of quoting the density, e.g. the density of mercury = (13.6 ×103 kg/m3), so r.d. mercury = 13.6.
2. Specific gravity
Specific gravity is the ratio of of the density of a substance to the density of a standard substance, usually with water, density 1.000 kg per litre at 4oC, or with dry air  density 1.29 kg per litre at 0oC and 1 atmosphere pressure. So carbon dioxide with density 1.976 g per litre at standard conditions has specific gravity = 1.976 / 1.29 = 1.532. As specific gravity is a ratio it has no units. Relative density was formerly called specific gravity, so S.G. water = 1. Specific gravity is still used to measure the concentration of the sulfuric acid electrolyte in a motor car battery, the brewing industry and laws applying to that industry and the processed foods industry.  It is a defining characteristic of  minerals. Specific gravity is measured with the hydrometer, Jolly balance, pycnometer, and the Westphal balance.
11.3.1 Relative density of a liquid, using a relative density bottle
Use a beam balance to measure the mass of a relative density bottle, specific gravity bottles, which accurately contain a known volume. Record the mass m1. Fill the bottle with a liquid whose density is unknown and insert the stopper. Wipe dry the surface of the bottle. Weigh the bottle, m2. Density of liquid = (m2 - m1) / V, where V = volume of the bottle. Pour the liquid out of the bottle then clean the bottle. Fill the bottle with water and insert the stopper. Wipe dry the surface of the bottle. Record the mass, m3. Calculate the relative density of a liquid. Density of liquid = (m2 - m1) / V, density of water = (m3 - m1) / V, where V = volume of the bottle. Density of a liquid relative to water = ([m2- m1] / V) / ([m3 - m1] /V). So the relative density of a liquid, RD = (m2 - m1) / (m3- m1) Repeat the above steps then calculate the relative density.
11.3.2 Hydrometers
Hydrometers include test-tube hydrometer, battery acid hydrometer, food testing hydrometers, constant weight hydrometer, constant volume hydrometer, and the Nicholson hydrometer and Mohr-Estphal balance are used with liquids of various density.
See diagram 11.3.2: Simple hydrometer
A hydrometer is a device for measuring the specific gravity of a liquid relative water, specific gravity of 1.0 measuring the density of the liquid in grams per cubic centimetre. Put a hydrometer in water then in alcohol. Show the buoyancy of hot and cold water with a hydrometer that sinks in warm water and floats in cold water. The Nicholson balance is a float that allows determination of loss of weight in water very accurately. Totally submerge the Nicholson hydrometer except for a small platform. Put it in water and load small weights on the platform until the water level reaches a mark on the wire stem. Then put the hydrometer in the unknown liquid, and add weights to the platform until the same mark on the wire stem is reached. Calculate the relative density of the unknown liquid knowing the mass of the hydrometer and the value of the two sets of masses used to bring the hydrometer to the reference line.
11.3.3 Triple scale wine hydrometer
See diagram 11.3.2: Wine hydrometer
By using this hydrometer you can follow the process of fermentation. As yeast converts sucrose sugar into ethanol the specific gravity of the juice of the crushed grapes, a called the "must or wort", decreases and the hydrometer sinks until fermentation is complete. If you put wine s.g. > 1.006 into bottles, the fermentation is incomplete and the bottles may burst from the extra carbon dioxide produced in the bottle. To test the specific gravity of the "must", use a plastic tube to siphon off a sample of the liquid. Put in the hydrometer so that it floats freely. Use your thumb and first finger to spin the hydrometer to spin off any bubbles clinging to the surface of the hydrometer. When the hydrometer stops spinning and does not touch the sides of the container, read the upper meniscus. The hydrometer will be calibrated to give correct readings at a certain temperature, e.g. 20oC. For other temperatures, you must apply a correction to the final specific gravity reading, e.g. 10oC (- 0.002), 15oC (- 0.001), 25oC (+ 0.001), 30oC (+ 0.003), 35oC (+ 0.004). You can estimate the percentage alcohol content if you measure the specific gravity before and after fermentation. based on the fact that 2,7 grammes of sugar gives 1 hydrometer degree in 1 litre of liquid and 17 grammes of sugar gives 1% of alcohol in one litre of wine. The wine hydrometer has its own container of known volume so besides a specific gravity scale it can also have a scale to estimate the percentage alcohol content if all the sugar is converted into alcohol. If initial specific gravity before fermentation = 1.090, then potential percentage alcohol by volume = 11.8%. If final specific gravity = 1.010 after fermentation, then potential percentage alcohol by volume = 1.3%, the fermentation has stopped. So alcohol contents = (11.8 - 1.3) = 10.5%. Also the hydrometer has a scale to estimate how much sugar to add to give a required alcohol content.
So the triple scales are as follows:
1. Specific gravity scale
2. Potential alcohol content scale
3. Amount of sugar to add scale
11.4.0 Buoyancy, flotation, Archimedes' principle, fluid density, fluid pressure
See diagram 11.4.0: Archimedes' principle, (Archimedes of Syracuse, about 287-212 BC)
Order online: Density Tubes Kit, density columns, buoyancy, miscible and immiscible liquids
The apparent loss in weight of a body immersed in a liquid equals the weight of the liquid displaced by the body.
The upthrust, or buoyancy force, on an object immersed in a fluid, is equal and opposite to the weight of the fluid displaced.
11.4.01 Buoyancy
Buoyancy force = weight of displaced fluid. An object displaces its own weight of fluid. If the upthrust force balances the weight, it will float. If the upthrust force is less than the weight, it will sink. When you immerse an object in a fluid, it feels an upward force equal to the weight of the fluid displaced by the object. This is called buoyancy. If the fluid is incompressible, then the buoyancy is given by F = rVg, where r is the fluid density, g is the acceleration of gravity, V is the volume of fluid displaced by the object.
11.4.02 Flotation
An object floats in a liquid when the weight of the body is equal to the weight of liquid displaced. When an object is placed in a liquid with greater relative density than the object it will sink until the weight of the liquid displaced is equal to the weight of the body.
11.4.03 Fluid density
Liquids and gases both have the capacity to flow so are called fluids. The mass of a substance divided by its volume is called its density, density air = 1.29 kg / m2, water = (1.00 X 103 kg / m2). Specific gravity or relative density is the ratio of the density of the substance to the density of water, e.g. Density of mercury = (13.6 X 103 kg / m3), so relative density of mercury = 13.6.
11.4.04 Fluid pressure
1. Fluids in an open condition, e.g. atmosphere, large swimming pool, river
The pressure at equal depths in a uniform liquid is the same, it acts in all directions, and always acts perpendicular to any surface with which it is in contact. The pressure on area due to force = force / area, newton / metre2, pascal, Pa. For a fluid, the force is due to the weight of the fluid above the area, A, so pressure = weight/area pascal = mg / A pascal. (m = height X area X density), so pressure = height X area X density X g /A = density X g X height). The atmospheric pressure at the earth's surface is the pressure due to mass of air above the earth. At the earth's surface, it can push mercury up an evacuated tube to a height of 0.76 metre. Pressure of air = pressure of mercury = density mercury X g X height pascal. If the top of an object is at depth h1 below surface of a fluid, and the bottom at depth, h2, the difference in pressure = density X g X (h2 - h1) newton / metre2, which provides the buoyancy due to the upthrust of the fluid.
2. Fluid in a closed condition
2.1 The fluid may be dynamic, e.g. when moving through a pipe, hydrodynamics,  or in a constrained flow, e.g. air moving around a wing, aerodynamics.
2.2 The fluid may be static, e.g. compressed in a syinge.
11.4.1 Buoyancy of water
1. Use a metal can that has a tightly fitting cover. With the cover on, push the can into a bucket of water, cover end down, and quickly let go of it. Observe the upthrust on the can. Put some water in the can and repeat the experiment. Keep adding water a little at a time and repeating until the can no longer floats. Fill the can with water and put the cover on. Put a double loop of string around the side of the can and then attach a large rubber band to the other end of the cord. Lift the can by holding the rubber band and observe how much the band stretches. Now lower the can in a bucket of water and observe the stretch in the rubber band. How do you account for the difference? The buoyant force a fluid exerts on a submerged block is equal to weight, mg, of the volume of fluid displaced.
2. Use an empty tin with a tight cover, e.g. a coffee tin. Close the coffee tin and hold it at the bottom of a bucket of water. The coffee tin will float upwards as soon as release the it. When putting the coffee tin into the water, your hand feels an upward force. Fill the coffee tin with water and hold it at the bottom of the bucket of water again. The coffee tin does not float and you may feel a smaller upward force. Take the coffee tin out of the water. Tie a cross tie around the coffee tin then attach an elastic strap. Suspend the coffee tin by the elastic strap and note the elongation of the elastic. Lower the coffee tin into the bucket of water but not touching the bottom. Observe the elongation of the elastic when the coffee tin is at rest. The elongation of the elastic has reduced compare to the elongation in the air. It shows that there is still buoyancy acting on the coffee tin and its direction is still upward.
3. Repeat the experiment with a string attached to a spring balance instead of the elastic.
4. Measure buoyant force. Lower a weight suspended from a spring scale into a beaker of water suspended from a spring.
5. Weigh a submerged block. Lower a 3 Kg block of aluminium suspended from a spring scale into water and note the new weight. An aluminium block on a spring scale is lowered into a beaker of water taped on a platform balance. Immerse a lead block suspended from a counter weighted balance in a beaker of water on a counter weighted platform balance and then transfer a weight to bring the system back into equilibrium.
11.4.1.1 Float an ice cube
1. Observe an ice cube floating in a jar of water. Fill the jar completely with water and place the jar on absorbent paper. Measure the proportion of the ice cube above the surface of the water. Observer the melting ice cube and note any overflow onto the absorbent paper. Again measure the proportion of the ice cube above the surface of the water. The water level in the jar does not change as the ice melts.
2. Repeat the experiment with an ice cube floating in salty water. The ice cube floats higher in the salty water. Observe any overflow of salty water + ice cube water. The icebergs that float in the antarctic ocean come from ice formed on the land so they are composed mainly of fresh water. So while the amount of salty sea water displaced by the iceberg is equal to the weight of the iceberg the volume of melted fresh water will be slightly higher than the displaced sea water so the sea water level will rise when the iceberg smelt.
11.4.2 Buoyancy of air
1. Put a brass weight counterbalanced by am aluminium sphere filled with air in a bell jar and evacuate it. Balance a toilet tank float against brass weights in air and in a vacuum. Balance a glass ball with a brass weight in a bell jar and then pump the air out.
2. Make a buoyancy balloon. Fill a balloon with dry ice, seal it then place it on a scale and watch the weight decrease as the balloon inflates.
11.4.3 Floating, sinking and rising under liquid
Floating is state of equilibrium in which an object rests on or suspended in the surface of a fluid (liquid or gas). According to Archimedes' principle, an object wholly or partly immersed in a fluid will be subjected to an upward force, or upthrust an instantaneous upward force, equal in magnitude to the weight of the fluid it has displaced. If the density of the object is greater than that of the fluid, then its weight will be greater than the upthrust and it will sink. However if the object's density is less than that of the fluid, the upthrust will be the greater and the object will be pushed upwards towards the surface. As the object raises above the surface the amount of fluid that it displaces (and therefore the magnitude of the upthrust) decreases. Eventually the upthrust acting on the submerged part of the object will equal the object's weight, equilibrium will be reached, and the object will float.
11.4.6 Floating in different liquids
See diagram 11.287: Floating in different liquids
1. Use a measuring cylinder or tall glass jar, water and kerosene. You will also need a piece of wood that at sinks in water paraffin wax or candle wax and a piece of cork. Pour water into the jar then carefully pour the kerosene into the jar on top of the water. Drop in the solid substances. The wood sinks in two liquids. The paraffin sinks in the kerosene but floats on the water. The cork floats on the kerosene. Floating condition: if the density of a solid is greater than that of the fluid, then it will sink, if the solid's density is equal to that of the fluid, the solid will float anywhere in the liquid. If the solid's density is less than that of the fluid, the solid will float above the surface of the liquid.
2. To understand the condition of a solid floating in a liquid, use a thin and tall glass bottle (or a glass test-tube, a glass cup) and liquids with different density, e.g. water, kerosene, honey or molasses. Solids: a steel ball (for example, ball bearing), iron bolt or screw, a small block of ebony or other sinkable into water wood block, a piece of solid paraffin, a small cork. Pour liquids into the glass bottle according to the order of density. You should pure the liquids slowly along the rim of the bottle under a glass stick. Do not make the surfaces between liquids mixed. Gently put the four solids into the liquid. Observe the floating in the different layers of liquids with different densities.
3. Float a test-tube in water, kerosene, and a combination kerosene and water.
4. Fill a test-tube with several immiscible liquids of different densities. Then add solid objects that will float at the various interfaces.
11.4.6.1 Liquids float on liquids, miscible and immiscible liquids
See 3.16: Miscible liquids, methylated spirit, glycerine, kerosene
1. Pour water into a bottle. Carefully pour the same amount of oil on top of the water.  Close the bottle and shake it thoroughly. The oil and water at first seem to mix together but after some time they separate into different layers. Oil and water do not mix, i.e. they are not miscible.They are immiscible. Alsothe density of oil is less than the density of water so oil floats on water.
2. Put corn syrup in a tall beaker and add red colouring, e.g. cochineal. Pour vegetable oil on the corn syrup. It floats on the corn syrup.
11.4.6.2 Density of different liquids
Material Relative density
Honey 1.36
Light maple syrup 1.33
Dish washing liquid 1.03
Water with food colouring 1.00
Vegetable oil 0.91
Rubbing alcohol (isopropyl alcohol) 0.87
Baby oil 0.82
Lamp oil 0.80
1. Add different food colouring to 20 mL of the liquids used in the experiment, e.g. water, cooking oil, honey or treacle or golden syrup. Pour the liquids into the centre of a measuring cylinder in order of density.
2. Use two exactly same size containers. Pour the lamp oil into one container and the water into the other container until they are overflowing. Put a sheet of
hard plastic on top of the container with the water. Invert the water container and place it over the oil container, keeping the sheet of plastic in place.
Pull the sheet of plastic 2 mm to one side to allow the liquids to mix.
3. Note how the liquids remain separate because of their different densities.
4. Put one branch of a Y-tube in brine (concentrated salt water) and the other in coloured water, then suck the stem of the Y-tube.
11.4.6.3 Density ball
Metal sphere barely floats in cold water and sinks in hot water.
11.4.6.4 Equidensity drops
 See 3.4.2.5.1: Ghost crystals, sodium polyacrylate:
A beaker of water has a layer of salt solution on the bottom. Place a drop of mineral oil on top and pipette in some coloured salt solution The drop in an oil sac sinks to the interface. A globule of oil floats at the interface in a bottle half full of water with alcohol on top. Aniline forms equidense and immiscible drops when placed in 25oC water. Pour 80 mL in cool water and heat. Orthotoluidine has the same density as water at 24oC and is immiscible.
11.4.7 Model diving bell, model submarine, diving bottle
See diagram 11.288: Model diving bell
1. Use a small wide mouth bottle with a two-holes stopper. Put some stones or metal washers in the bottle so it floats in an upright position. Insert one arm of an U-tube through the stopper so that it extends to the bottom of the bottle. Insert a short length of glass tubing through the other hole and attach a long rubber tube. Put the bottle in water. Sucking on the rubber tube. Water enters the bottle through the U-tube until the bottle sinks. You can make the bottle rise by blowing through the rubber tube. This model illustrates the principle of the tanks or pontoons used to lift sunken ships. Fasten a weight to the bottle, sink both in water and lift the weight by blowing air into the bottle.
2. Use a tall wide mouthed bottle and a tall, large, glass flume. Put some small stones into the bottle to spread uniformly on the bottom of the bottle. Pure some run paraffin on the small stones to fix them to the bottom of the bottle. It can make the bottle stand upright in water. Choose a fit cover for the bottle. Drill two holes on the cover. Pure water into the bottle. Cover the bottle with the cover. Choose a U-tube and a short glass to fit the holes. Insert one end of the U-tube into the bottle from a hole on the cover of the bottle and let the end reach nearly the bottom of the bottle. Insert one end of the glass into the bottle from the other hole on the cover of the bottle but do not insert the end into the bottle too deeply. Cover the other end of the glass with a long latex tube (wet the end of the latex tube beforehand so that it is easier to insert). Place the wide mouthed bottle into the flume full of water. Inspire or blow the latex tube, then the water at the bottle flows in or out, the bottle will sink down or float up in the water. This simulates the principle of a submarine. The equipment may simulate wrecking a sank boat [viz. saving a wrecking boat]. Use a weight on the bottom of the flume. Let the bottle dive into the bottom of the flume. Fasten the weight to the neck of the bottle. Blow the latex tube to make the weight and bottle float together up.
11.4.8 Archimedes' principle
See diagram 11.200.1: Archimedes' principle
1. Fill an overflow can. 2. Put a wooden block in the overflow can. 3. Collect the water displaced in a balance pan. 4. Remove the wooden block, dry it, put it in the other balance pan. The weight of the wooden block is equal to the weight of the water displaced. The apparent loss in weight of a body immersed in a liquid will equal the weight of the displaced liquid.
Buoyancy force = (force on top surface of object - force on bottom surface of object) = (F2 - F1) = (P1A - P2A) = (density x gh1A - density x gh2A) = density x gA (h2 - h1) = weight of displaced fluid The upthrust or buoyancy force on an object wholly or partially immersed in a fluid is equal in magnitude and opposite to the weight of the fluid it has displaced.
11.4.9 Archimedes' principle, bucket and cylinder experiment
See diagram 11.4.9: Archimedes' principle
A mass and bucket of the same volume hang from a spring scale. Lower the mass into water catch the overflow and pour the overflow into the bucket. Hang a cylinder and bucket of the same volume from a scale. Immerse the cylinder in water, catch the overflow and pour it into the bucket. Hang a cylinder turned to fit closely inside a bucket from the bottom of the bucket while suspended from the bottom of a balance Immerse the cylinder in water and then pour water into the bucket. Archimedes did not experience buoyancy, only how to measure volume.
See diagram 11.4 0.1: Archimedes' principle apparatus
Note the reading of the spring scale suspending a cylindrical mass and hanging bucket above an overflow beaker. The cylindrical mass fits exactly into the catch bucket. Raise the overflow beaker to submerge the mass and bucket and let the displaced water flow into a catch beaker. Lower the overflow beaker and remove the cylindrical mass from the bucket. Dry the hanging bucket then pour the water from the catch beaker into the catch bucket. The reading on the spring scale is the same as at the start of the experiment.
11.4.10 Measure buoyancy using method of weighing in water
See diagram 11.1.3: Weighing block in water
1. Weigh a block in air. Submerge the block in water and weigh it again. The difference in weights is the buoyant force. Note that the air provides a small upthrust on the block depending on the density of air at the time of weighing.
See diagram 11.4.10: Buoyancy
2. Measure buoyancy with cylinder and straw. Differently place an object and a cylinder full of water on the two sides of a beam balance. Suppose the beam balance balances. When you immerse the object in another fluid, the balance will be destroyed by the buoyancy. Reducing the water at the cylinder will be helpful to resume the balance. When the weight of the water reduced equals the magnitude of the buoyancy, the new balance is set up. Use a ruler of 30 cm length. Burn a small hole at the 15 cm mark on the ruler. Differently groove a shallow groove at 0 cm and 30 cm mark. Hang the ruler up through the middle hole and make the grooves upward. Use a plastic dish of diameter 8~10 cm. Burn 3 holes at the rim of the dish and make the distance between any two holes is equal. Tie a piece of string to each hole on the dish then hang the dish flatly to the ruler with 30 cm mark. Paste a gasket of M3 with adhesive plaster to each tie at the holes on the dish. The gaskets can also prevent the string from slipping away. Use a short piece of string and tie a nut of M10 to either end of the string then hang it at the other side of the ruler. The string with two nuts corresponds to the weight of a steelyard. Displace the "weight" to make the ruler balance then fix the weight with adhesive plaster at the position. You may put some pins or sand to counterbalance the little affection from the adhesive plaster. Use other piece of string and tie it to a heavy object (for example, a stone) then hand the string on the ruler with 0 cm mark. Place the cylinder of water in the dish to make the ruler balance again. Firstly let the side of the ruler with the cylinder lighter a bit, then make a little adjustment with pins or sand so that the ruler balances. Record the volume of the water at the cylinder V1 now. Pure water into a beaker and place it under the object. When the object immerses in the water, the ruler inclines towards the cylinder. Suck the water out of the cylinder with a medical sucker to make the ruler balance again. Record the volume of the water at the cylinder V2 now. The buoyancy is equal to dg (V1 - V2), where d is the density of water, g is the acceleration of the gravity. If you do the experiment with a refitted physical balance and microsucker, you can measure the buoyancy accurately.
11.4.11 Estimate the load of a boat
See diagram 11.4.11: Buoyancy of a boat
The magnitude of buoyancy acted on an object in water is equal to the weight of water displaced by it. The more the weight of the boat, the more the water displaced, and the greater the buoyancy acted on the boat. Use a piece of graph paper in 10 cm long and 2 cm wide. Draw a mark ruler on it. The scale on mark ruler begin at upper mark 1, then from upward to downward, 2, 3 . . . Tape the ruler you have just made on the paper box with transparent adhesive tape. Regard it as a "boat". Tape the mark ruler vertically, i.e. stand up, on the outside of the boat, and cut off the surplus part of the ruler at the bottom of the boat. Put the boat into a water tank. Note the boundary between water and ruler, called the water level, also called the depth of water by boat. Record the value of the water level. Put a 10 g weight in the centre of the boat to ensure the boat remains upright. Read the value of the water level and record it. Add weights 10 g every time. To note the place of the weight on the boat that should ensure the boat being in water vertically all the time. Record the value of water level every time. After adding weights on boat, decrease weights. Decrease 10 g weight every time, record the value of water level until the boat has been empty. Compare two water levels refer to each weight, and calculate the average of them. Analyse the value of water level and data refer to weights in the boat. There is a definite relation between the depth under water of boat and weight of boat. When you estimate the loads of a boat, you can use the conclusion from the experiment above. For example, let a person stand on a boat which floats on water, measure the depth which the boat drops, then according to the relation between the depth under water of boat and weight of boat use ed from the experiment above to estimate the loads of the boat. Thus, by this simple method you can finish an estimating on maximum loads of a boat.
11.4.12 Plimsoll line, load lines
See diagram 11.211: Plimsoll Line
Lines painted on both sides of a ship to indicate the minimum freeboard allowed in different parts of the world and at different seasons to prevent dangerous overloading of the ship.
11.4.13 Board and weights float
A board sinks equal amounts as you add equal weights.
11.4.17 Finger in beaker of water
See diagram 11.4.17: Balanced beakers of water
1. Put a beaker of water on a top-pan balance and note the weight. Put a finger down into the beaker of water. The weight shown on the balance increases equal to the weight of water displaced by the finger.
2. Balance two identical beakers containing the same original volume of water. Note the same original level of water in each beaker. Lower a square cross-section rod into the water in the right hand beaker and fix it in position. The level of water rises and the beaker moves down. Note the final level of water in the right hand beaker. Calculate the volume of (final level - original level) or calculate the volume of water displaced by observing the volume of the rod under water. Used a beaker to add water to the left hand beaker until the two beakers are level again. The volume of water added to the left hand beaker is equal to the volume of water displaced in the right hand beaker.
11.4.18 Floating square bar
A long bar floats in one orientation in alcohol and switches to another orientation when water is added
11.4.19 Float a battleship in a cup of water
Float a 2500 g juice can in 500 g water. A small amount of water floats a wood block shaped to just fit in a graduated cylinder. Float a cup three quarters full in a cup one quarter full. A small amount of water floats a wood block shaped to just fit in a graduated cylinder. Will a cup three quarters full float in a cup one quarter full?
11.4.20 Reaction balance
Immerse an empty test-tube in a beaker of water taped on a platform balance to displace the beaker of water. Then immerse your finger in the beaker of water.
11.4.21 Measure specific gravity of fluids
Raise water and an unknown liquid to different heights in vertical tubes by a common low pressure.
11.4.22 Spherical oil drop
Olive oil forms a large spherical drop in a stratified mixture of alcohol and water.
11.4.23 Rice grains rising and falling in aerated water
See 24.1.01: Nucleation
1. Drop some grains of rice, raw or cooked, into a glass of soda water or lemonade or any clear beverage made with aerated water. The rice grains first sink to the bottom of the glass. After a few minutes small bubbles form on the rice grains at nucleation sites. Later some of the rice grains with bigger bubbles attached rise to the surface of the aerated water. At the surface the bubbles burst and the rice grains sink again.
2. Repeat the experiment with cooked rice grains and other foods, e.g. salted peanuts. Note the relationship between number of nucleation sites and frequency of movements up to the surface of the aerated water.
11.4.24 Centre of buoyancy and centre of gravity of a boat
See diagram 11.4.24: Centre of buoyancy and centre of gravity of a boat
Centre of Gravity is the point in a body where the gravitational force may be taken to act.
Centre of Buoyancy is the center of the gravity of the volume of water which a hull displaces.
For a floating body to be in equilibrium the centre of gravity must be in the same vertical line as the centre of buoyancy. When the hull of a boat is upright the center of gravity and center of buoyancy is on the same vertical line, the hull is stable. For most hulls, the center of buoyancy is below the center of gravity and the hull is said to be metastable. When the hull tilts, the center of gravity remains in the same position related to the hull. The center of buoyancy moves to fit the new center of gravity of the volume of water replaced by the hull. At first the gravity force and the buoyancy force creates a  righting torque that tries to move the hull back to the upright position. However, if the hull is tilted to much, the center of buoyancy moves to a position where the buoyancy and gravitation force starts to create a moment that will capsize the hull.
4.118 Cold air is heavier than warm air
Use two identical paper bags that are the same size. Inflate each bag by blowing into them as if they are balloons. Tie the openings closed tightly with string. Tie the end of the string into a loop and suspend the bags from the end of a balanced rod. Move the loops along the rod until the inflated bags are exactly balanced. Gently heat the air beneath one of the bags with a small candle. The bag containing the heated air moves up and the bag containing the cooler air moves down. Move the candle to under the other bag to see the same result. [Comment: The bags are sealed and so the mass of gas is unchanged when heating or cooling takes place. This experiment shows Archimedes Principle in action, not mass change.]