Application of Archimede's principle on Submarines.

Archimedes Principle

A-  Introduction:

Archimedes' principle is the law of buoyancy. It states that "anybody partially or completely submerged in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body." The weight of an object acts downward, and the buoyant force provided by the displaced fluid acts upward. If these two forces are equal, the object floats. Density is defined as weight per volume. If the density of an object exceeds the density of water, the object will sink. Archimedes' principle is a law of physics fundamental to fluid mechanics. Archimedes of Syracuse formulated this principle, which bears his name.

Archimedes' Inspiration

Archimedes made two masses of the same weight as the crown, one of gold and the other of silver. He filled a large vessel with water to the very brim, and dropped the mass of silver into it. The amount of water that overflowed was equal in volume to that of the silver mass sunk in the vessel. Archimedes refilled the vessel and dropped the mass of gold into the full vessel. Not as much water overflowed because gold is more dense than silver, so the same weight takes up less volume. Finally, Archimedes filled the vessel again and dropped the crown itself into the water. He found that more water overflowed for the crown than for the mass of gold of the same weight. Hence, reasoning from the fact that more water was lost in the case of the crown than in that of the gold mass, he detected the mixing of silver with the gold, and made the theft of the contractor perfectly clear.

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If the weight of the water displaced is less than the weight of the object, the object will sink.

Otherwise the object will float, with the weight of the water displaced equal to the weight of the object.

Formulas:

The principle applies to both floating and submerged bodies and to all fluids, i.e., liquids and gases. It explains not only the buoyancy of ships and other vessels in water but also the rise of a balloon in the air and the apparent loss of weight of objects underwater. In determining whether a given body will float in a given fluid, both weight and volume must be considered; that is, the relative density, or weight per unit of volume, of the body compared to the fluid determines the buoyant force. If the body is less dense than the fluid, it will float or, in the case of a balloon, it will rise. If the body is denser than the fluid, it will sink.

The main formula for density is      

d = density

m = mass

v = volume

Volume of rectangular shape= Length x Breadth x Height

Volume of Object (in Liters) = Weight of Object in Air (in kilograms/grams) – Weight of Object in Water (in kilograms/grams)         

(This equation assumes that the object is completely submerged, and has a density of at least 1 kg/L)

v Weight of the liquid displaced by the object = buoyant force

ð weight=mass x acceleration due to gravity

The density of water is ρwater = 1 g/mL = 1 g/cm3 = 1 kg/L.

The volume of an object that is submerged = the volume of fluid displaced by the object.

B-    Application of Archimedes principle on Submarines:

Archimedes was one of the first to recognize a principle that water "presses up" or "buoys up" on objects,  even ones that are more dense than water (which sink), but especially objects that are less dense than water (which float). As an object sits in water, it displaces (pushes aside) some water. This principle enables ship made up of tons of steel floats easily on the surface of sea water if the buoyancy force that it receives is great enough to overcome the downward force of its weight.

The same principle is also applied to enable the operation of a submarine which can float or dive under water. A submarine has a large ballast tank used to control the density and weight of the submarine.

Whether a submarine is floating or submerging depends on the ship's buoyancy. Buoyancy is controlled by the ballast tanks. There are spaces in between the inner hull and the outer hull that can be either filled with water, or air. To sink a submarine, the ballast tank is filled with water to increase the density and weight of the submarine and make it larger than the buoyancy force of the water. To float a submarine, water is forced out of the ballast tank with compressed air thus decreases the density and weight of the submarine, when the buoyancy force of the water becomes larger than the density and weight of the submarine, it will easily float. If these spaces are filled with air, then the submarine is more buoyant and it tends to float to the surface. If these spaces are filled with water, then the submarine will sink. By adjusting the level of water and air in the spaces, the depth at which the submarine 'floats' can be varied. The exact depth can be controlled by adjusting the water to air ratio in the ballast tanks. Submerged, the submarine can obtain neutral buoyancy. That means the weight of the submarine equals the amount of water it displaces. The submarine will neither rise nor sink in this state.

Proving :

The model I have chosen for my assignment is submarine and the application of Archimedes principle on submarines. First of all I need some items to create my model (submarine). Since we are advised by the supervisor to create a simple model so I decided to choose a plastic bottle to create my submarine. I bought a small bottle of 100 plus, two nails, a medium size tub to reserve water, and few small rocks, to give a little weight to my model.

Table 1.0

Items	Size or mass
Bottle	50g
Nails	10g
Rocks	30g
Water tub	Medium size

To start the experiment we need to make some holes in the bottle, the holes are necessary so that the water can go in and out in the presence and absence of the air. After making several small holes, we have to make a bit larger hole for a pipe so that we can blow air through it and take out the water. Then we put some small pieces of rocks inside the bottle to give it some weight. The reason why I have put some rocks is that the submarines have a lot of weight due to its huge tank and the interior where the crew stays and operates. So the rocks can act as a tank and the interior.

Now we take a tub and put some water and then make hole in it so that the displaced water can pass through the pipe fixed in a hole into a cup, where we’ll store the water and measure it. The water displaced in the cup should be equal to the mass of the object which we had placed in the tub, to prove the Archimedes principle. To measure the mass we need the weighing scale, which can be found in the university’s lab or the shops. First we take the mass of the object and place it on the water and observe whether it will sink or float, and leave it for a while so that the displaced water can pass to the cup through the pipe. We have to repeat the experiment several times because the readings might be inaccurate for first few times. Hence after getting the same mass of water to that of an object we can now find the density and prove the Archimedes principle.

To find the density we need to know two main things, the mass of the object and the volume of the water. We already found the mass of the submarine which is 90g now we need to find the volume of the water. To find the volume of the water we need to measure the length, Breadth and the height of water in the tub.

V= L x B x H, where,  L= 25.50cm,    B= 18cm,   H= 7.50cm. 

        So, V= 25.50 x 18 x 7.50 = 3442.5cm3

After finding the volume and mass of the object and water we can easily find the density by applying the density formula:   d= m/v.

                                                     D= 90g/3442.5cm3,    So,              D= 0.026g/cm3

So the density of the 90g of submarine in the 3442.5cm3 of water in the tub is 0.026g/cm3.

Now the question which arises is when the submarines sink in the water does the density of the object changes and does it displace more water? The answer is no! The submarine sinks in water because it takes inside the amount of water around it through which the weight of the submarine gets more than that of the buoyant force. Which means the displaced water now goes inside the ballast tank in submarine rather than going out.

Hence when we keep the 90g submarine above the water it will first float due to its low mass, but after a while when the water starts entering the bottle through the pipes its weight starts increasing, when the plastic submarines weight is more than the buoyant force it will sink.

C-    Comparing:

Egg:

Now we take an egg and weigh its mass. I took an egg of 55g and same volume of water. Then I put the egg inside the water and left it for a while until the water was fully displaced through the pipe in to the cup. Due to its oval shape the egg will sink in the clean water. And the water displaced will be same as that of the mass of egg. After finding the mass now we can find the density of the egg inside the water. d= m/v

D= 55g/3442.5cm3,    So,         D = 0.016g/cm3

So the density of the 55g of egg in 3442.5cm3 water is 0.016g/cm3.

Plastic:

Plastics are usually very light, due to their light weight and density they float. For my experiment I took 35g plastic and same volume of water. We again put the plastic into the tub and wait until the water is fully displaced. The volume of water displaced is equal to that the mass of the plastic. After getting the correct mass now we can find the density.             D=m/v

                        D= 35g/3442.5cm3,    So,       D= 0.010g/cm3

So the density of the 35g of plastic in 3442.5cm3 water is 0.010g/cm3.

Wood:

As plastics woods are also light weighted, but the difference is wood dissolves water in it and increases the weight. I took 85g wood piece and same volume of water. We place the wood inside the water and again wait for it until the water displaced is equal to the mass of the wood. The volume of water displaced is equal to that the mass of the wood. Hence we can find the density of the wood inside the water. D= m/v

                        D= 85g/3442.5cm3,    So,       D= 0.025g/cm3

So the density of 85g of wood in 3442.5cm3 water is 0.025g/cm3.

Table: 1.1

Items	Mass/g	Volume/cm3	Density/ g/cm3
Submarine	90g	3442.5	0.026
Egg	55g	3442.5	0.016
Plastic	35g	3442.5	0.01
Wood	85g	3442.5	0.025

Conclusion:

Archimedes principle is applied everywhere now a days. So, to test his experiment we built our own model which is a submarine and then we compared it with three other objects which are egg, plastic and wood. Some of the objects were floating and some of them sank. We also found the mass of the object and the volume of the water to find the density. So we found out that different objects have different density and different object properties. But submarine could sink and float if its properties are changed manually. We can make it float by filling the ballast tank with air. In mean time we can sink it by filling the ballast tank with water. But the water displaced of the submarine will still remain the same. Which means when the submarine sinks or floats it will displace the same amount of water.

Refernces:

1-     The Columbia Electronic Encyclopedia, 6th ed. Copyright 2012, Columbia University Press. 

 Archimedes' principle | Infoplease.com http://www.infoplease.com/encyclopedia/science/archimedes-principle.html#ixzz2ab9qPg1D

2-     Allen, P. 1980. Mr. Archimedes' bath. New York: Lothrop, Lee & Shepard Books.

3-     Archimedes. and Heath, T. 1897. The works of Archimedes. Cambridge: University Press.

4-     Onr.navy.mil. n.d.. Blow the Ballast!. [online] Available at: http://www.onr.navy.mil/focus/blowballast/sub/work4.htm [Accessed: 31 Jul 2013].