Archimedes' Principle
Archimedes' Principle states that an object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. This principle explains why objects float or sink in fluids and is fundamental to understanding buoyancy. It is used to calculate the buoyant force acting on objects in various applications, such as shipbuilding and designing flotation devices.
7 Key excerpts on "Archimedes' Principle"
eBook - ePubThe Antikythera Mechanism
The Story Behind the Genius of the Greek Computer and its Demise
- Evaggelos G. Vallianatos(Author)
- 2021(Publication Date)
- Universal Publishers(Publisher)
...In other words, the object is buoyed by a force equal to the weight of the water the object displaces. The combined weight of the water and the immersed object must equal that of the water of the same volume. Weight is the gravity pulling the object downwards and buoyancy is a force pulling the object upwards. These principles make up the science of hydrostatics, which Archimedes explained in his work “On Floating Bodies.” The weight of the object is measured on a scale and the buoyancy is its volume. In an international conference on the legacy and influence of Archimedes, June 8–10, 2010, in Syracuse, two distinguished scientists, Stephanos Paipetis from Greece and Marco Ceccarelli from Italy, summed up the general consensus of the sixty contributors as follows: “Archimedes’ works are still of interest everywhere and, indeed, an in-depth knowledge of this glorious [Archimedean] past can be a great source of inspiration in developing the present and in shaping the future with new ideas in teaching, research, and technological applications.” 229 Archimedes also remains the paradigm for the science and technology that went into the Antikythera machine. A few scholars even connect Archimedes to the science of the twenty-first century. “Today the ancient scientist [Archimedes] is considered both a great theoretician and a model of scientific ingenuity,” Geymonat wrote. “It cannot be overemphasized that, as an inventor, Archimedes was truly inimitable, inasmuch as he obtained results that were both innovative and original. He presented these results simply and without grand eloquence, maintaining a tone of professionalism that transcends mere self-confidence, revealing the enormous potential of human intelligence.” 230 Vincent De Sapio, Sandia National Laboratory, and Robin De Sapio, Orinda Union School District, California, also highlight the modernity and continuous usefulness of Archimedes merging geometry with mechanics...
eBook - ePubIntroduction to Engineering Mechanics
A Continuum Approach, Second Edition
- Jenn Stroud Rossmann, Clive L. Dym, Lori Bassman(Authors)
- 2015(Publication Date)
- CRC Press(Publisher)
...In the previous section, we limited ourselves to the consideration of simple surfaces—walls, gates, and dams. However, if we recognize that the hydrostatic pressure acts on all surfaces, we see clearly how a resultant buoyancy force arises. The sketch in Figure 16.11 illustrates this. Archimedes (287–212 BC) was a Greek mathematician who invented the lever, fine-tuned the definition of pi, and “discovered” buoyancy. Though some details of this story have taken on the distinct patina of apocrypha, it is still a cracking-good yarn. Archimedes’ close friend, King Hiero of Syracuse, suspected that the gold crown he had recently received from the goldsmith did not include all of the gold he had supplied. He shared his suspicions with Archimedes, who (it is said) went home to ruminate in the bathtub. Archimedes, ever observant, noticed that his body displaced the bathwater—when he got into the tub, the water level rose. He quickly calculated that the weight of displaced water balanced his own weight, and celebrated this discovery by running through the streets shouting “Eureka (I have found it),” so intoxicated by hydrostatics that he neglected to dry off or don a bathrobe. The next day, so the story goes, Archimedes dunked his friend’s crown, as well as a lump of gold equal to what he had provided to the goldsmith, and found that they did not displace equal amounts of water. The crown did, in fact, contain less gold than the King had specified. The goldsmith, unable to produce the remainder of the gold, was beheaded posthaste. FIGURE 16.11 Distributed force due to hydrostatic pressure on a submerged object...
eBook - ePub- N. (Nehemiah) Hawkins(Author)
- 2018(Publication Date)
- Perlego(Publisher)
...THE HYDROSTATIC BALANCE. Every body immersed in a liquid is submitted to the action of two forces: gravity which tends to lower it, and the buoyancy of the liquid which tends to raise it with a force equal to the weight of the liquid displaced. The weight of the body is either totally or partially overcome by its buoyancy, by which it is concluded that a body immersed in a liquid loses a part of its weight equal to the weight of the displaced liquid. This principle, which is the basis of the theory of immersed and floating bodies, is called the principle of Archimedes, after the discoverer. It may be shown experimentally by means of the hydrostatic balance (Fig. 92). This is an ordinary balance, each pan of which is provided with a hook; the beam being raised, a hollow brass cylinder is suspended from one of the pans, and below this a solid cylinder whose volume is exactly equal to the capacity of the first cylinder; lastly, an equipoise is placed in the other pan. If now the hollow cylinder be filled with water, the equilibrium is disturbed; but if at the same time the beam is lowered so that the solid cylinder becomes immersed in a vessel of water placed beneath it, the equilibrium will be restored. By being immersed in water the solid cylinder loses a portion of its weight equal to that of the water in the hollow cylinder. Now, as the capacity of the hollow cylinder is exactly equal to the volume of the solid cylinder the principle which has been before laid down is proved. Fig. 92. Minerals, if suspected of containing spaces, should be coarsely pulverized, and then the second method may be conveniently applied to determine their density—thus prepared, a higher result will be obtained, and even metals when pulverized were found to give a greater specific gravity than when this is determined from samples in their ordinary state...
eBook - ePubBasic Engineering Mechanics Explained, Volume 1
Principles and Static Forces
- Gregory Pastoll, Gregory Pastoll(Authors)
- 2019(Publication Date)
- Gregory Pastoll(Publisher)
...Chapter 9 Buoyancy Definition and applications of buoyancy The effect of the densities of the fluid and of the immersed object on flotation The fraction of a floating object that will be submersed Flotation of closed compartment and open vessels How buoyancy affects submerged objects that are denser than the fluid Artist’s impression of the diving bell designed and built by Sir Edmond Halley (of comet fame) in 1790, for undersea work. The weighted barrel was filled with compressed air to replenish that used up by the divers. Illustration based upon contemporary engravings. The appearance of the diving suit and helmet are conjecture, based upon Halley’s partial description, as no detailed drawing of them could be found. Definition and applications of buoyancy When an object is placed in a fluid (either a liquid or a gas) it experiences an upward force exerted on it by the fluid. This phenomenon is called buoyancy. We have all had personal experience of buoyancy. You have seen boats and balls float on water, and have experienced feeling ‘lighter’ when standing in water than when standing in air. You also know that it takes a great deal of effort to submerge a beach ball or a soccer ball fully in water. The first person to quantify the value of the buoyancy force was Archimedes, whose famous principle states that the buoyancy force on an object that is either immersed or floating, is equal to the weight of the fluid that has been displaced. Archimedes’ principle may be confirmed by a simple experiment. Suspend a heavy solid object, such as a stone, by a thin thread attached to a spring balance. Note the weight of the object, from the reading on the spring balance. While it is still attached to the thread, dip the object into a container of water that is full to the brim. Now observe the reading on the spring balance, which indicates the (apparently diminished) weight of the object. Collect the displaced water, and weigh it...
eBook - ePub- W. Bolton(Author)
- 2015(Publication Date)
- Routledge(Publisher)
...Thus, as the first moment of area about O is AY, then: Figure 29.6 Example The second moment of area of a rectangular plate about an axis which is its upper edge is bd 3 /3, where b is its breadth and d its depth. Example Determine the position of the centre of pressure of a vertical rectangular plate of width b and depth d immersed in a fluid with one edge at the free surface of the fluid (Figure 29.6). The second moment of area of a rectangular plate about an axis through its upper edge is bd 3 /3. Hence: 29.5 Archimedes' Principle When an object is immersed in a fluid of density ρ, then the pressure p on its lower 2 surface must be greater than the pressure p at its upper surface since it is at a 1 greater depth in the fluid, for example the cube shown in Figure 29.7. If the height difference between the upper and lower faces is h then the pressure difference is: p 2 - p 1 = hρg Figure 29.7 Cube immersed in a fluid For the cube shown in Figure 29.7, we have p 1 = F 1 /A and p 2 = F 2 /A, thus we can write the above equation as: F 2 - F 1 = Ahρg But Ah is the volume of the cube and so Ahρg is the weight of the fluid displaced by the cube. Thus there is an upthrust acting on an immersed object equal to the weight of fluid it displaces. This is known as Archimedes’ Principle and applies to all objects immersed in fluids, regardless of their shape. Example What will be the upthrust acting on an object of volume 100 cm 3 when immersed in a liquid of density 950 kg/m 3 ? The upthrust is the weight of fluid displaced by the object and is thus, for a volume V, given by: Upthrust = Vρg = 100 x 10 −6 x 950 x 9.8 = 0.93 N 29.5.1 Floating When an object floats in a fluid then the weight of the object is just balanced by the upthrust. Thus if an object of volume V floats in a liquid with a fraction f of its volume below the surface of the liquid, then the upthrust is fVρg, where ρ is the density of the liquid...
- Melvyn Kay(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
...Indeed, this immersion technique is now a standard laboratory method for measuring the volume of irregular shaped objects and for determining their specific gravity. Figure 2.16 Archimedes principle. (a) Measuring the volume of an irregular object. (b) Demonstrating apparent loss in weight. (c) The ‘Cartesian Diver’. Still not convinced? Try this example with numbers. A block of material has a volume of 0.2 m 3 and is suspended on a spring balance (Figure 2.16b) and weighs 3,000 N. When the block is lowered into the water it displaces 0.2 m 3 of water. As the water weighs 10,000 N/m 3 (approximately), the displaced water weighs 2,000 N (i.e. 0.2 m 3 × 10,000 N/m 3). Now, according to Archimedes, the weight of this water should be equal to the weight loss by the block and so the spring balance should now be reading only 1,000 N (i.e. 3,000−2,000 N). To explain this, think about the space that the block (0.2 m 3) will occupy when it is lowered into the water (Figure 2.16b). Before the block is lowered into the water, the ‘space’ it would take up is currently occupied by 0.2 m 3 of water weighing 2,000 N. Suppose that the water directly above the block weighs 1,500 N (note that any number will do for this argument). Adding the two weights together is 3,500 N and this is supported by the underlying water and so there is an equal and upward balancing force of 3,500 N. The block is now lowered into the water and it displaces 0.2 m 3 of water. The water under the block takes no account of this change and continues to push upwards with a force of 3,500 N and the downward force of the water above it continues to exert a downward force of 1,500 N. The block thus experiences a net upward force or a loss in weight of 2,000 N (i.e. 3,500−1,500 N). This is exactly the same value as the weight of water that was displaced by the block...
eBook - ePub- William S. Janna(Author)
- 2020(Publication Date)
- CRC Press(Publisher)
...Substituting, we have d R b = ρ g z 2 − ρ g z 1 d A = ρ g z 2 − z 1 d A But the volume of the element is (z 2 − z 1) dA, and our equation becomes d R b = ρ g d V Integrating over the entire volume gives the total vertical force: R b = ρ g ∭ d V (2.32) Thus, the buoyant force equals the weight of the volume of fluid displaced. This concept is known as Archimedes’ principle. (Recall that pressure does not vary with horizontal distance, so there are no unbalanced forces in the x- or y -direction.) With reference to Figure 2.30, we can now evaluate the moment of the buoyant force about the origin: R b x r = ρ g ∭ x d V Combining with Equation 2.32, we obtain an expression for the line of action of R b : x r = ∭ x d V V (2.33) Thus, the buoyant force acts through the centroid of the submerged volume: the center of buoyancy. When the buoyant force exceeds the object’s weight while submerged in a liquid, the object will float in the free surface. A portion of its volume will extend above the liquid surface, as illustrated in Figure 2.31. In this case, FIGURE 2.31 A floating body. d R b = ρ g z 2 − ρ a g z 1 d A where ρ a is the air density or density of the fluid above the liquid. For most liquids, ρ a ≪ ρ and thus we can write d R b = ρ g z 2 d A = ρ g d V s where d V S is the submerged volume. Integration gives R b = ρ g ∭ d V s (2.34) Thus, the buoyant force exerted on a floating body equals the weight of the displaced volume of liquid. It can be shown that this force acts at the center of buoyancy of only the submerged volume. Example 2.17 Figure 2.32 shows a 4 cm diameter cylinder floating in a basin of water, with 7 cm extending above the surface. If the water density is 1 000 kg/m 3, determine the density of the cylinder. FIGURE 2.32 A cylinder floating in the surface of a liquid. Solution A free-body diagram of the cylinder includes gravity and buoyancy forces...
