Archimedes’principle

The result that Archimedes discovered was the first law of hydrostatics, better known as Archimedes Principle. Aixhimedes studied fluids at rest, hydrostatics, and it was nearly 2,000 years before Daniel Bernoulli took the next step when he combined Archimedes idea of pressure with Newton s laws of motion to develop the subject of fluid dynamics. 

The buoyant force is, by the well-known Archimedes principle, the product of the mass of the fluid displaced by the particles and the acceleration from the external force. The volume of the particle is fn/ps, where ps is the density of the particle, and the particle displaces this same volume of fluid. The mass of fluid displaced is (m/ps) pf, where pf is the density of the fluid. The buoyant force is, then,... 

Comparing this equation to that of a single particle (eq. (3.565)), it is evident that in applying the Archimedes principle to a particle in a fluidized suspension, it is an average suspension density, including the particle density, rather than that of the fluid alone, that determines the buoyancy force (Foscolo and Gibilaro, 1984). The gravity force is... 

Consider a body of water and a piece of styrofoam. Both are attracted by the earth because of gravity. However, when immersed in water, the styrofoam is effectively repelled by the earth due to the Archimedes principle. Use this analogy to explain the possibility of repulsive van der Waals forces between materials that, taken pairwise, experience only attractive forces. 

There is still another method by which the density of insoluble solids can be determined. It is based on an ancient principle known as Archimedes principle when an object is suspended in a fluid, it APPEARS to lose weight equal to the weight of the fluid displaced. We say that the object is "buoyed up," and that the "buoyancy" is equal to the apparent weight loss. In equation form, Archimedes principle could be stated as... 

The application of Archimedes principle to the determination of densities of liquids and solids is illustrated in the next two problems. 

Weight of metal object in air = 25.0 g Weight of metal object in water = 15.0 g Buoyancy = apparent weight loss = 10.0 g By Archimedes principle,... 

When a body of any kind is parlly or fully immersed in a static fluid, every part of the body surface in contact with the fluid is pressed on by the fluid. The pressure is greater on the areas more deeply immersed. The resultant of all these fluid pressure forces is an upward or buoyant force. The pressure on each part of the body is independent of the body material. Archimedes principle states that the buoyant force equals the weight of the displaced fluid. 

Archimedes principle applies to the determination above a body immersed in a fluid is subject to an upward force due to which its mass (apparently) decreases proportionally to the mass of the of the fluid is displaces . This means that ... 

A quick method of determining density utilizes Archimedes principle, which states that the buoyant force on an immersed object is equal to the weight of the liquid displaced. A bar of magnesium metal attached to a balance by a fine thread weighed 31.13 g in air and 19.35 g when completely immersed in hexane (density 0.659 g/cm3). Calculate the density of this sample of magnesium in SI units. 

If the sample is irregular in shape, the traditional Archimedes principle must be employed. The sample is first weighed in air on a laboratory scale and then suspended by a fine thread in water. The density is given by ... 

Pressure at the Same Depth 108 Pressure versus Container Shape 109 Pascal s Principle 110 Buoyancy 110 Archimedes Principle 111 Hydrometers 113 Hydrodynamics Moving Fluids 114 Flow Rate 114 Speed and Diameter 114 Equation of Continuity 115... 

A stationary particle suspended in a fluid experiences a buoyancy force Fb, evaluated from Archimedes principle as the weight of fluid displaced, pfgv, where pf is the fluid density, g is the acceleration due to gravity and v is the volume of the particle. If the particle begins to move the fluid will exert an additional force, the drag force, made up of two components the skin friction drag, which is a direct result of the shear stress at the surface due to fluid viscosity, and the form drag due to differences of pressure over the surface of the particle. 

For sedimentation to occur, it is necessary that F exceeds buoyancy only slightly in proportion to (Archimedes principle) and the frictional... 

The differences in the buoyancy effect (based on Archimedes principle) of materials in air at different barometric pressures is not as great as the buoyancy differences in water versus air, but it still exists and can affect accurate weighings. 

It is interesting to note that for both Table 2.12 and Table 2.14, there are corrections for 20°C and 760 mm of atmospheric pressure. Because the glassware is calibrated for this temperature and pressure, one may wonder why a correction is necessary. The reason goes back to Archimedes principle which cannot be accounted for when the glass is calibrated. The only way to avoid use of these tables at STP is to do all weighing in a vacuum to avoid the effects of air s weight. 

The fact that weights occupy space creates an interesting problem. The space occupied by a weight is normally occupied by air, and because air has weight, it provides a buoyancy effect (known as Archimedes principle) against the real weight of the object. This effect influences the measured weight of an object. 

From Newton s law for the gravitation force, Archimedes principle for the buoyant force, and the definition of the drag force, the force balance on a drop becomes... 

This automatic wet sieving machine determines a single point on the size distribution curve in a few minutes without the need to dry samples [1,16]. The sieving vessel is first filled with slurry and topped up with water to a precise level to allow accurate determination of the mass of solids added (W ) by application of Archimedes principle. The fine fraction is next removed from the vessel through a discharge valve. Screening is hastened by propeller agitation and with ultrasonics to maintain the sieve mesh free... 

Also based on the Archimedes principle are the various forms of hydro meters (Greek iidoq water, juerqov measure, as they were first used to measure... 

P6rot5 determined the densities of saturated vapours by exposing a vacuous globe to the vapour, closing it when full of vapour, and weighing after cooling. Bauer used Archimedes principle, weighing a float in the vapour. 

According to Archimedes principle, the mass of a floating object equals the mass of the fluid displaced by the object. Use this principle to solve the following problems. 

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