Archimedes’s Principle

To illustrate the compaction process that occurs in an extruder, a Maddock solidification [1] experiment (described in detail in Section 10.3.1) was performed using a 63.5 mm diameter machine [2]. The extruder was operated at a screw speed of 60 rpm with a poly(vinylidene chloride) copolymer (PVDC) powder. After the extruder reached a steady-state operation, screw rotation was stopped and full cooling was applied to the extruder. After several hours of cooling, the screw and PVDC resin were removed from the extruder and the density of the bed was measured using Archimedes s principle. The compaction phenomenon in the extruder is shown by the density measurements of the solid bed in Fig. 4.1. As shown in this figure, the density of the solid bed increased from the feedstock bulk density of 0.73 g/cm to nearly the solid density of 1.7 g/cmT... 

Archimedes used the experience to develop what has come to be known as Archimedes s principle.This principle states that when an object is placed in a fluid, it experiences an upward force that is equal to the weight of the fluid that is displaced. Also known as the principle of buoyancy, it determines whether something sinks or floats. 

Archimedes s Principle when an object is placed in a fluid, it experiences an upward force that is equal to the weight of the fluid that is displaced. 

The boat isn t solid iron. Instead, it is shaped into a hollow form that displaces water as it is placed into the water. From physics we find that the upward buoyant force acting on a boat is equal to the weight of the water the boat displaces (Archimedes s Principle). Add cargo and the boat will weigh more. This causes the boat to sink deeper into the water so that mote water is displaced. As mote water is displaced, the buoyant force increases to match the increased weight of the boat. For more details, be sure to enroll in a physics course. 

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... 

Let us consider a sphere of radius r, volume V and mass M = p V (ps being the sphere density) falling in a viscous fluid of density p (Figure D.l). It is subjected to three different forces (i) gravitational force, (ii) Archimedes reaction and (iii) viscous friction. Newton s principle is written... 

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. 

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. 

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... 

Bulk density of specimens was measured by the Archimedes principle. The Vickers hardness as well as indentation fracture toughness were determined at room temperature using a Vickers diamond indenter at a 10 kg load for 10 s. Microstructure observation was performed under a transmission electron microscope (TEM JEOL, Tokyo, Japan JEM-2010/200CX/21 OOF). Optical transmissions of the translucent samples in wavelength of 2.5-6.5pm were measured by FTIR spectrometer (EQU1NOX55, Bruker, Billerica, MA). 

Most numerical models use the continuity equation to calculate the velocity components and Bernoulli s equation to obtain pressure that is integrated on the hull for hydrodynamic forces. Then applying Archimedes principle, a vertical displacement and a trim angle are calculated. 

Piccini s scientific work began in 1874 as a student (Fig. 4.5) when he published a note about his invention of a new hydrometer. Applying Archimedes principle, he used his new device to conduct a series of determinations with solids and liquids. Already in this early note, written with youthful energy, one can discern the hallmarks of his later work clarity and erudition. After graduation he worked with Michele Piccini Fileti (1851-1914) conducting research in organic chemistry, explaining the mechanism of molecular transposition observed by Adolph Wurtz... 

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