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Continuum Mechanics
Continuum mechanics
Continuum mechanics
is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles
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Conservation Of Energy
In physics, the law of Conservation of Energy
Energy
states that the total energy of an isolated system remains constant, it is said to be conserved over time.[1] This law means that energy can neither be created nor destroyed; rather, it can only be transformed from one form to another. For instance, chemical energy is converted to kinetic energy when a stick of dynamite explodes
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Atmosphere
An atmosphere (from Greek ἀτμός (atmos), meaning 'vapour', and σφαῖρα (sphaira), meaning 'sphere'[1][2]) is a layer or a set of layers of gases surrounding a planet or other material body, that is held in place by the gravity of that body. An atmosphere is more likely to be retained if the gravity it is subject to is high and the temperature of the atmosphere is low. The atmosphere of Earth
Earth
is composed of nitrogen (about 78%), oxygen (about 21%), argon (about 0.9%) with carbon dioxide and other gases in trace amounts. Oxygen
Oxygen
is used by most organisms for respiration; nitrogen is fixed by bacteria and lightning to produce ammonia used in the construction of nucleotides and amino acids; and carbon dioxide is used by plants, algae and cyanobacteria for photosynthesis. The atmosphere helps to protect living organisms from genetic damage by solar ultraviolet radiation, solar wind and cosmic rays
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Buoyancy
In physics, buoyancy (/ˈbɔɪənsi, -əntsi, ˈbuːjənsi, -jəntsi/)[1][2] or upthrust, is an upward force exerted by a fluid that opposes the weight of an immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the pressure at the bottom of a column of fluid is greater than at the top of the column. Similarly, the pressure at the bottom of an object submerged in a fluid is greater than at the top of the object. This pressure difference results in a net upwards force on the object. The magnitude of that force exerted is proportional to that pressure difference, and (as explained by Archimedes' principle) is equivalent to the weight of the fluid that would otherwise occupy the volume of the object, i.e. the displaced fluid. For this reason, an object whose density is greater than that of the fluid in which it is submerged tends to sink
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Mixing (process Engineering)
In industrial process engineering, mixing is a unit operation that involves manipulation of a heterogeneous physical system with the intent to make it more homogeneous. Familiar examples include pumping of the water in a swimming pool to homogenize the water temperature, and the stirring of pancake batter to eliminate lumps (deagglomeration). Mixing is performed to allow heat and/or mass transfer to occur between one or more streams, components or phases. Modern industrial processing almost always involves some form of mixing.[1] Some classes of chemical reactors are also mixers. With the right equipment, it is possible to mix a solid, liquid or gas into another solid, liquid or gas. A biofuel fermenter may require the mixing of microbes, gases and liquid medium for optimal yield; organic nitration requires concentrated (liquid) nitric and sulfuric acids to be mixed with a hydrophobic organic phase; production of pharmaceutical tablets requires blending of solid powders
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Fracture Mechanics
Fracture
Fracture
mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture. In modern materials science, fracture mechanics is an important tool used to improve the performance of mechanical components. It applies the physics of stress and strain behavior of materials, in particular the theories of elasticity and plasticity, to the microscopic crystallographic defects found in real materials in order to predict the macroscopic mechanical behavior of those bodies. Fractography
Fractography
is widely used with fracture mechanics to understand the causes of failures and also verify the theoretical failure predictions with real life failures
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Plasticity (physics)
In physics and materials science, plasticity describes the deformation of a (solid) material undergoing non-reversible changes of shape in response to applied forces.[1][2] For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanent changes occur within the material itself. In engineering, the transition from elastic behavior to plastic behavior is called yield. Plastic
Plastic
deformation is observed in most materials, particularly metals, soils, rocks, concrete, foams, bone and skin.[3][4][5][6][7][8] However, the physical mechanisms that cause plastic deformation can vary widely. At a crystalline scale, plasticity in metals is usually a consequence of dislocations. Such defects are relatively rare in most crystalline materials, but are numerous in some and part of their crystal structure; in such cases, plastic crystallinity can result
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Surface Tension
At liquid–air interfaces, surface tension results from the greater attraction of liquid molecules to each other (due to cohesion) than to the molecules in the air (due to adhesion). The net effect is an inward force at its surface that causes the liquid to behave as if its surface were covered with a stretched elastic membrane. Thus, the surface becomes under tension from the imbalanced forces, which is probably where the term "surface tension" came from.[1] Because of the relatively high attraction of water molecules for each other through a web of hydrogen bonds, water has a higher surface tension (72.8 millinewtons per meter at 20 °C) compared to that of most other liquids. Surface tension
Surface tension
is an important factor in the phenomenon of capillarity. Surface tension
Surface tension
has the dimension of force per unit length, or of energy per unit area
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Viscosity
The viscosity of a fluid is a measure of its resistance to gradual deformation by shear stress or tensile stress.[1] For liquids, it corresponds to the informal concept of "thickness"; for example, honey has higher viscosity than water.[2] Viscosity
Viscosity
is a property of the fluid which opposes the relative motion between the two surfaces of the fluid that are moving at different velocities. In simple terms, viscosity means friction between the molecules of fluid. When the fluid is forced through a tube, the particles which compose the fluid generally move more quickly near the tube's axis and more slowly near its walls; therefore some stress (such as a pressure difference between the two ends of the tube) is needed to overcome the friction between particle layers to keep the fluid moving
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Conservation Of Mass
The law of conservation of mass or principle of mass conservation states that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time, as system's mass cannot change, so quantity cannot be added nor removed. Hence, the quantity of mass is conserved over time. The law implies that mass can neither be created nor destroyed, although it may be rearranged in space, or the entities associated with it may be changed in form. For example, in chemical reactions, the mass of the chemical components before the reaction is equal to the mass of the components after the reaction. Thus, during any chemical reaction and low-energy thermodynamic processes in an isolated system, the total mass of the reactants, or starting materials, must be equal to the mass of the products. The concept of mass conservation is widely used in many fields such as chemistry, mechanics, and fluid dynamics
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Gay-Lussac's Law
Gay-Lussac's law
Gay-Lussac's law
can refer to several discoveries made by French chemist Joseph Louis Gay-Lussac
Joseph Louis Gay-Lussac
(1778–1850) and other scientists in the late 18th and early 19th centuries pertaining to thermal expansion of gasses and the relationship between temperature, volume, and pressure. He is most often recognized for the Pressure
Pressure
Law which established that the pressure of an enclosed gas is directly proportional to its temperature and which he was the first to formulate (c
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Charles's Law
Charles's law
Charles's law
(also known as the law of volumes) is an experimental gas law that describes how gases tend to expand when heated. A modern statement of Charles's law
Charles's law
is:When the pressure on a sample of a dry gas is held constant, the Kelvin
Kelvin
temperature and the volume will be directly related.[1]This directly proportional relationship can be written as: V ∝ T displaystyle Vpropto T or V T = k , displaystyle frac V T =k, where:V is the volume of the gas, T is the temperature of the gas (measured in kelvins), k is a constant.This law describes how a gas expands as the temperature increases; conversely, a decrease in temperature will lead to a decrease in volume
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Boyle's Law
Boyle's law
Boyle's law
(sometimes referred to as the Boyle–Mariotte law, or Mariotte's law[1]) is an experimental gas law that describes how the pressure of a gas tends to increase as the volume of the container decreases. A modern statement of Boyle's law
Boyle's law
isThe absolute pressure exerted by a given mass of an ideal gas is inversely proportional to the volume it occupies if the temperature and amount of gas remain unchanged within a closed system.[2][3]Mathematically, Boyle's law
Boyle's law
can be stated as P ∝ 1 V displaystyle Ppropto frac 1 V or P V = k displaystyle PV=k where P is the pressure of the gas, V is the volume of the gas, and k is a constant. The equation states that the product of pressure and volume is a constant for a given mass of confined gas as long as the temperature is constant
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Combined Gas Law
The combined gas law is a gas law that combines Charles's law, Boyle's law, and Gay-Lussac's law. There is no official founder for this law; it is merely an amalgamation of the three previously discovered laws. These laws each relate one thermodynamic variable to another mathematically while holding everything else constant. Charles's law states that volume and temperature are directly proportional to each other as long as pressure is held constant. Boyle's law
Boyle's law
asserts that pressure and volume are inversely proportional to each other at fixed temperature. Finally, Gay-Lussac's law
Gay-Lussac's law
introduces a direct proportionality between temperature and pressure as long as it is at a constant volume
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Gas
Gas
Gas
is one of the four fundamental states of matter (the others being solid, liquid, and plasma). A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or compound molecules made from a variety of atoms (e.g. carbon dioxide). A gas mixture would contain a variety of pure gases much like the air. What distinguishes a gas from liquids and solids is the vast separation of the individual gas particles. This separation usually makes a colorless gas invisible to the human observer. The interaction of gas particles in the presence of electric and gravitational fields are considered negligible as indicated by the constant velocity vectors in the image. One type of commonly known gas is steam. The gaseous state of matter is found between the liquid and plasma states,[1] the latter of which provides the upper temperature boundary for gases
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Bernoulli's Principle
In fluid dynamics, Bernoulli's principle
Bernoulli's principle
states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.[1][2] The principle is named after Daniel Bernoulli
Daniel Bernoulli
who published it in his book Hydrodynamica
Hydrodynamica
in 1738.[3] Although Bernoulli deducted that pressure decreases when the flow speed increases, it was Leonard Euler
Leonard Euler
who derived Bernoulli's equation in its usual form in 1752.[4][5] The principle is only applicable for isentropic flows: so when the effects of irreversible processes (like turbulence) and non-adiabatic processes (e.g
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