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Bernoulli’s Principle
In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy. The principle is named after the Swiss mathematician and physicist Daniel Bernoulli, who published it in his book ''Hydrodynamica'' in 1738. Although Bernoulli deduced that pressure decreases when the flow speed increases, it was Leonhard Euler in 1752 who derived Bernoulli's equation in its usual form. The principle is only applicable for isentropic flows: when the effects of irreversible processes (like turbulence) and non-adiabatic processes (e.g. thermal radiation) are small and can be neglected. Bernoulli's principle can be applied to various types of fluid flow, resulting in various forms of Bernoulli's equation. The simple form of Bernoulli's equation is valid for incompressible flows (e.g. most liquid flows and gases moving at low Mach number). More advanced forms may be applied ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordinary Differential Equation
In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contrast with the term partial differential equation which may be with respect to ''more than'' one independent variable. Differential equations A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form :a_0(x)y +a_1(x)y' + a_2(x)y'' +\cdots +a_n(x)y^+b(x)=0, where , ..., and are arbitrary differentiable functions that do not need to be linear, and are the successive derivatives of the unknown function of the variable . Among ordinary differential equations, linear differential equations play a prominent role for several reasons. Most elementary and special functions that are encountered in physics and applied mathematics are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liquid
A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, and plasma), and is the only state with a definite volume but no fixed shape. A liquid is made up of tiny vibrating particles of matter, such as atoms, held together by intermolecular bonds. Like a gas, a liquid is able to flow and take the shape of a container. Most liquids resist compression, although others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly constant density. A distinctive property of the liquid state is surface tension, leading to wetting phenomena. Water is by far the most common liquid on Earth. The density of a liquid is usually close to that of a solid, and much higher than that of a gas. Therefore, liquid and solid are both termed condensed matte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Incompressible Flow
In fluid mechanics or more generally continuum mechanics, incompressible flow ( isochoric flow) refers to a flow in which the material density is constant within a fluid parcel—an infinitesimal volume that moves with the flow velocity. An equivalent statement that implies incompressibility is that the divergence of the flow velocity is zero (see the derivation below, which illustrates why these conditions are equivalent). Incompressible flow does not imply that the fluid itself is incompressible. It is shown in the derivation below that (under the right conditions) even compressible fluids can – to a good approximation – be modelled as an incompressible flow. Incompressible flow implies that the density remains constant within a parcel of fluid that moves with the flow velocity. Derivation The fundamental requirement for incompressible flow is that the density, \rho , is constant within a small element volume, ''dV'', which moves at the flow velocity u. Mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematically, density is defined as mass divided by volume: : \rho = \frac where ''ρ'' is the density, ''m'' is the mass, and ''V'' is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more specifically called specific weight. For a pure substance the density has the same numerical value as its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure. To simplify comparisons of density across different s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Energy Head
In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy. The principle is named after the Swiss mathematician and physicist Daniel Bernoulli, who published it in his book ''Hydrodynamica'' in 1738. Although Bernoulli deduced that pressure decreases when the flow speed increases, it was Leonhard Euler in 1752 who derived Bernoulli's equation in its usual form. The principle is only applicable for isentropic flows: when the effects of irreversible processes (like turbulence) and non-adiabatic processes (e.g. thermal radiation) are small and can be neglected. Bernoulli's principle can be applied to various types of fluid flow, resulting in various forms of Bernoulli's equation. The simple form of Bernoulli's equation is valid for incompressible flows (e.g. most liquid flows and gases moving at low Mach number). More advanced forms may be applied ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Total Pressure
In physics, the term total pressure may indicate two different quantities, both having the dimensions of a pressure: For compressible flow the Isentropic nozzle flow#Supersonic flow, isentropic relations can be used (also valid for incompressible flow): : p_t=p\left(1+\fracM^2\right)^{\frac{\kappa}{\kappa-1 At Standard_temperature_and_pressure, standard conditions the scientific community usually takes M<0.3 as the threshold to compressibility. Flows with a higher Mach number cannot approximate the total pressure using the incompressible formula given above. At non-standard conditions the flow may be considered compressible at lower Mach numbers. An example would be a flow through a long insulated pipe where wall friction is not neglected. Then the flow's temperature increases farther down the pipe and must be considered compressible after some length. The higher the pressure and temperature are, the less good the incompressible formula becomes. At standard ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton's Laws Of Motion
Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force. # When a body is acted upon by a force, the time rate of change of its momentum equals the force. # If two bodies exert forces on each other, these forces have the same magnitude but opposite directions. The three laws of motion were first stated by Isaac Newton in his '' Philosophiæ Naturalis Principia Mathematica'' (''Mathematical Principles of Natural Philosophy''), originally published in 1687. Newton used them to investigate and explain the motion of many physical objects and systems, which laid the foundation for classical mechanics. In the time since Newton, the conceptual content of classical physics has been reformulated in alternative ways, involving diff ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the greatest mathematicians and physicists and among the most influential scientists of all time. He was a key figure in the philosophical revolution known as the Enlightenment. His book (''Mathematical Principles of Natural Philosophy''), first published in 1687, established classical mechanics. Newton also made seminal contributions to optics, and shares credit with German mathematician Gottfried Wilhelm Leibniz for developing infinitesimal calculus. In the , Newton formulated the laws of motion and universal gravitation that formed the dominant scientific viewpoint for centuries until it was superseded by the theory of relativity. Newton used his mathematical description of gravity to derive Kepler's laws of planetary motion, account for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational Potential
In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that would be needed to move an object to that location from a fixed reference location. It is analogous to the electric potential with mass playing the role of charge. The reference location, where the potential is zero, is by convention infinitely far away from any mass, resulting in a negative potential at any finite distance. In mathematics, the gravitational potential is also known as the Newtonian potential and is fundamental in the study of potential theory. It may also be used for solving the electrostatic and magnetostatic fields generated by uniformly charged or polarized ellipsoidal bodies. Potential energy The gravitational potential (''V'') at a location is the gravitational potential energy (''U'') at that location per unit mass: V = \frac, where ''m'' is the mass of the object. Potential energy is equal (in magnitude, but negative) to the w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamic Pressure
In fluid dynamics, dynamic pressure (denoted by or and sometimes called velocity pressure) is the quantity defined by:Clancy, L.J., ''Aerodynamics'', Section 3.5 :q = \frac\rho\, u^2 where (in SI units): * is the dynamic pressure in pascals (i.e., kg/ m⋅ s2), * is the fluid mass density (e.g. in kg/m3), and * is the flow speed in m/s. It can be thought of as the fluid's kinetic energy per unit volume. For incompressible flow, the dynamic pressure of a fluid is the difference between its total pressure and static pressure. From Bernoulli's law, dynamic pressure is given by : p_0 - p_\text = \frac\rho\, u^2 where and are the total and static pressures, respectively. Physical meaning Dynamic pressure is the kinetic energy per unit volume of a fluid. Dynamic pressure is one of the terms of Bernoulli's equation, which can be derived from the conservation of energy for a fluid in motion. It can also appear as a term in the incompressible Navier-Stokes equation whic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internal Energy
The internal energy of a thermodynamic system is the total energy contained within it. It is the energy necessary to create or prepare the system in its given internal state, and includes the contributions of potential energy and internal kinetic energy. It keeps account of the gains and losses of energy of the system that are due to changes in its internal state. It does not include the kinetic energy of motion of the system as a whole, or any external energies from surrounding force fields. The internal energy of an isolated system is constant, which is expressed as the law of conservation of energy, a foundation of the first law of thermodynamics. The internal energy is an extensive property. The internal energy cannot be measured directly and knowledge of all its components is rarely interesting, such as the static rest mass energy of its constituent matter. Thermodynamics is chiefly concerned only with ''changes'' in the internal energy, not with its absolute value. Instea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kinetic Energy
In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body when decelerating from its current speed to a state of rest. Formally, a kinetic energy is any term in a system's Lagrangian which includes a derivative with respect to time. In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2. In relativistic mechanics, this is a good approximation only when ''v'' is much less than the speed of light. The standard unit of kinetic energy is the joule, while the English unit of kinetic energy is the foot-pound. History and etymology The adjective ''kinetic'' has its roots in the Greek word κίνησις ''kinesis'', m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
