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Strouhal Number
In dimensional analysis, the Strouhal number (St, or sometimes Sr to avoid the conflict with the Stanton number) is a dimensionless number describing oscillating flow mechanisms. The parameter is named after Vincenc Strouhal, a Czech physicist who experimented in 1878 with wires experiencing vortex shedding and singing in the wind. The Strouhal number is an integral part of the fundamentals of fluid mechanics. The Strouhal number is often given as \text = \frac, where ''f'' is the frequency of vortex shedding, ''L'' is the characteristic length (for example, hydraulic diameter or the airfoil thickness) and ''U'' is the flow velocity. In certain cases, like heaving (plunging) flight, this characteristic length is the amplitude of oscillation. This selection of characteristic length can be used to present a distinction between Strouhal number and reduced frequency: \text = \frac, where ''k'' is the reduced frequency, and ''A'' is amplitude of the heaving oscillation. Fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimensional Analysis
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measure (such as miles vs. kilometres, or pounds vs. kilograms) and tracking these dimensions as calculations or comparisons are performed. The conversion of units from one dimensional unit to another is often easier within the metric or the SI than in others, due to the regular 10-base in all units. ''Commensurable'' physical quantities are of the same kind and have the same dimension, and can be directly compared to each other, even if they are expressed in differing units of measure, e.g. yards and metres, pounds (mass) and kilograms, seconds and years. ''Incommensurable'' physical quantities are of different kinds and have different dimensions, and can not be directly compared to each other, no matter what units they are expressed in, e.g. metres and ... [...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] |
Richardson Number
The Richardson number (Ri) is named after Lewis Fry Richardson (1881–1953). It is the dimensionless number that expresses the ratio of the buoyancy term to the flow shear term: : \mathrm = \frac = \frac \frac where g is gravity, \rho is density, u is a representative flow speed, and z is depth. The Richardson number, or one of several variants, is of practical importance in weather forecasting and in investigating density and turbidity currents in oceans, lakes, and reservoirs. When considering flows in which density differences are small (the Boussinesq approximation), it is common to use the reduced gravity ''g' '' and the relevant parameter is the densimetric Richardson number : \mathrm = \frac which is used frequently when considering atmospheric or oceanic flows. If the Richardson number is much less than unity, buoyancy is unimportant in the flow. If it is much greater than unity, buoyancy is dominant (in the sense that there is insufficient kinetic energy to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scale Analysis (mathematics)
Scale analysis (or order-of-magnitude analysis) is a powerful tool used in the mathematical sciences for the simplification of equations with many terms. First the approximate magnitude of individual terms in the equations is determined. Then some negligibly small terms may be ignored. Example: vertical momentum in synoptic-scale meteorology Consider for example the momentum equation of the Navier–Stokes equations in the vertical coordinate direction of the atmosphere where ''R'' is Earth radius, Ω is frequency of rotation of the Earth, ''g'' is gravitational acceleration, φ is latitude, ρ is density of air and ν is kinematic viscosity of air (we can neglect turbulence in free atmosphere). In synoptic scale we can expect horizontal velocities about ''U'' = 101 m.s−1 and vertical about ''W'' = 10−2 m.s−1. Horizontal scale is ''L'' = 106 m and vertical scale is ''H'' = 104 m. Typical time scale is ''T'' = ''L''/''U'' = 105 s. Pressure diffe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roshko Number
In fluid mechanics, the Roshko number (Ro) is a dimensionless number describing oscillating flow mechanisms. It is named after the American Professor of Aeronautics Anatol Roshko. It is defined as : \mathrm = =\mathrm\,\mathrm : \mathrm= , : \mathrm = where * St is the dimensionless Strouhal number; * Re is the Reynolds number; * U is mean stream velocity; * ''f'' is the frequency of vortex shedding; * ''L'' is the characteristic length (for example hydraulic diameter); * ''ν'' is the kinematic viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the int ... of the fluid. Correlations Roshko determined the correlation below from experiments on the flow of air around circular cylinders over range Re=50 to Re=2000: : \mathrm = 0.212 \mathrm - 4.5 valid over [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flow Meter
Flow measurement is the quantification of bulk fluid movement. Flow can be measured in a variety of ways. The common types of flowmeters with industrial applications are listed below: * a) Obstruction type (differential pressure or variable area) * b) Inferential (turbine type) * c) Electromagnetic * d) Positive-displacement flowmeters, which accumulate a fixed volume of fluid and then count the number of times the volume is filled to measure flow. * e) Fluid dynamic (vortex shedding) * f) Anemometer * g) Ultrasonic * h) Mass flowmeter (Coriolis force). Flow measurement methods other than positive-displacement flowmeters rely on forces produced by the flowing stream as it overcomes a known constriction, to indirectly calculate flow. Flow may be measured by measuring the velocity of fluid over a known area. For very large flows, tracer methods may be used to deduce the flow rate from the change in concentration of a dye or radioisotope. Kinds and units of measurement Both gas a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metrology
Metrology is the scientific study of measurement. It establishes a common understanding of units, crucial in linking human activities. Modern metrology has its roots in the French Revolution's political motivation to standardise units in France when a length standard taken from a natural source was proposed. This led to the creation of the decimal-based metric system in 1795, establishing a set of standards for other types of measurements. Several other countries adopted the metric system between 1795 and 1875; to ensure conformity between the countries, the Bureau International des Poids et Mesures (BIPM) was established by the Metre Convention. This has evolved into the International System of Units (SI) as a result of a resolution at the 11th General Conference on Weights and Measures (CGPM) in 1960. Metrology is divided into three basic overlapping activities: * The definition of units of measurement * The realisation of these units of measurement in practice * Traceabi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Womersley Number
The Womersley number (\alpha or \text) is a dimensionless number in biofluid mechanics and biofluid dynamics. It is a dimensionless expression of the pulsatile flow frequency in relation to viscous effects. It is named after John R. Womersley (1907–1958) for his work with blood flow in arteries. The Womersley number is important in keeping dynamic similarity when scaling an experiment. An example of this is scaling up the vascular system for experimental study. The Womersley number is also important in determining the thickness of the boundary layer to see if entrance effects can be ignored. This square root of this number is also referred to as Stokes number, \text=\sqrt, due to the pioneering work done by Sir George Stokes on the Stokes second problem. Derivation The Womersley number, usually denoted \alpha, is defined by the relation \alpha^2 = \frac = \frac = \frac = \frac \, , where L is an appropriate length scale (for example the radius of a pipe), \omega is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weissenberg Number
The Weissenberg number (Wi) is a dimensionless number used in the study of viscoelastic flows. It is named after Karl Weissenberg. The dimensionless number compares the elastic forces to the viscous forces. It can be variously defined, but it is usually given by the relation of stress relaxation time of the fluid and a specific process time. For instance, in simple steady shear, the Weissenberg number, often abbreviated as Wi or We, is defined as the shear rate \dot times the relaxation time \lambda. Using the Maxwell model and the Oldroyd-B model, the elastic forces can be written as the first Normal force (N1). :\text = \dfrac = \frac = \frac= 2 \dot \lambda.\, Since this number is obtained from scaling the evolution of the stress, it contains choices for the shear or elongation rate, and the length-scale. Therefore the exact definition of all non dimensional numbers should be given as well as the number itself. While Wi is similar to the Deborah number The Deborah number ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deborah Number
The Deborah number (De) is a dimensionless number, often used in rheology to characterize the fluidity of materials under specific flow conditions. It quantifies the observation that given enough time even a solid-like material might flow, or a fluid-like material can act solid when it is deformed rapidly enough. Materials that have low relaxation times flow easily and as such show relatively rapid stress decay. Definition The Deborah number is the ratio of fundamentally different characteristic times. The Deborah number is defined as the ratio of the time it takes for a material to adjust to applied stresses or deformations, and the characteristic time scale of an experiment (or a computer simulation) probing the response of the material: : \mathrm = \frac, where stands for the relaxation time and for the "time of observation", typically taken to be the time scale of the process. The numerator, relaxation time, is the time needed for a reference amount of deformation to occur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The MIT Press
The MIT Press is a university press affiliated with the Massachusetts Institute of Technology (MIT) in Cambridge, Massachusetts (United States). It was established in 1962. History The MIT Press traces its origins back to 1926 when MIT published under its own name a lecture series entitled ''Problems of Atomic Dynamics'' given by the visiting German physicist and later Nobel Prize winner, Max Born. Six years later, MIT's publishing operations were first formally instituted by the creation of an imprint called Technology Press in 1932. This imprint was founded by James R. Killian, Jr., at the time editor of MIT's alumni magazine and later to become MIT president. Technology Press published eight titles independently, then in 1937 entered into an arrangement with John Wiley & Sons in which Wiley took over marketing and editorial responsibilities. In 1962 the association with Wiley came to an end after a further 125 titles had been published. The press acquired its modern name afte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hooke's Law
In physics, Hooke's law is an empirical law which states that the force () needed to extend or compress a spring (device), spring by some distance () Proportionality (mathematics)#Direct_proportionality, scales linearly with respect to that distance—that is, where is a constant factor characteristic of the spring (i.e., its stiffness), and is small compared to the total possible deformation of the spring. The law is named after 17th-century British physicist Robert Hooke. He first stated the law in 1676 as a Latin anagram. He published the solution of his anagram in 1678 as: ("as the extension, so the force" or "the extension is proportional to the force"). Hooke states in the 1678 work that he was aware of the law since 1660. Hooke's equation holds (to some extent) in many other situations where an elasticity (physics), elastic body is Deformation (physics), deformed, such as wind blowing on a tall building, and a musician plucking a string (music), string of a guitar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
