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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 in Hertz, ''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 oscilla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton's Laws Of Motion
Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: # A body remains at rest, or in motion at a constant speed in a straight line, unless it is acted upon by a force. # At any instant of time, the net force on a body is equal to the body's acceleration multiplied by its mass or, equivalently, the rate at which the body's momentum is changing with time. # 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. In the time since Newton, new insights, especially around t ... [...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 velocity, flow shear (fluid), shear term: : \mathrm = \frac = \frac \frac where g is gravitational acceleration, 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 (buoyancy), Boussinesq approximation), it is common to use the Boussinesq approximation (buoyancy)#Advantages, 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 ... [...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 Primitive equations, 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 viscosity, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Propulsive Efficiency
In aerospace engineering, concerning aircraft, rocket and spacecraft design, overall propulsion system efficiency \eta is the efficiency with which the energy contained in a vehicle's fuel is converted into kinetic energy of the vehicle, to accelerate it, or to replace losses due to aerodynamic drag or gravity. Mathematically, it is represented as \eta = \eta_\mathrm \eta_\mathrm, where \eta_\mathrm is the cycle efficiency and \eta_\mathrm is the propulsive efficiency. The cycle efficiency is expressed as the percentage of the heat energy in the fuel that is converted to mechanical energy in the engine, and the propulsive efficiency is expressed as the proportion of the mechanical energy actually used to propel the aircraft. The propulsive efficiency is always less than one, because conservation of momentum requires that the exhaust have some of the kinetic energy, and the propulsive mechanism (whether propeller, jet exhaust, or ducted fan) is never perfectly efficient. It is great ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Frequency
Natural frequency, measured in terms of '' eigenfrequency'', is the rate at which an oscillatory system tends to oscillate in the absence of disturbance. A foundational example pertains to simple harmonic oscillators, such as an idealized spring with no energy loss wherein the system exhibits constant-amplitude oscillations with a constant frequency. The phenomenon of resonance occurs when a forced vibration matches a system's natural frequency. Overview Free vibrations of an elastic body, also called ''natural vibrations'', occur at the natural frequency. Natural vibrations are different from forced vibrations which happen at the frequency of an applied force (forced frequency). If the forced frequency is equal to the natural frequency, the vibrations' amplitude increases manyfold. This phenomenon is known as resonance where the system's response to the applied frequency is amplified.. A system's ''normal mode'' is defined by the oscillation of a natural frequency in a sine ... [...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 Canadian 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 Viscosity is a measure of a fluid's rate-dependent drag (physics), resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for e ... 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 using devices called flowmeters in various ways. The common types of flowmeters with industrial applications are listed below: * Obstruction type (differential pressure or variable area) * Inferential (turbine type) * Electromagnetic * Positive-displacement flowmeters, which accumulate a fixed volume of fluid and then count the number of times the volume is filled to measure flow. * Fluid dynamic (vortex shedding) * Anemometer * Ultrasonic flow meter * Mass flow meter (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 measur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metrology
Metrology is the scientific study of measurement. It establishes a common understanding of Unit of measurement, 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 ''International Bureau of Weights and Measures, 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 * ... [...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. The square of this number is also referred to as the Stokes number, \text=^2, 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 ang ... [...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 o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
