Search results
Results from the WOW.Com Content Network
Chemical engineering, material science, mechanics (A scale to show the energy needed for detaching two solid particles) [13] [14] Cost of transport: COT = energy efficiency, economics (ratio of energy input to kinetic motion) Damping ratio
For example, if x is a quantity, then x c is the characteristic unit used to scale it. As an illustrative example, consider a first order differential equation with constant coefficients: + = (). In this equation the independent variable here is t, and the dependent variable is x.
Scale analysis rules as follows: Rule1-First step in scale analysis is to define the domain of extent in which we apply scale analysis. Any scale analysis of a flow region that is not uniquely defined is not valid. Rule2-One equation constitutes an equivalence between the scales of two dominant terms appearing in the equation. For example,
This technique can ease the analysis of the problem at hand, and reduce the number of free parameters. Small or large sizes of certain dimensionless parameters indicate the importance of certain terms in the equations for the studied flow. This may provide possibilities to neglect terms in (certain areas of) the considered flow.
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
[19] [20] Examples of quotients of dimension one include calculating slopes or some unit conversion factors. Another set of examples is mass fractions or mole fractions, often written using parts-per notation such as ppm (= 10 −6), ppb (= 10 −9), and ppt (= 10 −12), or perhaps confusingly as ratios of two identical units (kg/kg or mol/mol).
The scale of analysis encompasses both the analytical choice of how to observe a given system or object of study, and the role of the observer in determining the identity of the system. [ 2 ] [ 3 ] This analytical tool is central to multi-scale analysis (see for example, MuSIASEM , land-use analysis).
steepest rate of temperature change at a particular location K/m L −1 Θ: vector Torque: τ: Product of a force and the perpendicular distance of the force from the point about which it is exerted newton-metre (N⋅m) L 2 M T −2: bivector (or pseudovector in 3D) Velocity: v →: Moved distance per unit time: the first time derivative of ...