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# Topic: Dimensionless

###### In the News (Mon 27 May 19)

 Equations and dimensionless variables Dimensionless variables (shown with tildas below) are defined by introducing the length of a cell of the grid x Equations (2-5) can be rewritten in terms of dimensionless variables: of the critical density, then the transformations from dimensionless variables given by the code to dimensional variables are given by astro.nmsu.edu /~aklypin/PM/pmcode/node2.html   (232 words)

 Dimensionless quantity - Wikipedia, the free encyclopedia A dimensionless quantity (or more precisely, a quantity of dimension 1) is a physical quantity consisting of only a numerical number without any physical units. Dimensionless quantities are widely used in the fields of physics and engineering but also in everyday life. The power consumption of a stirrer with a particular geometry is a function of the density and the viscosity of the fluid to be stirred, the size of the stirrer given by its diameter, and the speed of the stirrer. en.wikipedia.org /wiki/Dimensionless_number   (770 words)

 Mirror for Internet Encyclopedia - Wikinfo | Dimensionless number   (Site not responding. Last check: 2007-11-02) A dimensionless number is a quantity which describes a certain physical system and which is a pure number without any physical units. Dimensionless numbers are widely applied in the Field of Mechanical and Chemical engineering. According to the π-theorem, the n=5 variables can be reduced by the k=3 dimensions to form p=n-k=5-3=2 independent dimensionless numbers which are in case of the stirrer www.internet-encyclopedia.us /index.php/wiki.php?title=Dimensionless_number   (556 words)

 Dimensionless Numbers and Numbers with Dimension   (Site not responding. Last check: 2007-11-02) While dimensionless numbers refer to those of trigonometry, the number of degrees in a circle, the numbers relating to exponents of powers; that sort of thing. The dimensionless number 3n is a four dimensional number (2 x 2 = 4 x 2) that produces a fifth dimension (16). The dimensionless number 4n is a sixth dimensional number (2 x 2 = 4 x 2 = 8 x 2) that produces a seventh dimension (16). www.earthmatrix.com /extract83.html   (2400 words)

 Math Forum - Ask Dr. Math   (Site not responding. Last check: 2007-11-02) A radian is the ratio of an arc length to a radius, and the ratio of two lengths is dimensionless. An angle of one radian (1 rad) causes the ratio of the length of the arc of the circle's circumference to the radius of the circle to be one. Introduction to the Aerodynamics of Flight http://history.nasa.gov/SP-367/appendb.htm The measure of the central angle of a circle is defined as the ratio of the subtended arc of the circle divided by the radius, that is, a ratio of two lengths. mathforum.org /library/drmath/view/64034.html   (1273 words)

 Dimensional analysis - Wikipedia, the free encyclopedia This is essentially due to the requirement for the Taylor expansion of these functions to be dimensionally homogeneous, which means that the square of the argument must be of the same dimension as the argument itself. For scalar arguments, this means the argument must be dimensionless, but certain dimensioned tensors are dimensionally self-square (Hart, 1995) and may be used as arguments to these functions. Then when adding two quantities of like dimension, but expressed in different units, the appropriate conversion factor, which is essentially the dimensionless 1, is used to convert the quantities to identical units so that their numerical values can be added or subtracted. en.wikipedia.org /wiki/Dimensional_analysis   (3227 words)

 Dimensionless number 1 - Wikipedia, the free encyclopedia   (Site not responding. Last check: 2007-11-02) Start the Dimensionless number 1 article or add a request for it. Look for "Dimensionless number 1" in the Wikimedia Commons, our repository for free images, music, sound, and video. Promotional articles about yourself, your friends, your company or products; or articles written as part of a marketing or promotional campaign, may be deleted in accordance with our deletion policies. www.sciencedaily.com /encyclopedia/dimensionless_number_1   (188 words)

 BIPM - dimensionless quantities The coherent SI unit of all such dimensionless quantities, or quantities of dimension one, is the number one, since the unit must be the ratio of two identical SI units. Another class of dimensionless quantities are numbers that represent a count, such as a number of molecules, degeneracy (number of energy levels), and partition function in statistical thermodynamics (number of thermally accessible states). All of these counting quantities are also described as being dimensionless, or of dimension one, and are taken to have the SI unit one, although the unit of counting quantities cannot be described as a derived unit expressed in terms of the base units of the SI. www.bipm.fr /en/si/si_brochure/chapter2/2-2/2-2-3.html   (382 words)

 Re: Permittivity and Permeability Constants of Vacuum Normally, yes it would be dimensionless, because area is determined from length through a *mathematical* procedure. If you say it is *physically* dimensionless, you are implying that you do not wish to doubt Newtonian mechanics, which may be a practical thing to do. Here too, saying it is *physically* dimensionless, you are implying that you do not wish to doubt Maxwell mechanics, which may be a practical thing to do if you are for example an engineer. www.lns.cornell.edu /spr/2000-01/msg0020636.html   (517 words)

 Dimensionless quantity   (Site not responding. Last check: 2007-11-02) A dimensionless number is a quantity which describes a certain physical system and which is a pure numberwithout any physical units. For the purposes of the experimenter, different systemswhich share the same description by dimensionless numbers are equivalent. According to the π-theorem, the n=5 variables can be reduced by the k=3dimensions to form p=n-k=5-3=2 independent dimensionless numbers which are in case of the stirrer www.therfcc.org /dimensionless-quantity-107761.html   (475 words)

 Dimensionless Numbers in Heat Transfer   (Site not responding. Last check: 2007-11-02) We have invented dimensionless numbers to be able to take our knowledge from experimenting with one system to learning about another system with different dimensions. Dimensionless numbers allow us to experiment with model cars, airplanes and ships and predict the behavior of the big thing under actual conditions. Heat transfer gurus have invented another dimensionless number called the Prandtl number which is a grouping of the properties of the fluid but it has a significance to our discussion. www.coolingzone.com /Content/Library/Tutorials/Tutorial%201/DNHT.html   (2128 words)

 Dimensionless number   (Site not responding. Last check: 2007-11-02) Such a number is typically defined as aproduct or ratio of quantities which do have units, in such a way that all units cancel. The power -consumption of a stirrer with a particular geometry is a function ofthe density and the viscosity of thefluid to be stirred, the size of the stirrer given by its diameter, and the speed of the stirrer. The system of natural units chooses its base units in such a way as tomake several physical constants such as the speed of light intosimple dimensionless constants by definition. www.therfcc.org /dimensionless-number-57285.html   (475 words)

 Definition of Dimensionless number However, it is sometimes helpful to use the same units in both the numerator and denominator, such as kg/kg, to show the quantity being measured. A dimensionless number has the same value regardless of the measurement units used to calculate it. However, a number may be dimensionless in one system of units (e.g., in a nonrationalized cgs system of units with the electric constant ε www.wordiq.com /definition/Dimensionless_number   (650 words)

 85-4 Dimensionless correlations for forced convection heat transfer to spherical particles under tube-flow conditions   (Site not responding. Last check: 2007-11-02) The objective of this research was to develop dimensionless correlations for relating heat transfer coefficients for spherical particles under forced convection tube-flow conditions. Dimensionless correlations were developed to relate values of hfp under tube-flow conditions. Dimensionless correlations, like the ones developed in these studies, are useful in generalizing the influence of process variables and scale-up conditions. ift.confex.com /ift/2000/techprogram/paper_4357.htm   (388 words)

 The BASELINE Project FAQ List: User Validation Methods and Tools A dimensionless metric is one whose scale is independent of the object being measured to such an extent that two or more objects can be compared meaningfully on the same metric. Another dimensionless metric is the average of a set of responses by a user to a set of standardised questions about the usability of a system. Dimensionless metrics are important because they enable us to make increasingly general statements about the usability of computer systems. www.ucc.ie /research/hfrg/baseline/methods_tools.html   (1762 words)

 Dimensionless number   (Site not responding. Last check: 2007-11-02) A dimensionless number is a quantity which describes a certain physical system and which is a pure number without any physical unit s. The power -consumption of a stirrer with a particular geometry is a function of the density and the viscosity of the fluid to be stirred, the size of the stirrer given by its diameter, and the speed of the stirrer. Mass M [kg] According to the π-theorem, the n=5 variables can be reduced by the k=3 dimensions to form p=n-k=5-3=2 independent dimensionless numbers which are in case of the stirrer www.serebella.com /encyclopedia/article-Dimensionless_number.html   (1522 words)

 Dimensionless number   (Site not responding. Last check: 2007-11-02) A dimensionless number is a quantity which describes a physical system and which is a pure without any physical units. Dimensionless numbers are widely applied in the of mechanical and chemical engineering. For the purposes the experimenter different systems which share the description by dimensionless numbers are equivalent. www.freeglossary.com /Dimensionless_parameter   (703 words)

 Design Hydrographs The SCS dimensionless hydrograph is an idealized shape that approximates the flow from an intense storm from a small watershed. The second factor is w and is the ratio of the peak runoff for the design storm to the peak flow of 100 on the dimensionless hydrograph. The coordinates of the design hydrograph are obtained by multiplying the ordinates and abscissas of the dimensionless hydrograph by w and k respectively. www.egr.msu.edu /~northco2/BE481/SCShydrograph.htm   (757 words)

 Dimensionless: Origins of Dimensionless Groups of Heat and Mass Transfer PREPARED BY French mathematician and physicist famous for his pioneer work on the representation of functions by trigonometric series, was born at Auxere on March 21, 1768, the son of a tailor. He was the first to measure the velocity and temperature field in a free convection boundary layer and the large heat transfer coefficients occuring in droplet condensaton. Although not known formally, perhaps, as a dimensionless parameter, the empirical Colburn J-Factor is indeed an operational one. www.ichmt.org /dimensionless/dimensionless.html   (3178 words)

 Dimensional Analysis in Operations Research The physical parameters of the pendulum problem, in addition to the period of oscillation, t [T], are the mass of the pendulum bob, m [M], the length of the string, L [L], the acceleration of gravity, g [LT ] and (perhaps) the maximum angle of oscillation measured in radians, A. Silver [12] uses some dimensionless numbers to plot indifference curves in a continuous review stochastic (s, S) system and Ewing [6] proposed the use of dimensionless expressions rather than the original measurements in analysing data in the social sciences. Probability is dimensionless in nature but random variables usually have a dimension of their own, depending on the particular model. www.mcs.vuw.ac.nz /~vignaux/docs/diminor.html   (3179 words)

 [No title] Chemical engineers become accustomed to dealing with dimensionless groups such as the Reynold's number, the Prandtl number, the Grasshof number, etc. These dimensionless groups arise when the differential equations describing the process are recast in terms of dimensionless variables. This means that the solution of Newton's equation of motion yields identical dimensionless velocities and trajectories for all LJ fluids; i.e., the trajectory of the system through dimensionless phase space is identical for all conformal fluids at the same dimensionless state point. Thus, the results of the simulation are not just dependent upon the dimensionless state of the system, but also upon the nature of the second component; i.e., upon the ratio of the model energy and size parameters. www.et.byu.edu /~rowley/mmtf/WEB_units1.htm   (2607 words)

 Materials Algorithms Project To obtain the variation of dimensionless supersaturation with Pclet number and the ratio of the needle tip radius and the critical radius for nucleation. To obtain the variation of small values of dimensionless supersaturation with Pclet number and the ratio of the plate tip radius and the critical radius for nucleation. To obtain the variation of dimensionless supersaturation with Pclet number and the ratio of the plate tip radius and the critical radius for nucleation. www.msm.cam.ac.uk /map/kinetics/kineticprog.html   (639 words)

 Dimensionless Units There are also a lot of dimensionless things that are used as units, but (as far as I know) don’t have a named unit to go with them. If you take the SI definitions literally, a mole is not dimensionless, but has dimensions of its own, namely “amount of substance”. Just as it is often fruitful to re-interpret luminous intensity in terms of simpler SI dimensions of time, length, and mass, so it is often fruitful to re-interpret the mole as a dimensionless unit, just like a "dozen", except larger. www.av8n.com /physics/dimensionless-units.htm   (797 words)

 Dimensionless numbers   (Site not responding. Last check: 2007-11-02) Dimensionless numbers often correlate with some performance parameter and greatly aid engineering analysis and design. The same properties used in pipes will give a dimensionless number in another system if the units are consistent. In the quest for something to use for V, the revolutions per second of the impeller is chosen even though it not a velocity. www.rpi.edu /dept/chem-eng/Biotech-Environ/AERATION/dimnum.htm   (491 words)

 he Asian Tsunami in Sri Lanka: A Personal Experience: Discussion   (Site not responding. Last check: 2007-11-02) , where d is the water depth, g is the gravitational acceleration, and ω is the angular frequency, and a dimensionless wave number, K = kd, where k is the wave number, and the dispersion relationship for gravity water waves is The dispersion curves for this function are shown in Figures 1 and 2. The phase and group velocities for gravity water waves, derived from the dispersion curve in Figure 1.  The dashed lines show the long-wavelength approximations. www.agu.org /eos_elec/000929e1.html   (494 words)

 WARSSS PLA Phase ¦ EPA These reference curves are needed in order to establish sediment rating curves for the calculation of flow-related sediment increases and to establish an annual sediment yield estimate for proportioning various contributing sediment sources. Examples of dimensionless suspended and bedload rating curves are shown in Figures 56 and 57 and discussed in the Dimensionless SRCs reference section. Dimensionless suspended sediment rating curves for "Good/Fair" streams/stability- Pagosa Springs, Colorado. www.epa.gov /warsss/pla/box13.htm   (131 words)

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