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# Topic: Dimensionless number

###### In the News (Sun 18 Aug 19)

 Dimensionless number - Wikipedia, the free encyclopedia Such a number is typically defined as a product or ratio of quantities which have units of identical dimension, in such a way that the corresponding units can be converted to identical units and then cancel. Dimensionless numbers are widely used in the fields of mathematics, 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   (0 words)

 Reynolds number - Wikipedia, the free encyclopedia It is the most important dimensionless number in fluid dynamics and provides a criterion for determining dynamic similitude. Laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion, while turbulent flow, on the other hand, occurs at high Reynolds numbers and is dominated by inertial forces, producing random eddies, vortices and other flow fluctuations. In this sense, the Reynolds number is an indicator of the range of scales in the flow. en.wikipedia.org /wiki/Reynolds_number   (0 words)

 Dimensionless Numbers and Numbers with Dimension The numbers of trigonometry, the degrees of a circle and angles, reflect fixed proportions within the numbers themselves, within spacetime, within the proportion and boundaries (dimensions) of a the circle. The numbers relating to exponents of powers reflect specific relationships of the numbers themselves, which we have seen reflect even the behavior of the planets in their apparently circular orbits around the sun. In the square of this particular number, one might consider the exponent (2n) as being a dimensionless number in relation to a number with dimension (756feet). www.earthmatrix.com /extract83.html   (0 words)

 Dimensionless: Origins of Dimensionless Groups of Heat and Mass Transfer   (Site not responding. Last check: 2007-11-06) Mach's name is associated with the Mach Number, which expresses the speed of matter relative to the local speed of sound. 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   (0 words)

 Dimensionless numbers   (Site not responding. Last check: 2007-11-06) In equations for calculating head losses in pipes, diameter is the I.D. of the pipe, V is the fluid velocity, rho is the fluid density, and µ is the viscosity of the fluid. Reynolds number has been so valuable for dealing with flow in pipes that analogous numbers are desirable for other flow situations such as mixing in tanks and transfer from gas bubbles. The logical choices for a Reynolds number for a rising bubble are bubble diameter, relative velocity of the bubble versus the fluid, fluid density, and fluid viscosity. www.rpi.edu /dept/chem-eng/Biotech-Environ/AERATION/dimnum.htm   (0 words)

 Dimensionless number 1 - Wikipedia, the free encyclopedia   (Site not responding. Last check: 2007-11-06) Start the Dimensionless number 1 article or add a request for it. Look for Dimensionless number 1 in the Commons, our repository for free images, music, sound, and video. Check for Dimensionless number 1 in the deletion log, or visit its deletion vote page if it exists. www.sciencedaily.com /encyclopedia/dimensionless_number_1   (0 words)

 HYLE 6-2 (2000): Modeling in Chemical Engineering The latter are powers of dimensionless numbers, all of which depend on the Reynolds number in complex ways: equations with up to four terms, containing natural logarithms in various places, several occurrences of the Reynolds number, as well as dimensionless numbers characterizing the geometry of the system. A special problem for dimensional analysis are dimensionless magnitudes, in particular shape factors such as the ratio of the length and diameter of a pipe, the relative roughness of a surface, the particle shape factor, or the tortuosity of pores in a packed bed reactor. First, there are a number of background assumptions (models) that apply to all contexts where measurement takes place, in particular a measurement theory (consisting of axioms and operational definitions) for each of the relevant magnitudes, the choice of fundamental units, and the requirement that all equations containing magnitudes have to be dimensionally invariant. www.hyle.org /journal/issues/6/vanbrak.htm   (0 words)

 1) Knudsen number dimensionless number defined as the ratio of the molecular dimensionless number which measures the enhancement of heat transfer from a surface which occurs in a 'real' situation, compared to the heat transfer that would be measured if only conduction could occur. dimensionless number approximating the ratio of momentum diffusivity and www.ent.ohiou.edu /~hbwang/fluidynamics.htm   (0 words)

 Studies on Two-Phase Flows at Normal and Microgravity Conditions   (Site not responding. Last check: 2007-11-06) In space, the number of dimensionless groups required to characterize two-phase flows is reduced by two because of the absence of the magnitude of gravity and the angle of orientation with respect to gravity. It also reduces the number of dimensionless groups required to characterize two-phase flows by two, because of absence of the magnitude of gravity and the angle of orientation with respect to gravity. A number of tests were carried out during the last year to validate the proposed slug-annular flow pattern transition boundary for microgravity two phase flows with low Suratman numbers. www.isso.uh.edu /publications/A9798/bala.htm   (0 words)

 Dimensionless numbers The Reynolds number (Re) is a dimensionless number that gives a measure of the balance of forces, between inertial and viscous forces, that are acting on a fluid. The Reynolds number of a fluid is defined as: Rayleigh number (Ra) is a dimensionless number that is used to predict the likelihood of convection in a system. www.geology.um.maine.edu /geodynamics/analogwebsite/Projects2004/Hooks/Reynolds.htm   (0 words)

 Drag Force   (Site not responding. Last check: 2007-11-06) The Reynolds number has been found to be a useful dimensionless number that can characterize the drag coefficient's dependence upon the velocity. The Reynolds number is basically the ratio of the inertial force of the medium over its viscous force. For small values of the Reynolds number - called laminar flow since the flow is nonturbulant - the drag coefficient is inversely proportional to the velocity. www.ac.wwu.edu /~vawter/PhysicsNet/Topics/Dynamics/Forces/DragForce.html   (0 words)

 [No title] In this case, the number of molecules, N, the simulation cell volume, V, and the total energy, E, are all held constant. 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:8080 /~rowley/mmtf/WEB_units1.htm   (0 words)

 [No title] In this case, the number of molecules, the system volume, and the temperature are all fixed at specific values, but the energy fluctuates in time. 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 when computed with an MD simulation. If the values of dimensionless properties are generated at a given dimensionless state point, those values can then be used to calculate the actual property for any conformal fluid. www.et.byu.edu:8080 /~rowley/mmtf/WEB_units.htm   (0 words)

 Doppler measurement and dimensionless speed   (Site not responding. Last check: 2007-11-06) The formulas in relativity don't work unless the speed is represented by a plain dimensionless number (v/c, or beta)--almost as if nature is suggesting that we think of speed that way instead of in terms like "meters per second." Moreover, Doppler speed measurement has become an increasingly common part of life. The relativistic Doppler frequency-ratio formula (notice it is for a dimensionless ratio ƒ of frequencies, not for a difference expressed in terms of some unit) is ƒ=square root[(1+s)/(1-s)]. The speed has to be a pure unit-free number or else it wouldn't work: could not be added to one. www.planck.com /doppler1.htm   (0 words)

 [No title] The Schmidt number, often abbreviated Sc, is a dimensionless quantity with important applications to transport phenomena. According to Bird, Stewart, and Lightfoot, "The Schmidt number is the ratio of momentum diffusivity to mass diffusivity and represents the relative ease of molecular momentum and mass transfer. It is analogous to the Prandtl number, which represents the ratio of the momentum diffusivity to the thermal www.owlnet.rice.edu /~chbe402/proj02/jessica7/sccalc.html   (0 words)

 Dimensionless number Info - Encyclopedia WikiWhat.com Those n=5 variables are built up from k=3 dimensions which are: 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 There are literally thousands (to be precise: infinite) dimensionless numbers including those being used most often: (in alphabetical order, indicating their field of use) www.wikiwhat.com /encyclopedia/d/di/dimensionless_number_1.html   (0 words)

 [No title] In this appendix it is shown how the material balance equation may be reduced into a dimensionless form. A full treatment leads to the result that the dimensionless current may be expressed as a sole function of two mass transport parameters, a dimensionless time parameter and a number of dimensionless rate constants. The Nusselt number is a constant (from the integral) multiplied by P physchem.ox.ac.uk /~rgc/john/Thesis/A1/a1.html   (0 words)

 Symbols and Abbreviations mass, meters* (length), slope of a linear graph, magnetic moment (current x area), magnetic quantum number (dimensionless, denotes orientation of angular momentum) numbers of mols (dimensionless), number of loops (dimensionless), neutron, principle quantum number (dimensionless, denotes energy level), index of refraction (dimensionless) Avogadro's number (dimensionless number of objects in a mol = 6.022 x 10 www.rwc.uc.edu /koehler/biophys/symb.html   (0 words)

 debris flow dimensionless numbers N = number of grains above grain surface like the Bingham number, but characterizes stresses borne by distinct solid and fluid phases. shear strain rate, density solids, characteristic diameter, number of grains above slip surface, density solid, density fluid, gravitational acceleration, angle of internal friction www.seismo.berkeley.edu /~lhsu/dim_num.html   (0 words)

 [No title] Notice that in certain cases (like flat plates) one can define a local dimensionless number by using x, the distance down the object in the direction of the flow. Finding the local Nusselt number would allow one to then solve for hx, the “local” heat transfer coefficient. We’re generally not interested in knowing what the heat transfer coefficient at one particular point on the surface is, though—we want the average h (which is the one we’re familiar with from all the heat transfer work we have done), and this is precisely the one we get from NuL. lyre.mit.edu /3.185/2002/handout-nusselt.doc   (0 words)

 Power number : Power-Number (also known as Newton number) is a dimensionless number relating the resistance force[?] to the inertia force. In engineering, this number, along with the Reynolds number, is one of the most widely employed dimensionless numbers. E.g., for stirrers[?] the power number is defined as: www.fastload.org /po/Power-Number.html   (0 words)

 [No title] List units, determine number of relations needed¡4 24ð`² ðx c ð\$A Ú?¿ÿ?ð0 k ð Á Úð`² ðx c ð\$A ò?¿ÿ?ðò@  ð Á òð`² ðx c ð\$A 1?¿ÿ?ðÇ ª¯à ð Á 1ð`² ð x c ð\$A ?¿ÿ?ð0 k ð Á ðH ðx  ð0“”Þ½h¿ÿ ?ð ÿÿÿÌ33ÌÌÌÿ²²²î*ï ÚðÒpð ðjð( ð ðð ð ³ ðBt Î¿¿ÀÿðÀ n¬ ð—¨d5. Express the constituitive relations in terms of the smallest group of dimensionless variables¡aaªEð`² ð c ð\$A A?¿ÿ?ðËÐI pð Á AðÎ ð “ ð6HvÎ¿¿Àÿð À ì  ðh¨68. Express the constituitive relation in terms of dimensionless variablesª.ðm ð4 ³ ðBøá¿¿Àÿð* Ø ðû¨qaDp-a/2ra/2Ao-agc-a/2 = ¡ 2 çÿª\$ ð`² ð4 c ð\$A )?¿ÿ?ðd w pð Á )ð ¢ ð4 £ ð www.nd.edu /~aostafin/CHEG255/lecture/Lecture5.ppt   (0 words)

 LjSEEK.com: LiveJournal Blogs Search Engine   (Site not responding. Last check: 2007-11-06) About 3 months have passed since our last news update. We've implemented number of new features in this time and started few new projects. Huh, we're late with update this month, also instead of description of new nice features we've implemented you've got downtime warning in the start of October. www.answers-zone.com /article/Dimensionless_number   (0 words)

 [No title]   (Site not responding. Last check: 2007-11-06) ARDP(PM) A 336 ANOMALIES RELATIVE TO DOMINANT PARADIGM (DIMENSIONLESS) NODP A 520 NUMBER OF DOMINANT PARADIGMS (DIMENSIONLESS) NOSNDP A 328 NUMBER OF STRONGEST NON-DOMINANT PARADIGMS (DIMENSIONLESS) web.mit.edu /jsterman/www/SDG/files/SCIREV.DOC   (0 words)

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