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Topic: Dimensionless quantity

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	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)

	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.
		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.
		Mass as a measure of quantity is to be considered dimensionally distinct from mass as a measure of inertia.
	en.wikipedia.org /wiki/Dimensional_analysis (3227 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-31)
		Other angle measurements, such as degrees, are also dimensionless, though they are defined by different ratios, such as the ratio of the arc length to 1/360 of a circle, which results in the need for a multiplier.
		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)

	Quantities and Numbers
		A unit-declaration declares the derived quantity unit-name to be equivalent to this quantity.
		A quantity may be written in binary, octal, decimal, or hexadecimal by the use of a radix prefix.
		If min or max is used to compare quantities of mixed exactness, and the numerical value of the result cannot be represented as an inexact quantity without loss of accuracy, then the procedure may report a violation of an implementation restriction.
	www.jclark.com /dsssl/IS/dsssl49.htm (2479 words)

	BIPM - dimensionless quantities
		As discussed in Section 2.2.3, the coherent SI unit for dimensionless quantities, also termed quantities of dimension one, is the number one, symbol 1.
		For the quantity plane angle, the unit one is given the special name radian, symbol rad, and for the quantity solid angle, the unit one is given the special name steradian, symbol sr.
		For the logarithmic ratio quantities, the special names neper, symbol Np, bel, symbol B, and decibel, symbol dB, are used (see 4.1 and Table 8).
	www.bipm.fr /en/si/si_brochure/chapter5/5-3-7.html (515 words)

	Dimensionlessl Analysis...Measuroo.com
		Such a number is typically defined as a product or ratio of quantities which do have units, in such a way that all units cancel.
		Dimensionless numbers are widely applied in the field of mechanical and chemical engineering.
		However, a number may be dimensionless in one system of units (e.g., in a nonrationalized cgs system of units with the electric constant e0 = 1), and not dimensionless in another system of units (e.g., the rationalized SI system, with e0 = 8.85419×10
	www.measuroo.com /dimensionsnumber.html (516 words)

	Fluid Mechanics/Ch4 - Wikibooks, collection of open-content textbooks
		Dimensionless analysis is just as it sounds, the analysis of fundamental units of dimensions: mass, length, and time; usually abbreviated as MLT for short.
		Dimensionless analysis is commonly used to determine the relationships between several variables, i.e.
		Which is a dimensionless quantity, and a function of only 2 variables instead of 5.
	en.wikibooks.org /wiki/Fluid_Mechanics/Ch4 (1154 words)

	Hadley Centre: GDT netCDF conventions (Site not responding. Last check: 2007-10-31)
		This attribute is mandatory unless the quantity is dimensionless (a pure number), in which case the units may be given as a pure number.
		Each quantity in Appendix D will be labelled with the version of the appendices at which it was introduced, enabling an application to deduce the complete set of quantities which was available to the application which generated the file.
		Whether two physical quantities are different or the same is often not a question with a well-defined answer.
	www.met-office.gov.uk /research/hadleycentre/models/GDT/ch12.html (886 words)

	Dimensionless number : Dimensionless (Site not responding. Last check: 2007-10-31)
		A dimensionless number is a quantity which describes a certain physical system and which is a pure number without any physical units.
		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.explainthis.info /di/dimensionless.html (483 words)

	[No title] (Site not responding. Last check: 2007-10-31)
		The mindset to enter such equations is to make all quantities that must be expressed in particular units into dimensionless quantities which have the correct numerical value.
		Convert the quantity within the ln() term into a dimensionless number that has the value of pressure when pressure is expressed in {atm}.
		where the pressure drop on the LHS is in psi, y is the fraction vapor by weight (i.e., dimensionless), Vg and Vl are the specific volumes of gas and liquid respectively in ft3/lbm, G is the mass velocity in lbm/hr/ft2 and g is the acceleration by gravity and equal to 4.18x108 ft/hr2.
	pye.dyndns.org /ascend/manual/howto-dimeqns.html (1270 words)

	ME5247 - scaling
		An underlying concept for model and experiment scaling is to compare the values of pure numbers or unit-less or dimensionless quantities for the model-size and full size objects or processes.
		Similarity parameter - the dimensionless quantity selected to describe the correspondence between the behaviors of model-size and fill-size objects.
		Defining n physical quantities of interest that take m primary dimensional quantities to define, there are k = n - m independent unit-less or dimensionless products of the p's and these are similarity parameters that can be used for model scaling and experiments.
	www.me.umn.edu /education/courses/me5221/Tutorials/Scaling/scaling.html (1769 words)

	Units and Angles (Site not responding. Last check: 2007-10-31)
		We measure an angle like the angle of the blue sector in the picture at the left by dividing the length, L, of the arc cut-off by the angle by the length, R, of the radius of the circle.
		Since we are dividing two quantities, both of which are measured in the same units of length, the result is a dimensionless quantity -- that is, a quantity that has no associated units.
		Since R is measured in units of length and neither pi nor theta have associated units, the net result of this computation is measured in units of length.
	www.math.montana.edu /frankw/ccp/units/angles/body.htm (202 words)

	dimensional analysis
		Given the definition of a physical quantity, or an equation involving a physical quantity, you will be able to determine the dimensions and SI units of the quantity.
		Now that you can determine the dimensions of physical quantities, it'll be useful to write the SI units for the quantities.
		The argument of a trig function is an angle, of course, so it's "dimensionless"; and an exponent of an exponential function is the same thing as a logarithm so it's "dimensionless".
	www.physics.uoguelph.ca /tutorials/dimanaly (1082 words)

	Reynolds number - HighBeam Encyclopedia (Site not responding. Last check: 2007-10-31)
		REYNOLDS NUMBER [Reynolds number] [for Osborne Reynolds ], dimensionless quantity associated with the smoothness of flow of a fluid.
		It is an important quantity used in aerodynamics and hydraulics.
		At low velocities fluid flow is smooth, or laminar, and the fluid can be pictured as a series of parallel layers, or lamina, moving at different velocities.
	www.encyclopedia.com /doc/1E1-rynldsnum.html (302 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-31)
		A radian is a dimensionless quantity (this is probably the crux) 3.
		The variable x represents a (dimensionless) angle, so the Taylor series represents a dimensionless quantity, as does the sine of x.
		You can see that dimensional analysis isn't much use in investigating what is special about radians as a measure of angles.
	mathforum.org /library/drmath/view/54181.html (551 words)

	Angle (JScience v3.1 API) (Site not responding. Last check: 2007-10-31)
		This interface represents the figure formed by two lines diverging from a common point.
		The system unit for this quantity is "rad" (radian).
		Holds the SI unit (Système International d'Unités) for this quantity.
	jscience.org /api/javax/quantities/Angle.html (43 words)

	Mid-Term Solution
		(Write the m-l-t units of each quantity on the right hand side and cancel, leaving no net units.) Or you can recognize that the unit is a dimensionless length ratio, by definition.
		is a particular value of the dimensionless transverse (in cylindrical coordinates, radial) distance where the interface between unoxygenated and oxygenated hemoglobin is located.
		The general (not particular) dimensionless radius was termed p by Lightfoot.
	www.columbia.edu /~leonard/TISSSite/e4502-samfnl.html (2359 words)

	VisAD: Class QuantityDimension
		This class represents the dimension of a quantity.
		Indicate whether or not this dimension of a quantity is the same as another.
		Indicate whether or not this dimension of a quantity is dimensionless.
	www.ssec.wisc.edu /~dglo/visad/visad/QuantityDimension.html (172 words)

	RMP Lecture Notes
		When we say a quantity is dimensionless, we mean one of two things.
		Pi is a dimensionless number representing the ratio of the circumference of a circle to its diameter
		These are often called "dimensionless groups" or "dimensionless numbers" and often have special names and meanings.
	www.cbu.edu /~rprice/lectures/units.html (438 words)

	[No title]
		, the constant is multiplied by the quantity associated with the unit.
		, the constant is multiplied by the quantity associated with the number name raised to the power of the following number.
		, the constant is divided by the quantity associated with the
	www.jclark.com /dsssl/split/dsssl-49.html (2249 words)

	Definition and Printing of Quantities
		A quantity constant is simply a number followed by a set of units.
		A quantity variable is simply a quantity constant assigned to a variable name.
		Otherwise, the quantity will be printed as a floating point number, and if needed, in exponential format.
	www.isr.umd.edu /~austin/aladdin.d/quantity-defn.html (921 words)

	Chemical engineering other topics - Friction factor correlation/dimensionless quantity?
		This can be written in terms of quantities that don't involve the pipe radius/diameter, so that if you know flow and pressure drop, you can determine the required pipe size.
		As I mentioned earlier, this last quantity can be expressed in terms that do not involve the pipe diameter: thus, given known flow specifications, one can derive a line size.
		Second, it's interesting that no name has yet been assigned to this quantity, and that a trial/error approach is still the case: that says to me that nobody has yet established a spreadsheet-friendly analytical correlation.
	www.eng-tips.com /viewthread.cfm?qid=149386&page=1 (1916 words)

	Short Communication
		Historically the quantity needed a unit because it was, and still is, used as a base quantity.
		ISO/TC 12 defines it as a derived, dimensionless quantity, and the International System of Units (SI) gives it the 'dimensionless unit' radian, which now means no more than 'one'.
		ISO/TC 12, however, defines the quantity independently of plane angle as a dimensionless quantity to which, nevertheless, the SI assigns a 'unit'.
	stacks.iop.org /0026-1394/42/L23 (251 words)

	coulomb - a Whatis.com definition (Site not responding. Last check: 2007-10-31)
		The coulomb (symbolized C) is the standard unit of electric charge in the International System of Units (SI).
		It is a dimensionless quantity, sharing this aspect with the mole.
		A quantity of 1 C is equal to approximately 6.24 x 10
	searchsmb.techtarget.com /gDefinition/0,,sid44_gci530341,00.html (269 words)

	[No title]
		There's been discussion of a quantity library at the Boost list, and one person's real-world experience with such a system (their home-grown system), and their domain was robotics, was that they really wanted to be able to distinguish angle from dimensionless quantities.
		One thing that also came up on the Boost list (someone submitted a simple quantity library, but it didn't model the SI system, and was not meant for that), was the possibility to define the result type different from the arguments, e.g.
		I agree that the quantity is "temperature", and the unit is "kelvin".
	homepage.ntlworld.com /mark.easterbrook/mentored/digest017.txt (4710 words)

	VisAD: Class BaseUnit
		Create a new base unit from from the name of a quantity, the name of a unit, and the unit's abbreviation.
		Create a new base unit from from the name of a quantity, the name of a unit, the unit's abbreviation, and whether or not the unit is dimensionless.
		A unit is dimensionless if it is a measure of a dimensionless quantity like angle or concentration.
	www.ssec.wisc.edu /~dglo/docs/visad/BaseUnit.html (1301 words)

	Quantity
		The most familiar case is for numbers, in which orders of magnitudes typically correspond with powers of 10; thus, in any given numerical quantity, the 100's dominate the 10's or the units, which are negligible with respect to the hundreds.
		That is, each instance of IUT is a function used to measure quantities in units that are convertible into units measured by any of the other functions in IUT.
		#$Unity is the standard unit of measure for dimensionless quantities.
	www.cyc.com /cycdoc/vocab/quantity-vocab.html (4070 words)

	[No title] (Site not responding. Last check: 2007-10-31)
		For instance, if your variables include a height and a length, then their ratio is a dimensionless number.
		In the case where no dimensionless quantities can be formed from your variables (Step 3), then $f$ is simply an undetermined constant.
		{\bf Step 3:} The only dimensionless quantity that can be formed from the variables $v,\theta,g$ is $\theta$ itself.
	www.astro.umd.edu /~hamilton/teaching/ASTR430fall03/handouts/dimens.txt (465 words)

	dimensionless - OneLook Dictionary Search
		Tip: Click on the first link on a line below to go directly to a page where "dimensionless" is defined.
		Dimensionless : Online Plain Text English Dictionary [home, info]
		Phrases that include dimensionless: dimensionless number, dimensionless numbers, dimensionless quantities, dimensionless quantity, dimensionless unit
	www.onelook.com /?w=dimensionless (164 words)

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