# dimensionless number

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Related to dimensionless number: Biot number

## dimensionless number

[də′men·chən·ləs ′nəm·bər]
(mathematics)
A ratio of various physical properties (such as density or heat capacity) and conditions (such as flow rate or weight) of such nature that the resulting number has no defining units of weight, rate, and so on. Also known as nondimensional parameter.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
where [Q.sub.CO] is the CO emission ([m.sup.2]/s); [q.sub.CO] is the baseline CO emission ([m.sup.2]/(veh x km)); [f.sub.a(CO)] is the coefficient of vehicle condition (dimensionless number); [f.sub.d] is the coefficient of vehicle density (dimensionless number); [f.sub.h(CO)] is the coefficient of altitude (dimensionless number); [f.sub.iv(CO)] is the coefficient of longitudinal slope and vehicle speed (dimensionless number); [f.sub.m(CO)] is the vehicle-type coefficient (dimensionless number); n is the vehicle-type number (dimensionless number); and [N.sub.m] is the traffic quantity of corresponding type (veh/h).
An extra dimensionless number [[PI].sub.3] is introduced to the analysis with the addition of thickness (t) to the dimensional analysis with the value:
The Grashof number is a dimensionless number in fluid dynamics that approximates the ratio of the buoyancy force to the viscous force acting on a fluid.
Then the dimensionless numbers, supracritical Reynolds ([Re.sub.supra]) number and resistive index (Res), are computed using flow velocities and the quantitative degrees are applied to screen the DOS.
with: [x.sub.ij] = response of alternative j on objective i; j = 1, 2, ...,m; m the number of alternatives; i = 1, 2, n; n the number of objectives; [x.sub.ij.sup.*] = a dimensionless number representing the response of alternative j on objective i, meaning that the number is no more expressed in money, weights, length, volume etc.
where [gamma] is a dimensionless number that is the ratio of an arbitrary air supply speed to a reference air supply speed, [u.sub.r] is the reference velocity field when [gamma]=1.
where m is the gravitational parameter, M is magnetic parameter, [beta] is non-Newtonian effect, [LAMBDA] is slip parameter, [lambda] is heat dimensionless number, [R.sub.e] is the local Reynolds number, and [alpha] is the nondimensional variable using the above dimensionless variables in (10) and in (12) and dropping bars we obtain
Reynolds, a British scientist, showed that the transition from laminar to turbulent flow is directly related to a dimensionless number defined as the Reynolds number .
[x.sup.*.sub.ij] = a dimensionless number representing the response of alternative j on objective i.
with: [X.sub.ij] = response of alternative j on objective i j = 1,2,...,m; m the number of alternatives i = 1,2,...n; n the number of objectives [X.sub.ij*] = a dimensionless number representing the normalized response of alternative j on objective i.
An important dimensionless number of magnetohydrodynamics which represents the ratio of the Lorentz force to the viscosity has been named as Chandrasekhar number in his honour.

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