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).
The dimensionless number
K was calculated by the relation (13) where:
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.