Definitions of means

The correction of mean free path, hi by the nanoscale effect function results in a smaller mean free path, or a smaller Knudsen number in other word. As a matter of fact, a similar effect is able to be achieved even if we use the conventional definition of mean free path, / = irSn, and the Chapmann-Enskog viscosity equation, /r = (5/16)... 

The holdup is calculated from the definition of mean residence time of solid particles ... 

In many applications, a mean droplet size is a factor of foremost concern. Mean droplet size can be taken as a measure of the quality of an atomization process. It is also convenient to use only mean droplet size in calculations involving discrete droplets such as multiphase flow and mass transfer processes. Various definitions of mean droplet size have been employed in different applications, as summarized in Table 4.1. The concept and notation of mean droplet diameter have been generalized and standardized by Mugele and Evans.[423] The arithmetic, surface, and volume mean droplet diameter (D10, D2o, and D30) are some most common mean droplet diameters ... 

Table 4.1. Definitions of Mean Droplet Diameters and Their Applications 423 ...

We conclude this section by giving, for the sake of clarity, the most general definition of mean bond dissociation enthalpy. For any molecule AYmXn, where A is a central atom and X and Y are any mono- or polyatomic groups, the A-X... 

The method to find the mean time to reach equilibrium without calculating the full concentration evolution curve is as follows. By comparing the definition of mean reaction time (Equation 1-60) d /dt=—( - ao)hr and Equation 2-17, the following is obtained ... 

The two parameters, Tf and Tb, are very useful in inferring cooling rates and it is helpful to give their expression under a more general cooling history. The expressions of Tf and Tb can be obtained using the definition of mean times (Equation 1-60) ... 

A quantitative test for the determination of anti-insulin antibodies is not possible due to the different nature of insulin antibodies that can be formed. The criteria for evaluation of antibody positive samples are somewhat arbitrary, e.g. selected pool of healthy blood donors, definition of mean + 3 standard deviations, varying binding with different tracer batches, consider an absolute change in binding values > 10 % B/T in clinical studies from baseline to endpoint when measured in the same ran as significant. 

Practice often requires the detailed knowledge or prognosis for different sizes of droplets for instance, a question can arise about which droplets overcome a certain distance after a spraying system. But mostly the prognosis concerns only the mean droplet size, especially in the course of preliminary investigations. The decision about how to choose the mean size is often made unrigorously. Usually, one of the following definitions of mean diameter is used ... 

Using the definitions of mean molar and partial molar quantities, Eqn (3.14) becomes... 

It is seen that this definition of mean quantities eliminates terms that are linear in the fluctu-ating quantities. Moments of the fluctuating quantities that are retained in a boundary layer are pV, (pv) u, (pv)V, (pv) i, and (pv) Ai , which represent the turbulent flux of mass, momentum, heat, and species concentration in the direction normal to a surface. These quantities are added to their molecular counterparts. Details of these derivations can be found in several sources, e.g., Refs. 65, 71, 74, and 75. 

The magnetic susceptibility is introduced as a thermodynamic quantity which requires a partial differentiation of the magnetisation according to the applied field. This differential (isothermal) magnetic susceptibility differs from the frequent definition of mean magnetic susceptibility if the behaviour of the magnetic material is nonlinear. 

Table 9.6 summarizes many definitions of mean diameter. Note that the definition for number can be substituted for mass. The number length mean becomes the mass length mean—the symbol would be Z)m[l,0]. Most often, data is reported as mass fraction and, therefore, to apply the number definitions requires a transformation from the mass fractions ... 

The definition of mean time to first state failure is "The average operating time from start-up in full operating condition (state 0) to failure in the state of interest." This time period includes interruption in failure states other than the one of interest. The method for calculating this metric is ... 

A way out of a building or structure. It may not comply with the formal definition of means of egress, but does provide an alternative avenue to evacuate a facility. See also Evacuation Exit. 

As shown in section 2.4, there is a bewildering variety of different definitions of mean particle size. Most textbooks quote the definitions either in the form of summations or as integrals, the latter being more appropriate if the particle size distributions are generated as continuous curves. Few textbooks, however, give any hints as to which of the definitions are to be used and when. This is a serious omission because the correct choice of the most appropriate mean is vital in most applications. 

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