Rosin-Rammler equation

Table II. Rosin-Rammler Equation Characteristics When n Equals 3...

Q = enthalpy increase of vaporizing fuel, measured from initial liquid temperature R = volume or mass fraction of droplets larger in diameter than x according to Rosin-Rammler equation... 

Rosin-Rammler Equation—Rosin and Rammler (1933) proposed an equation which in some respects is similar to Roller s basic equation, Eq (3-32). Their equation fits size-frequency data of friable material such as coal, but otherwise does not have the wide application of the Hatch-Choate and Roller equations. The Rosin-Rammler equation is... 

Related Calculations. Sometimes the Rosin-Rammler equation is used to represent the size distribution graphically. The dashed line on Fig. 13.1 corresponds to the Rossin-Rammler equation in the form y = 100 — lOOexp [—(x/A)b], where, in this case, A = 1558 and b = 1.135. 

This equation is useful for monitoring grinding operations for highly skewed distributions, but should be used with caution since the device of taking logs always reduces scatter hence, taking logs twice is not to be recommended. An alternative form of the Rosin-Rammler equation is ... 

It is further observed that there is an empirical function that can describe the particle size distribution of the powders prepared by using mechanical milhng, which is the Rosin-Rammler equation. One of the modified forms of the equation is given by ... 

Several en irical equations have been developed to describe distributions that may arise with certain materials or within the technology of a particular industry. The Rosin-Rammler equation was devised for use with mineral breaking processes, especially coal, and takes the form ... 

An empirical function that has been observed to describe the particle size distribution of milled powders is the Rosin-Rammler equation. The equation has undergone a number of modifications one form is... 

Rosin-Rammler Equation. An equation relating to fine grinding for most powders that have been prepared by grinding, the relationship between R, the residue remaining on any particular sieve, and the grain-size in microns (x) is exponential ... 

The various mean sizes available may be easily calculated from the Rosin-Rammler equation they all involve the Gamma functions which can be readily evaluated from mathematical tables. 

Fig. 28. Effects of the grain aze distributicHi of the spherical silica fillers on the viscosity of the epoxy moldiiig compounds, (n is an index in Rosin Rammler equation and indicates grain size distribution. Smaller n broader grain size distribution and larger n nanover grain size distrir bution.

Alternative width parameters are standard deviations for ensembles described by normal or log-normal distributions or the parameter N in the Rosin Rammler equation. These, of course, require the ensemble to be a good fit to the appropriate equation. More detailed comparisons are possible by examining the cumulative volume undersize curves, but this is a graphical comparison. 

Figure 7 Goodness of fit of Rosin Rammler equation of particle population on reticle, Hirleman et al " ...

Droplet Size Distribution. Most sprays comprise a wide range of droplet sizes. Some knowledge of the size distribution is usuaUy required, particularly when evaluating the overaU atomizer performance. The size distribution may be expressed in various ways. Several empirical functions, including the Rosin-Rammler (25) andNukiyama-Tanasawa (26) equations, have been commonly used. 

This mathematical form of the size distribution does not take account of the fact that die particle size does not stretch over die range from minus to plus infinity but has a limited range, and a modification such as the empirical Rosin-Rammler (1933) equation... 

CSD on Rosin-Rammler Chart. lognogn/RjVlog p. Figure 1 shows some examples of CSD on R-R chart. As mentioned above, R based on Equation 4 does not obey the R-R s expression except for Rn at j=l and Rn, Rw at j=. Nevertheless, as can be seen from Figure 1, it was found that there exists an approximate linear relationship between R and p (or L) on R-R graph paper in the... 

Cumulative data often are represented closely by the Rosin-Rammler-Sperling (RRS) equation... 

Three widely used distribution equations, discussed by Bevans (JL), include the Rosin-Rammler (7L) and Nukiyama-Tanasawa (6L) equations as well as the log-probability equation. A fourth relationship, the upper-limit equation of Mugele and Evans (5L), is also discussed. Hawthorne and Stange also discuss the Rosin-Rammler relationship (4L, 8L). An excellent analysis of distributions is given by Dubrow (SL), who has studied atomized magnesium powders. 

Equation (1.35b) shows that a linear relationship exists when ln[ln( 1 // )] is plotted against In d. From the slope and intercept of this straight line, a and fl can be determined, a and fl are typically obtained from the particle size distribution data based on sieve analyses. Table 1.5 provides a list of typical values of a and fl for some materials for the Rosin-Rammler density function with d in the function having the unit micrometers (/tm). 

Knudsen s model led to the prediction that, if linear kinetics were followed, the age at which 50% of the cement has hydrated is proportional to the fineness constant (or xj in the Rosin/Rammler distribution (equation 4.1) for parabolic kinetics, it predicted that this age is proportional to (K40). Evidence was presented in support of this conclusion for cements considered to follow linear kinetics. The theory did not predict any relation to the breadth of the particle size distribution, which is represented by the slope of the Rosin-Rammler curve. 

The property of the spray that is of greatest practical importance is the combustion efficiency, which is given by equation (18). When Gj q is of the generalized Rosin-Rammler form [equation (22)], by using equations (12) and (23) in equation (18), we find that... 

Rotarv kim reactors. 575, 590 Roughness factor, pipelines, 94 Rounds equation, friction factor, 94 RRS (Rosin-Rammler-Sperling) equation, 525,530-532 Rules of thumb... 

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