Interface
#include <codecogs/engineering/materials/rosin_rammler.h>
| double | Rosin_CDF (double Dm, int n, double D) Rosin-Rammler cumulative distribution |
Function Documentation
The Rosin-Rammler distribution is frequently used to describe the particle size distribution of powers of various types and sizes. The function is particularyly suited to representing particles generated by grinding, milling and crushing operations. The conventional Rosin-Rammler function is described by
where R is the retained weight fraction of particles with a diameter greater than D, D is the particle size and
is the mean particle size, and n is a measure of the spread of particle sizes.
The Cumulative Distribution Function (CDF) is therefore
As an additional note, the PDF is:
If you have observed data, then a least square regression analysis can used to fit the data points.
Parameters:
| Dm | mean particle diameter |
| n | measure of the spread of particle sizes |
| D | particle size |
References:
- K.M. Djamarani and I.M. Clark, 1997. Powder Technology, Elsevier Science. 93, No 2, pp. 101-108(8)
Authors:
- Will Bateman (2006)
Source Code:
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Last Modified: 16 Mar 08 @ 21:58 Page Rendered: 2008-05-09 11:07:03
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![\displaystyle R = exp \left [ - \left ( \frac{D}{D_m} \right )^n \right ]](/latexrender/sites/www.codecogs.com/85d6bef60cf7a613ebe52b72de21935f.gif "\displaystyle R = exp \left [ - \left ( \frac{D}{D_m} \right )^n \right ]")
![\displaystyle R_{cdf} = 1- exp \left [ - \left ( \frac{D}{D_m} \right )^n \right ]](/latexrender/sites/www.codecogs.com/64fb870e2bc2ea624b2592275d6a84f9.gif "\displaystyle R_{cdf} = 1- exp \left [ - \left ( \frac{D}{D_m} \right )^n \right ]")
![\displaystyle R_{pdf} = -\frac{n}{D} \left ( \frac{D}{D_m} \right )^n exp \left [- \left( \frac{D}{D_m} \right )^n \right ]](/latexrender/sites/www.codecogs.com/d5d0284e35ce06b3198fc5f4112a5a1b.gif "\displaystyle R_{pdf} = -\frac{n}{D} \left ( \frac{D}{D_m} \right )^n exp \left [- \left( \frac{D}{D_m} \right )^n \right ]")
