Next: Averages over the Up: Appendix B: Using Previous: Assumption 1: Uniform

Assumption 2: Uniform distribution by radius

In this case, the fraction of the aggregate volume represented by particles with radii in the range (r, r+dr), contained in the ith sieve, is given by

so that the integral of p(r)dr over the interval (r_i, r_i+1) will be equal to c_i. Similar to the previous case, the fraction of the total number of aggregate particles with radii in the range (r, r+dr), contained in the ith sieve, is given by

where V = 4<π r ³ / 3 is the volume of a (spherical) particle in this range. Eq. (24) must obey the normalization (20), implying that the value of ρ is

or

Therefore, the average of Rⁿ over the particle number density is