Download Lecture 40

M E 433
Professor John M. Cimbala
Lecture 40
Today, we will:
•
Continue discussing aerosol particle statistics
•
Introduce and define mass distribution and cumulative mass distribution.
Review so far of statistical definitions (aerosol particle statistics):
• Dp,50 = median particle diameter (half are bigger and half are smaller)
• Dp,am = arithmetic mean particle diameter (simple average diameter)
• Dp,gm = geometric mean particle diameter (like an average, but with products, not sums)
• σg = geometric standard deviation [lnσg is the standard deviation of ln(Dp) instead of the
standard deviation of Dp itself]
• ln(Dp),am = arithmetic mean of ln(Dp) [simple average of ln(Dp)]
For our sample aerosol distribution on the class handout:
Dp,50 = 9.0 µm, Dp,am = 11.2 µm, Dp,gm = 8.98 µm, σg = 1.97 µm, and ln(Dp),am = 2.2.
Example: Log-probability plots
Given: A sample (in terms of grouped data) is shown below.
To do:
Calculate the geometric standard deviation σg (to 3 significant digits).
=
σg
Solution:
D p ,84.1 (number) D p ,50 (number)
=
=
D p ,50 (number) D p ,15.9 (number)
D p ,84.1 (number)
D p ,15.9 (number)
Log-probability paper for particle distributions (created by J. M. Cimbala)
Dp,max,j
Dp,84.1
Dp,50
Dp,15.9
Mass Distribution
Additional analysis of the sample particle data (class handout; also see Excel spreadsheet):
Mass of particles
in class j:
mj
Mass of particles in
class j divided by class
width:
mj /(∆Dp, j)
Cumulative mass
distribution function:
G(Dp) [sometimes
written as Mj/mt]
Mass fraction of
particles in class j:
g(Dp, j) = mj/mt
When plot this on logprobability paper,
remember to use
Dp,max, j, not Dp, j since the
cumulative distribution
function includes the entire
bin from min to max.
Number distribution and mass distribution for the sample data of the class handout
Mass
distribution
Number
distribution