Stokes law - Settling velocity and rate

[Maharg]

Homework Statement

1. A fly ash (ρ =1.8 g/mL) aerosol consists of particles averaging 13 μm in diameter and with a concentration of 800μg/m3. Use the average diameter to calculate the settling velocity (cm/s) and settling rate (μg/m/s) of the particles in air.
The Stokes-Cunningham slip correction factor is 1.015.

Homework Equations

vt = (pp - pa)C*g*dp^2/ 18n

vt = settling velocity in m/s
pp = particle density g/m3
pa = air density g/m3
C = stokes-cunningham slip correction factor (given in question)
g = acceleration due to gravity
dp = particle diameter in m
n = viscosity of air

The Attempt at a Solution

So first I had to figure out what each part of equation is since I was not given all of it.

pp was given in question as 1.8 g/mL converted to 1.8E6 g/m3 (is that correct conversion?)

pa I found online air density to be 1.184E3 g/m3 at 25 Celsius (note no textbook for this class)

g = 9/8 m/s2

n = 1.86E-2 g/m*s I also found this online

After this I plugged it all into equation.

vt = [(1.8E6 g/m3 - 1.184E3 g/m3)(1.015)(9.8 m/s2)(13E-5 m)]/[18(1.86E-2 g/m*s)]

= 2403.654 g/m / 0.3348 g/m*s
= 7179 = 7.2E3 s

my units don't make sense. everything cancels out but seconds. How go I get this in m(cm) a second. I don't know how to make it so m doesn't cancel?

Also I do not know how to do settling rate. We have never talked about rate in class. Any suggestions?

 

[Dunhausen]

I think you forgot to square one of the terms which is why you are missing an m.

I assumed the settling rate was just the previous number * the concentration, although you are right, the book did not discuss it!

("Environmental Chemistry: a global perspective" by Gary w vanLoon and Stephen J. Duffy is full of errors and questions which does not reflect the material covered.)

Anyway, this was code to solve the problem:

#!/usr/bin/env python
from __future__ import division
from scipy import pi


p_p=1.8*10**6 #g/mL
d_p=13e-06 #m
C=1.016
p_a=1.2e03 #g/m^3
eta=1.2e-02 #g/ms
g=9.81 #m/s/s
N= 800 #ug/m^3


Vt=(p_p-p_a)*C*g*d_p**2/(18*eta)

print 'Problem 6.4'
print '==========='
print 'Settling velocity = ' + str(Vt) + ' m/s =' +str(Vt*100) + ' cm/s'
print 'Settling rate = ' + str(Vt*N) + ' ug/m^2/s'