# Stokes law - Settling velocity and rate

by Maharg
Tags: settling stokes
 P: 23 1. The problem statement, all variables and given/known data 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. 2. Relevant 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 3. 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? 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution
 P: 30 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'

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