Stokes law - Settling velocity and rate

  1. 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
     
  2. jcsd
  3. 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:

    Code (Text):

    #!/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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