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Particle Settling (Stoke's flow equation)

  1. Oct 9, 2015 #1
    1. The problem statement, all variables and given/known data
    I have been given a question which I can't seem to get my head around fully for one reason. I keep finding myself stuck with 2 unknown variables. Here is the information given..

    V (terminal velocity) = Unknown
    g (gravity acc.) = 9.81m/s2
    d (diameter of particle) = ???
    Pp = 1,100kg/m^3
    Pm or "Pf" = 1,000kg/m^3
    μ = 0.0012 Ns/m^2

    I need to find the terminal velocity but this has been the only information specified about D's value in the question.
    "Vary D in a power law fashion, i.e.:
    Di = 2Di−1 i = 1,2, . . ,10 D0 = 0.01mm "

    2. Relevant equations

    stokes_law_terminal_velocity.png and l_stokes_law_particle_diameter.png

    3. The attempt at a solution

    I have set up the equation using all the given information however I don't understand the instructions given in terms of the particle's diameter d's value. It is a programming assignment and I can't see myself progressing with it having 2 unknowns (As my code won't even function without a declared value for d). Is the above quote just telling me to use 0.01mm as my value for the diameter? I don't understand what varying "D in a power law fashion" is supposed to mean.
    I tried using the 2nd equation shown above to calculate the diameter by hand with the given information but I cannot do that either because I don't have the terminal velocity!! and that is what I am looking for to begin with.
    Just wondering if the reason I don't have a value for d is because of my understanding of the given quote or if I am lacking information to complete the question to begin with. If it happens to be a lack of information, am I by any chance overlooking something in the question? Because after I find the value of the terminal velocity I am supposed to find the Re (Reynold's Number) which implements both diameter and terminal velocity into the equation.

    Any help to the understanding of D's value given the information would be greatly appreciated by anyone. Understanding what is going on is always the hardest thing for me when it comes to programming, the coding usually serves little problem.
  2. jcsd
  3. Oct 9, 2015 #2


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    Could it be they want you to do the v calculation for D = 0.01, then for 0.02, 0.04, 0.08, etc. all the way to 10.24 mm ? [edit] make that 5.12 mm....
  4. Oct 9, 2015 #3
    Maybe the rule for increasing diameter is

    Di = 2Di−1 for i = 1,2, . . ,10 with D0 = 0.01mm

    Then you can solve the equation for variable D and you are able to draw a graph v=f(D)
  5. Oct 9, 2015 #4
  6. Oct 9, 2015 #5
    Well, the assignment says, that the output of the code shall be a table, with D as variable value. So it is exactly what BvU wrote. For each D you calculate the v, Re and depending on Re you classify the flow - you get a table with four columns in each column one of the quantities corrisponding to the D in the same row.
  7. Oct 9, 2015 #6
    When you say "Depending on the Re you classify the flow". There are 3 given equations in the assignment for various settling and flows. How would I know which ones to use? Like if I use the stokes one but the number indicates that it is a Newtonian flow? Sorry I am terrible at comprehending word explanations.
    Could somebody explain it in terms of the information given? I want to be able to get cracking on this before evening comes along. Thanks to everyone though for clarifying what D is.
  8. Oct 9, 2015 #7
    I think that's part of the task. You use one formula and if the achieved Re is too large for it, you have to use the next one - it is an iterative process. The limits set to identify are sharp - the equations are not. Plus you can use the information you gained from the computing step i for the step i + 1. I'm sure, as soon as start you will figure out what to do and find solutions for these "problems".
  9. Oct 9, 2015 #8


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    From the PDF I read it a bit more complicated: You have to use all three expressions to calculate a value for u, and Re, then pick the one (or two ?) that has Re in the right range .

    Nice exercise !
  10. Oct 9, 2015 #9
    He is pretty innovative with his assignments haha. In class its just like "write some code to add a + bc" then in assignments he comes out with this sort of stuff. Creative assignments but the assumed knowledge for this is ridiculous, he puts far too much faith in us.
  11. Oct 9, 2015 #10


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    Your professor seems like a fair chap.

    I read the complete assignment which was given to you. The prof laid out all of the requisite formulas in black and white. He provided all of the necessary data to compute the results for this assignment, which was basically to generate a set of data and then display it. Everything needed to complete this assignment was contained on the prof's handout.

    This was not an assignment where you were asked to discuss the differences between the various types of flow, or even where you needed to have studied fluid mechanics at all: it was a simple plug-and-chug task, with a fair amount of calculation mixed in with some decision making about what type of flow was applicable given the size of the particle tested.
  12. Oct 15, 2015 #11
    I think it is 10.24 as D10 = 2D9 = 10.24mm.
  13. Oct 15, 2015 #12


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    Fine too. I thought d10 = 29 since d0 = 20 (times 0.01 mm)
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