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Terminal Velocity In Glycerin 2.10 in Classical Mechanics

  1. Sep 17, 2011 #1
    Terminal Velocity In Glycerin 2.10 in "Classical Mechanics"

    1. The problem statement, all variables and given/known data
    For a steel ball bearing (diameter 2mm and density 7.8g/cm3) dropped in glycerin (density 1.3g/cm3 and viscosity 12 N s/m2 at STP) the dominant drag force is linear drag given by flin = 3*pi*n*D*v where D is the sphere's diameter, v is velocity, n is the viscosity of the fluid
    a) Find the Characteristic time and terminal speed vter. Include Archimedes buoyant force as a 3rd force.
    b) How long after it is dropped from rest will the ball bearing have reached 95% of its terminal velocity
    c) Use flin = 3*pi*n*D*v and fquad=kpAv2 (p being density) with k = 1/4 and compute fquad/flin at the terminal speed


    2. Relevant equations
    v(t) where t = characteristic time = 0.63vter
    vter = g*t
    0.95vter = 3t where t = characteristic time
    Fbouyancy = (pi/6)d3p*g (p being density of fluid)


    3. The attempt at a solution

    So far I've gotten for part a)
    (3.2672x10-8 kg)*9.8m/s = 3.202E-7 N (for gravitational force)
    3*pi*n*D*v = 3.202E-7N - (pi/6)d3p*g

    Is this correct? Solve for v above and that's terminal velocity? if so I'm good for the rest of the problem.
     
  2. jcsd
  3. Sep 17, 2011 #2

    rude man

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    Re: Terminal Velocity In Glycerin 2.10 in "Classical Mechanics"

    Looks A-OK. I did not check your gravitational force number.
     
  4. Sep 17, 2011 #3
    Re: Terminal Velocity In Glycerin 2.10 in "Classical Mechanics"

    Yeah it's actually 3.2019E-4 N for the F... my mistake
     
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