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Air Bubbles and Terminal Velocity-> why is my answer wrong? (all work shown)

  1. Apr 4, 2010 #1
    Air Bubbles and Terminal Velocity--> why is my answer wrong? (all work shown)

    1. The problem statement, all variables and given/known data
    Air bubbles of 1.0mm radius are rising from a scuba diver to the surface of the sea. Assume a
    water temp of 20C.
    a) If viscosity of water = 1.0 X 10-3 Pa.s, what is the terminal
    velocity of the bubbles
    b) What is the largest rate of the pressure change tolerable for the diver
    according to this rule?
    (Rule is divers cannot rise faster than their air bubbles when riding to the surface
    * helps avoid rapid pressure changes that cause the bends)


    2. Relevant equations
    r = 1.0mm = 1.0 x 10-3m
    T= 20C <--I have no idea what to do with this!
    [tex]\eta[/tex]= 1.0 x 10-3 (viscosity of water)
    [tex]\rho[/tex]= 1000kg/m3
    im assuming density of water will be needed


    3. The attempt at a solution

    With terminal velocity you produce the right drag so the net force is 0.
    And with the air bubbles i know that the terminal velocity is upward

    first i set Fnet = 0
    and its in the y directions, so
    Fy= FD + FB=0
    FD= 6[tex]\pi[/tex][tex]\eta[/tex]rv (v=velocity)
    ^This is known as Stoke's Law

    next i solved for vt v = vt

    vt= mass water(g)/ 6[tex]\pi[/tex][tex]\eta[/tex]r
    =4/3[tex]\pi[/tex]r3g([tex]\rho[/tex]water/(6[tex]\pi[/tex][tex]\eta[/tex]r)

    next i simplified it by taking out pi and
    =4/3r2g([tex]\rho[/tex]water/(6[tex]\eta[/tex])

    and i got .22
    but the answer is suppose to be 2.2 m/s upward-WHAT did i do wrong???

    please help me!
    thanks.

    NOTE the greek letters ARE NOT in subsrcipt. i dont know why it does that-but it is not an exponent.
     
    Last edited: Apr 4, 2010
  2. jcsd
  3. Apr 4, 2010 #2

    ideasrule

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    Homework Helper

    Re: Air Bubbles and Terminal Velocity--> why is my answer wrong? (all work shown)

    Check your calculations. Using your final equation, I do get 2.2 m/s.
     
  4. Apr 4, 2010 #3
    Re: Air Bubbles and Terminal Velocity--> why is my answer wrong? (all work shown)

    i have been trying it all day
    and just did it again.
    now im getting 2177777

    how did u put in ur calc?
     
  5. Apr 4, 2010 #4

    ideasrule

    User Avatar
    Homework Helper

    Re: Air Bubbles and Terminal Velocity--> why is my answer wrong? (all work shown)

    I put 1E-3 for r, 9.8 for g, 1000 for rho, and 1E-3 for eta. If you don't know how to use your calculator, I can't help you there; my calculator is likely different from yours, and all I can suggest is to watch how the calculator responds to each key you press to make sure it's doing what you want it to.
     
  6. Apr 4, 2010 #5
    Re: Air Bubbles and Terminal Velocity--> why is my answer wrong? (all work shown)

    hmm i did the same thing-ill check my settings then.
    oh well.
    the important thing is that my setup for the prblm was right! =)
     
  7. Dec 18, 2011 #6
    Re: Air Bubbles and Terminal Velocity--> why is my answer wrong? (all work shown)

    I'm working on the same problem, but I don't understand where the 4/3(Pi)(r^3) came from. I'm not sure how to sub density for the masses (which aren't given).
     
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