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Calculating drag of an object under water(Help!)

  1. Nov 23, 2013 #1
    Dear Experts,

    I really need help with the calculation of virtual mass and drag of an object.
    Firstly, I am doing final year project called Drag reduction in swim cap. Before I go into using swim cap. I am try to measure the drag using accelerometer that inside a bottle but I am damn confuse... the requirement is just equations of motion according to my supervisor.

    F_Buoyancy = buoyancy force = density, displaced volume x gravity
    F_Drag = Drag force = Cd. 1/2 x density . Velocity^2 . Area
    F_w = weight = mass x gravity

    ok when an object rises F_B > F_W which means the object accelerate up. If we include drag after some point terminal velocity will reach and the object no longer accelerate.
    when F_B < F_W the object sinks

    I was told to calculate virtual mass which is the mass added when the object pushes a finite amount of water away when it accelerates

    The equation of motion can be given as

    F_B - F_W - F_D = (m + mh)a
    Where mh is added mass.

    I really wondering how do I measured the drag by using accerelometer??? :confused:
    I already launch the object from water and the accelerometer show the g-force either increasing or decrease depends on how I point it.

    I am very grateful if some dynamic people could point it out.

  2. jcsd
  3. Nov 24, 2013 #2

    Simon Bridge

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    You need to use the acceleration vs time data in conjunction with a mathematical model for drag.
    That's where the equations come in.

    You may need to model mh in terms of the instantaneous speed of the bottle and it's cross-section area.

    Your accelerometer reads differently with different orientations perhaps because acceleration is a vector.
    Is it measuring the component of the acceleration in the direction it is pointing in?

    (By g-force, you mean that your accelerometer measures acceleration in units of g?)
  4. Nov 24, 2013 #3


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    Two comments:

    1. Calculating the virtual mass is very hard, compared with everything else in your OP.
    2. If a = 0 (i.e. the velocity is constant), the virtual mass has no effect, so you don't need it.

    The easiest way to do fluid flow experiments is at constant velocity, not when things are accelerating.
  5. Nov 24, 2013 #4

    Simon Bridge

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    I was thinking that the situation needs to be finessed so the bottle gets it's terminal velocity very quickly... ie. ballast to make it only a little buoyant.
  6. Nov 24, 2013 #5


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    Yup, that's the standard way to measure drag forces.

    An accelerometer seems like the wrong measuring device to use for this.
  7. Nov 24, 2013 #6

    Simon Bridge

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    The only use I can think for it would be to have a record for when the acceleration is zero.
    Maybe an acceleration-time curve can be interpolated to find the speed for constant velocity?
    Drag is different for different speeds.

    However - as an assigned project "use this sub-optimal equipment to make the following measurement" would be a common learning exercise. I'm seeing a few odd projects using accelerometers cropping up recently - tech du jour I guess.
  8. Nov 25, 2013 #7


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  9. Nov 25, 2013 #8
    Hi, Thanks for the reply
    I got this data doing the test using a bottle with accelerometer fitted. The first one is without mass inside just accelerometer. The center of mass is not aligned with the bottle and it shot up very fast(haven't reach constant velocity/terminal I guess).

    The second test I put nickel and silver penny inside and the object rises constantly by using naked eye but I am not sure whether it is still accelerating. And the good part is the bottle is very straight almost normal to the water surface!

    Attached Files:

  10. Nov 25, 2013 #9
    Hello I got the follow result
    1) Bottle with accelerometer and off center of mass
    2) Bottle with acc with aligned center of mass

    I already attach the image in Simon posts, cant duplicate. Thx!
  11. Nov 25, 2013 #10
    Yeah, I need to reach terminal velocity as quickly as possible. My supervisor mention getting terminal velocity correctly is a challenge. my water tank is about 3m depth.
  12. Nov 25, 2013 #11


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    Thinking about it, you could probably measure the added mass effect in this experiment. (As a native English speaker I think "calculate" means "do a theoretical calculation," but that might not be what you and supervisor meant).

    The added mass only depends on the shape of the object, not on its real mass. The same is true for the buoyancy force. The drag force F_D depends on the shape, and also the velocity.

    So, if you can do two experiments with different masses m1 and m2, and measure the accelerations at the same velocity, you have
    ##F_B - F_{W_1} - F_D = (m_1 + m_h)a_1##
    ##F_B - F_{W_2} - F_D = (m_2 + m_h)a_2##
    and you can eliminate the unknown drag force ##F_D## to find ##m_h##.
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