terminal speed of two raindrop

a large raindrop has twice diameter of a small raindrop, which one has the largest terminal speed and why??

係咪用 D=0.5 CpAv^2 來explain??

2 個解答

  • tc
    Lv 6
    1 十年前

    Yes, you are right. We can apply this formula:

    D = 1/2 C ρ A v²

    where D = drag force

    C = drag coefficient

    ρ = density

    A = cross-sectional area

    v = speed

    To find the terminal velocity, setting the drag force D equal to the gravity of the raindrop, i.e.

    D = mg = ρ(4/3 π r³) g, where r is the radius of the raindrop

    => ρ(4/3 π r³) g = 1/2 C ρ π r² v²

    => v = √ [(8/3 r g ) / C]

    Hence, v is proportional to the square root of the radius of the raindrop.

    Therefore, the bigger raindrop has higher terminal speed.

    Note: The drag coefficient, C, is only approximately constant for the raindrops of different sizes. The shape of the raindrops are only approximately spherical.

  • 志仁
    Lv 6
    1 十年前

    I do not understand your last sentence.

    The force addes on the raindrop is F=mg-bv, m is the mass of the raindrop.

    m=pV, V is the volume, p is density.b is the air resistance constant depend on the surface area. V=4/3(pi)r^3. (Volume of a sphere)

    Asume the two raindrops are sphere in shape.

    And the terminal speed, F=0. => mg=bv, b=2(pi)r^2 x c (Area of half of sphere), c is a constant.

    v=mg/b=p 4/3(pi)r^3 / c [2(pi)r^2] = p/c x (2r/3)

    v is proprotional to r, that mean if the r is double, the terminal speed is double.

    2007-06-14 16:27:12 補充:

    Since p, c are the same for the same matter.