In the course of an experiment with first-year students, they are to find the density of glass spheres -allegedly spherical- by using a balance, a pycnometer and DI water. They are told to use 6 spheres of about 6 mm in diameter. Simple.
The question may arise, however: why 6? Why 6 spheres?
Accidentally, I came across with the answer, I believe. Later on in the experiment, the students are to calculate the drag coefficient of glass spheres of different sizes falling down in a cylinder full of fluid. The momentum balance -assuming measurements are to be taken after terminal velocity is reached- is, simply: (force due to gravity) - (force due to drag) - (force due to buoyancy) = 0. The drag force is assumed to be equalled to (drag coeff) * (projected area of sphere in the direction of motion) * (kinetic energy at terminal velocity of the fluid past the sphere). All parameters are found experimentally, apart from the drag coefficient, which is to be calculated from the over-mentioned equation.
A priori, the drag is written as a function of the mass of the sphere, as well. In order to write it in terms of diameter and the density of the glass, the assumption of spheres being perfectly spherical is made.
The density of a sphere perfectly spherical is (6*mass) = Pi*(Diameter^3). That's the reason for the 6!!
The density of the glass so calculated is about 15 % different from the density calculated experimentally (not considering the perfect-sphere assumption). However, the assumption that spheres are spherical is made in order to calculate the drag coefficient; thus, such error shall invariantly be in the experimentation, down to the final results.
I find these kind of revelations juicy. It looks possible to me that the staff who designed the experiment years ago must wanted to show more than what we show today -crap, because of lack of interest. It's like doing Science Archaeology, Modern Science Archaeology, and enquire in the minds of people 10, 20, 40 years ago, most interesting. Don't you think?
(PLEASE, LEAVE YOUR COMMENT).
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