In his
lecture on viscosity
Walter Lewin
measures the terminal velocity
vterm
of various metal bearing balls of different diameters,
but of the same density,
falling vertically in a container filled with Karo light corn syrup.
The diameters of the metal bearing balls
are so accurate that Walter Lewin does not indicate
the experimental errors on them.
For the measurements of the time that each ball bearing
takes for a vertical displacement of 4.0 cm,
Walter Lewin gives varying experimental errors,
depending on whether that takes several seconds, or just a few.
In the table which is shown below, we have collected his results.
diameter
time (s)
vterm=(4 cm)/time
vterm /
diameter2
vterm / √diameter
0.125 inch
5.66 - 5.93
0.69±0.02 cm/s
44±1 cm/s/inch2
1.95±0.05 cm/s/√inch
0.156 inch
3.80±0.10
1.05±0.03 cm/s
43±1 cm/s/inch2
2.66±0.08 cm/s/√inch
0.188 inch
2.69±0.20
1.49±0.11 cm/s
42±3 cm/s/inch2
3.44±0.26 cm/s/√inch
0.250 inch
1.40 - 1.68
2.60±0.24 cm/s
42±4 cm/s/inch2
5.20±0.50 cm/s/√inch
In the third column we show the resulting terminal velocities
for the various bearing balls in
cm/s,
whereas, in the fourth and fifth columns, we show the ratios
of the terminal velocity and respectively
the square and the square root of the diameter.
We observe that the terminal velocity is clearly
not proportional to the square root of the diameter
d,
but rather to its square: