Question

Viruses are much smaller than bacteria. For example, the novel coronavirus is a spherical particle of outer diameter 120 nm, while streptococcus bacteria are 1.8 μμm in diameter. The virus is also found to be slightly more dense than the bacteria, with the density of coronavirus being 1.15 kg/L and that of strep being 1.1 kg/L. During an infection, both are found in the bloodstream (blood density is 1.05 kg/L; blood viscosity is 3.5×10^-3 Pa⋅s).

(a) A sample of blood containing streptococcus is placed in a centrifuge and spun at 18,000 revolutions per minute (RPM). Under these conditions, it is found that the bacteria sediment with a terminal speed of 0.5 mm/s. What would be the sedimenting terminal speed of coronavirus under the same conditions?

vvirus = ______ mm/s

(b) What is the Reynolds number for the bacteria as it sediments in the centrifuge?

Re = ______

(c) Once the sample of coronavirus has been fully sedimented it is left in the vial for a few days. It is found that at a position 4 mm above the bottom of the vial the concentration of the virus particles is 43% of the concentration at the bottom of the vial. What is the relative concentration at a position 14 mm above the bottom of the vial?
(give your answer as a percent)

C/C₀ = ______ %

Answer 1