Question

Consider a spherical bacterium, with radius 1.7 μm , falling in water at 20° C.

Find the terminal speed of the spherical bacterium in meters per second, ignoring the buoyant force on the bacterium and assuming Stokes' law for the viscous force. You will first need to note that the drag force is equal to the weight at terminal velocity. Take the density of the bacterium to be 1.3 × 10³ kg/m³. The viscosity of water at 20 °C is 1.002 × 10^-3 kg/m·s and the density is 998 kg/m³.

Answer 1

Stoke's law for viscous force,

At terminal velocity,

Drag force is equal to weight ,

substituting the given values ,

$\rho=1.3*10^3\,kg/m^3\,,\,\rho_w=998\,kg/m^3$

$R=1.7\,\mu m=1.7*10^{-6}\,m$

$v=\frac{4(1.3*10^3-998)(1.7*10^{-6})^2*9.81}{18*1.002*10^{-3}}$

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