The terminal velocity of a small sphere settling in a viscous fluid varies as the

The terminal velocity of a small sphere settling in a viscous fluid is given by Stokes' law for low Reynolds numbers, which is expressed as:

v = (2/9) * (r² * g * (ρ_s - ρ_f)) / μ

Here: v = terminal velocity r = radius of the sphere g = acceleration due to gravity ρ_s = density of the sphere ρ_f = density of the fluid μ = dynamic viscosity of the fluid

From the equation, it is evident that the terminal velocity is inversely proportional to the viscosity of the fluid (μ). A higher viscosity results in lower terminal velocity, while a lower viscosity increases the terminal velocity.

Thus, the terminal velocity varies as the inverse of the fluid viscosity.