A.2.10—Viscous drag

Stokes drag

For a small sphere moving slowly through a viscous fluid,

$$F_d=6\pi\eta r v$$

where $\eta$ is viscosity, $r$ is sphere radius and $v$ is speed relative to the fluid.

Drag opposes motion

The drag force points opposite the sphere’s velocity. As speed increases, drag increases linearly in this model, reducing the resultant force when the driving force is fixed.

Approach to terminal speed

For a falling sphere, weight drives the motion and viscous drag grows with speed. When drag balances the effective weight, acceleration becomes zero and terminal speed is reached.

Common trap

Do not treat viscosity $\eta$ as the same quantity as drag force, and do not forget that the formula applies to the stated small-sphere, viscous-flow model.