Summarizing Drag Forces

Summary

• Drag forces acting on an object moving in a fluid oppose the motion. For larger objects (such as a baseball) moving at a velocity \(v\) in air, the drag force is given by
  \({F}_{\text{D}}=\frac{1}{2}{\mathrm{C\rho Av}}^{2},\)
  where \(C\) is the drag coefficient (typical values are given in this table in Drag Forces), \(A\) is the area of the object facing the fluid, and \(\rho \) is the fluid density.
• For small objects (such as a bacterium) moving in a denser medium (such as water), the drag force is given by Stokes’ law,
  \({F}_{\text{s}}=6\text{πηrv},\)
  where \(r\) is the radius of the object, \(\eta \) is the fluid viscosity, and \(v\) is the object’s velocity.

Glossary

drag force

\({F}_{\text{D}}\), found to be proportional to the square of the speed of the object; mathematically

where \(C\) is the drag coefficient, \(A\) is the area of the object facing the fluid, and \(\rho \) is the density of the fluid

Stokes’ law

\({F}_{s}=6\mathrm{\pi r\eta v}\), where \(r\) is the radius of the object, \(\eta \) is the viscosity of the fluid, and \(v\) is the object’s velocity