Summarizing Motion of an Object in a Viscous Fluid

Summary

• When an object moves in a fluid, there is a different form of the Reynolds number \({N\prime }_{\text{R}}^{}=\cfrac{\rho \text{vL}}{\eta }\text{(object in fluid),}\) which indicates whether flow is laminar or turbulent.
• For \({N\prime }_{\text{R}}^{}\) less than about one, flow is laminar.
• For \({N\prime }_{\text{R}}^{}\) greater than \({\text{10}}^{6}\), flow is entirely turbulent.

Glossary

viscous drag

a resistance force exerted on a moving object, with a nontrivial dependence on velocity

terminal speed

the speed at which the viscous drag of an object falling in a viscous fluid is equal to the other forces acting on the object (such as gravity), so that the acceleration of the object is zero