The Drag Force on a Sphere - Donley, H. E. (1997)
Fluids resist the motion of objects traveling through them. ("Fluid" refers to either a liquid or a gas.) You work against this resistance, called a drag force, every time you go swimming or put your hand out of the window of a moving car. What causes this drag force and how do we construct a mathematical model for it? We will answer these questions for the case of a sphere moving through a fluid, or equivalently, a fluid flowing past a sphere. The drag force is in the opposite direction of the velocity of the object, tending to retard the motion of the object. The drag force has several sources--the friction of fluid flowing over the object and the difference in the pressure of the fluid immediately upstream and downstream of the object. The parameters effecting this force are: the velocity of the object (or the fluid), the size of the object, the shape of the object (we will consider only spherical objects), thedensity of the fluid, and the viscosity of the fluid. Viscosity is the internal frictional force per unit area of one layer of fluid passing over another layer. When you stir a pitcher of lemonade, it is viscosity that causes the lemonade to eventually come to rest after you withdraw the spoon, because the lemonade adhering to the sides of the pitcher slows down the moving lemonade in the interior of the pitcher. Appendix I lists the densities and viscosities of the fluids referred to in this unit.