5.13 Viscous Drag and Stokes' Law

5.13 Viscous Drag and Stokes' Law

The frictional effect between different layers of a flowing fluid is described in terms of viscosity of the fluid. Viscosity measures, how much force is required to slide one layer of the liquid over another layer. Substances that do not flow easily, such as thick tar and honey, etc., have large coefficients of viscosity, usually denoted by Greek letter $\eta$. Substances which flow easily, like water, have small coefficient of viscosity. Since liquids and gases have non zero viscosity, therefore, a force is required if an object is to be moved through them. Even the small viscosity of the air causes a large retarding force on a car as it travels at high speed. If you stick out your hand out of the window of a fast moving car, you can easily recognize that considerable force has to be exerted on your hand to move it through the air. These are typical examples of the following fact.

An object moving through a fluid experiences a retarding force called a drag force. The drag force increases as the speed of the object increases.

Even in the simplest cases, the exact value of the drag force is difficult to calculate. However, the case of a sphere moving through a fluid is of great importance.

The drag force $F$ on a sphere of radius $r$ moving slowly with speed $v$ through a fluid of viscosity $\eta$ is given by Stokes' law as under:

However, at high speeds the force is no longer simply proportional to speed.

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