Viscous Drag

We probably have discussed what Viscosity is. Now we know that viscosity opposes motion, just like friction.

The opposing force experienced by an object when it moves through a viscous fluid is called the Viscous Drag.

What is the force that drives you backward when you want to swim across water? It's viscosity. It is the force (air drag) that pushes your car backwards when you go at a high speed.

Let's see what the expression for Viscous Drag is.

Consider a small body of radius $r$ moving at constant velocity $v$ through a fluid of viscosity $\eta$.

Then, the viscous drag ($F$) working upon the object is given by

$F= 6 \pi\, \eta \,r \,v$

Now we'll look at what Terminal Velocity is!

Have you ever watched rain with patience on a random romantic rainy day? Did you notice that the rain is falling at an uniform velocity rather than an uniform speed?

This is called a Terminal Velocity. Let us try to find out why this happens.

Consider a small spherical object of radius $r$ of density $\sigma$ falling through a liquid of density $\rho$.

There must be a point when the two forces will balance each other and a constant velocity will be reached.

Since, the forces balance each other, we can write the following:

$\frac{4}{3} \pi r^3 \sigma g = 6 \pi\, \eta \,r \,v + \frac{4}{3} \pi r^3 \rho g$

We conclude that this is the expression for terminal velocity:

$v = \frac{2}{9} \frac{r^2}{\eta} (\rho - \sigma) g$