# Linear drag in a liquid and terminal velocity

## Homework Statement

An object moving in a liquid experiences a linear drag force: D =(bv, direction opposite the motion), where b is a constant called the drag coefficient. For a sphere of radius R, the drag constant can be computed as b = 6 pi n R, where n is the viscosity of the liquid.

1. Find an algebraic expression for the terminal speed Vterm of a spherical particle of radius R and mass m falling through a liquid of viscosity n.

2. Water at 20C has viscosity n = 1.0 x 10^-3N. Sand grains have density 2400 kg/m^3. Suppose a 1.1mm diameter sand grain is dropped into a 55m-deep lake whose water is a constant 20C. If the sand grain reaches terminal speed almost instantly (a quite good approximation), how long will it take the sand grain to settle to the bottom of the lake?.

## Homework Equations

Vterm = sqrt(4mg / A)

D = 1/4 A v^2

Area = 2 pi r^2 [cross section of spherical partical to calculate drag]

## The Attempt at a Solution

I'm puzzled where to go. I have my Vterm formula, but I don't know where the drag coefficient (b) plays into that. I've looked through my textbook a few times and I'm missing a clear explanation of how this works.

It's the hardest problem from the set (first year physics for engineers). <_____<

## Answers and Replies

When the sphere attains terminal velocity, what forces balance?