Question

How to calculate terminal velocity while doing viscosity?

Answer 1

hey,

Terminal velocity is the highest velocity attainable by an object as it falls through a fluid (air is the most common example). It occurs when the sum of the drag force (Fd) and the buoyancy is equal to the downward force of gravity (FG) acting on the object.

hope it helps.........

Answer 2

I'm assuming this is for the standard case for a sphere falling in a liquid.

Let the terminal velocity be $v_{t}$.

Now assume the densities of the sphere and the liquid to be $\rho_{s}$ and $\rho_{l}$ respectively.

Hence, the buoyant force on the sphere is equal to:

$F_{b} = V * \rho_{l} * g$

The gravitational force is equal to:

$F_{g} = V * \rho_{s} * g$

The volume, V, is equal here, to:

$V = \frac{4}{3} \pi r^3$

And finally, the force due to viscosity is equal to:

$F_{v} = 6\pi \eta rv_{t}$

(assuming terminal velocity has been achieved, equal to $v_{t}$)

Since terminal velocity doesn't change, the net force must be zero on the body. Hence:

$F_{v} + F_{b} - F_{g} = 0$

Substituting and solving, the final equation is:

$v_{t} = \frac{2}{9} \frac{r^2 * (\rho_{s} - \rho_{l}) * g}{\eta}$

Finally, substitute the values of these constants (that should be given, or be derivable in the question) to find the terminal velocity.