Let us derive a simplistic formula for terminal velocity:

Assume a spherical liquid drop of radius \(r\), density \(\rho\) and coefficient of viscosity \(\eta\). It is falling through air of density \(\sigma\).

The forces acting on it are:

Downward - Gravity

Upward - Viscous drag (in accordance with Stokes' Law)

Upward - Buoyant force (weight of displaced air)

At terminal velocity, our drop is in equilibrium:

\[\dfrac{4}{3} \pi r^3 \rho g = 6 \pi \eta r V_T + \dfrac{4}{3} \pi r^3 \sigma g\]

Simplifying this, we obtain the expression for terminal velocity:

Correct the key here is that they will attain the terminal velocity..!!
We can have a bonus question now..
If two identical drops fall from clouds at different heights, which will hit the groud with greater speed, the one from the higher cloud or the other one?

Assuming they both manage to reach terminal velocity (a very reasonable assumption), they will both hit the ground at the same speed (terminal velocity).

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestLet us derive a simplistic formula for terminal velocity:

Assume a spherical liquid drop of radius \(r\), density \(\rho\) and coefficient of viscosity \(\eta\). It is falling through air of density \(\sigma\).

The forces acting on it are:

At terminal velocity, our drop is in equilibrium:

\[\dfrac{4}{3} \pi r^3 \rho g = 6 \pi \eta r V_T + \dfrac{4}{3} \pi r^3 \sigma g\]

Simplifying this, we obtain the expression for terminal velocity:

\[\boxed{V_T = \dfrac{2 r^2 g}{9 \eta} (\rho -\sigma)}\]

This shows that a drop with larger radius will reach the ground at a higher terminal velocity.

Log in to reply

Correct the key here is that they will attain the terminal velocity..!!

We can have a bonus question now..

If two identical drops fall from clouds at different heights, which will hit the groud with greater speed, the one from the higher cloud or the other one?

Log in to reply

Assuming they both manage to reach terminal velocity (a very reasonable assumption), they will both hit the ground at the same speed (terminal velocity).

Log in to reply

Log in to reply

Assuming drops to be spheres, just use that odd equation for terminal velocity of bodies.

Log in to reply

Comment deleted Jun 09, 2015

Log in to reply

If drag force is more then weight is more as well... Which one is gonna dominate and why??

Log in to reply