Class 11

Physics

Mechanics

Mechanical Properties of Fluids

Two equal drops of water are falling through air with. steady velocity v. If the drops coalesced, what will be the new velocity ?

When the two equal drops coalesces, volume of water remains same and a bigger drop is formed. Lets say $r$ is radius of drop before these combine and $R$ is radius after these combine.

We have

$2×34 πr_{3}=34 πR_{3}⇒R=2_{1/3}r$

and we know that terminal velocity $V_{T}∝$ radius$_{2}$, so we have

$V_{T}V_{T} =r_{2}R_{2} $

$⇒V_{T}=(rR )_{2}V_{T}$

$=(2_{1/3})_{2}v$

$=2_{2/3}vm/s$