Question

N identical liquid drops are falling with terminal velocity V0 if they combine to form a single drop then new terminal velocity of the big drop will be

Answer 1

new terminal velocity is (N⅔)v0

terminal velocity is given as, v = 2r²(ρ - σ)g/η

here it is clear that terminal velocity is directly proportional to r².

now, N identical drops coalesce and form a big drop.

so, N × volume small drop = volume of small drop

⇒N × 4/3πr³ = 4/3πR³

⇒Nr³ = R³

⇒R = (³√N )r

now, terminal velocity ratio, v1/v2 = (r/R)²

⇒v0/v = {r/(³√N)r}² = 1/N⅔

⇒v = N⅔ v0

hence, new terminal velocity is (N)⅔ v0.

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