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

Explanation

The terminal velocity `upsilon` of a drop of radius r, density `rho` while falling through a viscous medium of viscosity `eta` and density `sigma` is
`upsilon = (2r^(2)(rho-sigma)g)/(9eta)` ..(i)
If R is the radius of the new drop formed when two drops coalesced, then
` 4/3 pt R^(3) = 4/3 pi r^(3) +4/3 pi r^(3) or R = (2)^(1//3)r`.
`:.` New terminal velocity of drop of radius R is
`upsilon' = (2[(2)^(1//3)r]^(2)(rho - sigma)g)/(9 eta) = (2)^(2//3)upsilon`
From (i) `.