First slide

Viscosity

Question

Two rain drops of same radius coalesce. Before doing so, each was moving with terminal velocity v. What is the terminal velocity of the single drop so formed ?

Easy

A

v / 2
B

2 v
C

v / 3
D

$(2)^{2 / 3}$

Solution

The radius R of the single drop so formed will be
$R = (2)^{1 / 3} r where r = radius of each drop. For each drop, mg = 6 πηrV For combined droP 2 mg = 6 {πηRv}^{'} From eqs . (i) and (ii), we get 2 \times 6 πηrv = 6 {πηRv}^{'} V^{'} = \frac{2 rv}{R} Now V^{'} = \frac{2 rv}{[(2)^{1 / 3} r]} = (2)^{2 / 3} v$

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