A large number of droplets, each of radius, r coalesce to form a bigger drop of radius, R . An engineer designs a machine so that the energy released in this process is converted into the kinetic energy of the drop. Velocity of the drop is ( T= surface tension, = density)

Step-by-step solution

When small droplets coelesce to form a bigger drop, energy released in this process is given by, 4 R^3 T [ 1 r - 1 R ] Where, R= radius of big drop r= radius of small drop T= surface tension According to question aligned & 1 2 m v^2=4 R^3 T [ 1 r - 1 R ] & 1 2 [ 4 3 R^3 ] v^2=4 R^3 T [ 1 r - 1 R ] V^2 & = 6 T [ 1 r - 1 R ] V= [ 6 T ( 1 r - 1 R ) ]^ 1 2 aligned