Fluid mechanics.

Classical Mechanics Level 3

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

( 3 T ρ ( 1 r − 1 R ) ) 1 2 \left(\frac{3T}{\rho}\left(\frac{1}{r}-\frac{1}{R}\right)\right)^{\frac{1}{2}} ( T ρ ( 1 r − 1 R ) ) 1 2 \left(\frac{T}{\rho}\left(\frac{1}{r}-\frac{1}{R}\right)\right)^{\frac{1}{2}} ( 6 T ρ ( 1 r − 1 R ) ) 1 2 \left(\frac{6T}{\rho}\left(\frac{1}{r}-\frac{1}{R}\right)\right)^{\frac{1}{2}} ( 2 T ρ ( 1 r − 1 R ) ) 1 2 \left(\frac{2T}{\rho}\left(\frac{1}{r}-\frac{1}{R}\right)\right)^{\frac{1}{2}}

Sahil Silare by Sahil Silare , 20, India

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