Sixty-four identical spherical drops fall through a viscous gas with terminal speed 5 cm/s. They coalesce into one spherical drop of the same material. Assuming Stokes' law remains valid, the new terminal speed is N cm/s. Find N.
Physics · Properties of solid and fluid · viscosity and terminal velocity
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Question

Sixty-four identical spherical drops fall through a viscous gas with terminal speed 5 cm/s. They coalesce into one spherical drop of the same material. Assuming Stokes' law remains valid, the new terminal speed is N cm/s. Find N.

Physics · Properties of solid and fluid · viscosity and terminal velocity

G1 Physics · Accepted Answer

Volume conservation gives R³ = 64r³. Therefore, R = 4r. For the same material and medium, vₜ ∝ r². Hence, v(new) = 5×(4)² = 5×16 = 80 cm/s. Therefore, N = 80.