A ring of bubbles released underwater has radius

PHYSICS · Subjective · Fermi University Physics · Fluids & Continuum Physics · Kinematics, conservation laws and ideal flow · Kinematics, conservation laws and ideal flow

Fluid Dynamics, Ch Vorticity: its sources, its field and the motion of vortices

Problem

A ring of bubbles released underwater has radius R=3 cmR=3\,\mathrm{cm}, core radius a=3 mma=3\,\mathrm{mm}, and circulation Γ=0.02 m2 s−1\Gamma=0.02\,\mathrm{m^2\,s^{-1}}. Using Kelvin's formula for the self-induced speed of a thin vortex ring, U=Γ4πR[ln⁡ ⁣(8Ra)−14],U=\frac{\Gamma}{4\pi R}\left[\ln\!\left(\frac{8R}{a}\right)-\frac14\right], find the speed at which the ring translates.

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