A hydrophone in the pool below a weir records the sound of bubbles that the plunging…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Solid continuum mechanics and complex fluids · Solid continuum mechanics and complex fluids

Bending, Ringing, Breaking and Flowing, Ch Bubbles, drops and cavitation

Problem

A hydrophone in the pool below a weir records the sound of bubbles that the plunging water carries down and releases at a depth of about

5\,\mathrm m

, where they ring. The spectrum peaks at

2.0\,\mathrm{kHz}

. Take water with

\rho = 1000\,\mathrm{kg\,m^{-3}}

and

\gamma = 0.072\,\mathrm{N\,m^{-1}}

, air with

\kappa = 1.4

, atmospheric pressure

101.3\,\mathrm{kPa}

at the surface and

g = 9.8\,\mathrm{m\,s^{-2}}

. ((a)) Estimate the radius of the bubbles behind the peak. ((b)) An analyst who uses the surface pressure instead of the pressure at the bubbles' depth would infer what radius, and by what factor would that estimate be wrong? ((c)) Show that surface tension may be neglected here.

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