A ripple tank is filled to a depth of with silicone oil of density and surface tension

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Waves, acoustics and compressible flow · Waves, acoustics and compressible flow

Fluids and Continuum Physics, Ch Surface gravity and capillary waves

Problem

A ripple tank is filled to a depth of

0.25\ \mathrm{m}

with silicone oil of density

\rho = 960\ \mathrm{kg\,m^{-3}}

and surface tension

\gamma = 0.021\ \mathrm{N\,m^{-1}}

. Take

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

, treat the oil as inviscid and incompressible and the waves as small-amplitude and irrotational. ((a)) Find the minimum possible phase speed of a wave on this oil surface and the wavelength at which it occurs, quoting the capillary length

\ell_c = \sqrt{\gamma/(\rho g)}

. ((b)) A vertical wire of diameter

1.0\ \mathrm{mm}

is drawn through the surface at

0.40\ \mathrm{m\,s^{-1}}

. Compute the Weber number

\mathrm{We} = \rho U^{2} d/\gamma

of the wire, using the wire diameter

d

as the length scale. ((c)) The tank also carries a wave of wavelength

0.30\ \mathrm{m}

and amplitude

4.0\ \mathrm{mm}

. Show that at this wavelength the wave is a deep-water gravity wave (surface tension negligible), and find its phase speed and the energy flux per metre of crest.

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