A fine water jet of radius ( , ) breaks up under Rayleigh's inviscid instability

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Instability, transition and turbulence · Instability, transition and turbulence

Fluid Dynamics, Ch Hydrodynamic instability: the normal-mode method

Problem

A fine water jet of radius

a = 0.50\,\mathrm{mm}

(

\rho = 998\,\mathrm{kg\,m^{-3}}

\gamma = 0.0728\,\mathrm{N\,m^{-1}}

) breaks up under Rayleigh's inviscid instability. For a water jet of radius

1.0\,\mathrm{mm}

the fastest-growing wavelength is

9.02\,\mathrm{mm}

with an

e

-folding time of

11\,\mathrm{ms}

, and one wavelength of liquid forms one drop. ((a)) Find the fastest-growing wavelength for the

0.50\,\mathrm{mm}

jet. ((b)) Find its

e

-folding growth time. ((c)) Find the radius of the drop that each wavelength of liquid forms.

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