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- W2139567269 abstract "The collapse time of a closed cavity that is initially at rest in an incompressible, inviscid fluid of density ρ and ambient pressure p ∞ has the form [ t_1 = {rho/(p_{infty} - p_c)}^{frac{1}{2}}ell, ] where p c is the internal pressure, which is assumed to remain constant during collapse, and [ell ] is a length that depends only on the geometry of the cavity. A variational formulation of the dynamical problem is constructed from Jacobi's statement of the principle of least action. A single-degree-of-freedom approximation is developed from the similarity hypothesis that the cavity collapses through a family of similar surfaces with volume as the generalized co-ordinate. Two-degree-of-freedom approximations are given for both prolate and oblate spheroidal cavities and are used to obtain error estimates for the similarity approximation (approximately 2% for the limiting case of a needle-like, prolate spheroid and approximately ½ % for a disk-like, oblate spheroid). A perturbation analysis is developed for an approximately spherical cavity, which is found to have the same collapse time as a spherical cavity of equal volume within a factor 1 + O ( e 4 ), where e is a representative eccentricity. A first-order correction for surface tension is obtained." @default.
- W2139567269 created "2016-06-24" @default.
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- W2139567269 date "1966-08-01" @default.
- W2139567269 modified "2023-09-23" @default.
- W2139567269 title "The collapse time of a closed cavity" @default.
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- W2139567269 doi "https://doi.org/10.1017/s0022112066000387" @default.
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