Inferring the shape of a solid inside a draining tank from its liquid level dynamics
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913499965292544 |
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| author | Fabusola, Gbenga Simon, Cory M. |
| author_facet | Fabusola, Gbenga Simon, Cory M. |
| contents | We aim to reconstruct the shape of an exogenous, heavy solid contained in a tank from measurements of the liquid level in the tank as it drains (driven by gravity) through a small orifice in its side. (Because the solid displaces liquid, the rate of decrease of the liquid level provides information about the cross-sectional area of the solid at that height; as the liquid level drops, it "scans" the area of the solid as a function of height.) We combine mathematical modeling, Bayesian statistical inversion, Monte Carlo simulation, and wet experiments of a tank draining of water to demonstrate and test our ability to infer the cross-sectional area of the exogenous solid as a function of height. In our experiment, the posterior distribution over the [held-out] shape of the solid (a bottle) agreed reasonably well with our length-measurements (<10% mean reconstruction error on its radius). Our approach may be practically useful to non-destructively characterize the geometry of an unknown solid, or a packed bed of solid particles, contained in an opaque tank. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_14503 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inferring the shape of a solid inside a draining tank from its liquid level dynamics Fabusola, Gbenga Simon, Cory M. Fluid Dynamics We aim to reconstruct the shape of an exogenous, heavy solid contained in a tank from measurements of the liquid level in the tank as it drains (driven by gravity) through a small orifice in its side. (Because the solid displaces liquid, the rate of decrease of the liquid level provides information about the cross-sectional area of the solid at that height; as the liquid level drops, it "scans" the area of the solid as a function of height.) We combine mathematical modeling, Bayesian statistical inversion, Monte Carlo simulation, and wet experiments of a tank draining of water to demonstrate and test our ability to infer the cross-sectional area of the exogenous solid as a function of height. In our experiment, the posterior distribution over the [held-out] shape of the solid (a bottle) agreed reasonably well with our length-measurements (<10% mean reconstruction error on its radius). Our approach may be practically useful to non-destructively characterize the geometry of an unknown solid, or a packed bed of solid particles, contained in an opaque tank. |
| title | Inferring the shape of a solid inside a draining tank from its liquid level dynamics |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2408.14503 |