Oscillations of Water Levels in Vertical Semi-Immersed Tubes: Analytical Solutions and Experimental Verification
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Bibliographic record
Abstract
Experimental results for water level oscillations in vertical tubes, together with a theoretical solution for the flow in such tubes considering local and distributed energy losses, are presented and compared. The experimental data were obtained in small scale experiments, allowing adequately controlling the oscillations. The governing equation for the oscillations was obtained by applying the conservation laws of mass, momentum and energy for fluids. It is a second order nonlinear differential equation which was reduced to a first order differential Bernoulli equation. The obtained solution is composed by two different equations, one for the upwards motion and the other for the downwards motion, which together reproduce the oscillatory damped behavior of such flows. Numerical solutions of the differential equation were also checked. The experimental data and the theoretical and numerical results showed a good agreement between measured and calculated values of velocity and surface level for the first periods of oscillation.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it