A Simple Universal Equation for Grain Settling Velocity
Why this work is in the frame
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Bibliographic record
Abstract
Abstract A new equation is presented for sediment fall velocity as a function of grain diameter for given values of fluid viscosity and fluid and solid density. Sediment fall velocity is a fundamental parameter in the modeling and interpretation of fluviatile and coastal deposition. The equation applies to the entire range of viscous to turbulent conditions, and its simple explicit form makes it easy to use in computer models and other applications in sedimentology, geomorphology, and engineering. The equation is derived from dimensional analysis and converges on Stokes' law for small grains and a constant drag coefficient for large grains. Its two physically interpretable parameters are easily adjusted for shape effects or for the use of sieve diameter rather than nominal grain diameter. It gives a close fit to published and new experimental data for both quartz sand and low-density materials, with no more error than previous equations of more complicated form.
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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 | 0.002 | 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) | 0.001 | 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