A Dynamic Approach to Determining the Surface Tension of a Fluid
Bibliographic record
Abstract
A new formulation has been developed that predicts flow rate of a stream draining from an orifice under the influence of gravity. This model is different from conventional formulations in that it includes the surface tension of the liquid. Results with water and ethylene glycol at various temperatures indicate that it is necessary to account for surface tension under certain conditions including small orifice diameters and operation under low head values. This model is most relevant for liquids of high surface tension including melts such as molten metals, slags and salts. These conditions are accounted for in the Bond number (ρgroh/σ) which is a dimensionless quantity useful in determining conditions when surface tension is expected to have considerable impact. When an operation is such that the 1/Bo approaches unity, the formulation has the greatest relevance. The formulation provides unique possibilities in measuring surface tension since this property is related to flow rate and head which are two variables that can be experimentally determined. Calibrations of the discharge coefficient, Cd, are required to determine frictional losses in the orifice. The surface tension of water at 321.5 K was calculated to be 0.067 N/m which is 1.75% from the value quoted in the literature. The measurement is highly susceptible to error. A rigorous error analysis was performed on the formulation and it was determined that as 1/Bo approaches unity, accuracy in the surface tension measurement significantly improves. It is expected that melt systems are best suited for such measurements since these liquids often exhibit large values of 1/Bo for a given orifice design.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".