A Simple Algorithm to Relate Measured Surface Roughness to Equivalent Sand-grain Roughness
Bibliographic record
Abstract
One of the most important resources available in the field of fluid mechanics, the Moody Chart gives Darcy friction factor as a function of Reynolds number and relative roughness. The experimentalists who generated the data correlated in the Moody Chart, however, roughened pipe surfaces by coating their internal surfaces with a monolayer of sand, the pipe wall roughness being defined as the average diameter of the sand grains. Thus, the sand-grain roughness values required for use with the Moody Chart are not derived from any direct measure of roughness using modern surface characterization equipment, such as an optical profilometer. Using direct measurements of surface roughness in fluid flow calculations may therefore result in significant error. In this paper we present a simple algorithm with which various measured surface roughness parameters can be converted to equivalent sand-grain roughness. For nearly every surface roughness value converted to equivalent sand-grain roughness using the algorithm, better agreement with fluid flow experiments is seen over using the raw roughness value.
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 0.005 |
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".