Power Law Turbulent Velocity Profile in Transitional Rough Pipes
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Bibliographic record
Abstract
Abstract Alternate power law velocity profile u+=Aζα in transitional rough pipe fully turbulent flow, has been proposed, in terms of new appropriate inner rough wall variables (ζ=Z+∕ϕ, uϕ=u∕ϕ), and new parameters Rϕ=Rτ∕ϕ termed as the roughness friction Reynolds number, Reϕ=Re∕ϕ termed as the roughness Reynolds number and ϕ termed as roughness scale (along with normal wall coordinate Z=y+ϵr where ϵr is the shift of the origin of boundary layer due to the rough wall, Z+=Zuτ∕ν and u+=u∕uτ). The envelope of the power law shows that the power law constants α and A depend on the parameter Rϕ (i.e., α=α(Rϕ) and A=A(Rϕ)) but explicitly independent of the wall roughness parameter h∕δ (roughness height h in pipe of radius δ). The roughness scale ϕ has been related to the roughness function ΔU+ of Clauser representing the velocity shift caused by wall roughness. The present results of the velocity profile, just slightly above the wall roughness level h, remain valid for all types of wall roughness. The data of Nikuradse for sand-grain roughness, in transitional and fully rough pipes, has been considered, which provides good support to the predictions of an alternate power law velocity profile, based on single parameter Rϕ, the roughness friction Reynolds number.
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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)
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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