Velocity Profile Representation for Fully Developed Turbulent Flows in Pipes: A Modified Power Law
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
In the design practices of many engineering applications, gross information about the flow field may suffice to provide magnitudes of the parameters that are essential to complete the design with reasonable accuracy. If such design parameters can be estimated following simpler steps, it may be possible to abandon the need to conduct expensive numerical and/or experimental works to produce them. In this work, we are interested in providing a generalized power law that depicts the velocity profile for fully developed turbulent flows. This law incorporates two fitting parameters m and n that represent the exponents of (1) a nondimensional length scale and (2) an overall exponent, respectively. These two parameters may be determined by fitting the experimental and/or computational data. In this work, fitting benchmark experimental and computational fluid dynamics (CFD) data found in the literature reveals that the parameter m changes over a relatively smaller range (between 1 and 2), while the parameter n changes over a wider range (between 1 and 12 for the range of Reynolds number considered). These two parameters (m and n) are, generally, not universal, and they depend on the Reynolds number (Re). A correlation was also developed to correlate n and Re in the turbulent flow region. In order to preserve the continuity of the derivative of the velocity profile at the centerline, a value of m equals 2 over the whole range of Re is recommended. Apart from the near wall area, the new law fits the velocity profile reasonably well. This generalized law abides to a number of favorable stipulations for the velocity profile, namely the continuity of derivatives and reduction to the laminar flow velocity profile for lower values of Re.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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