Friction Factor Prediction for Newtonian and Non-Newtonian Fluids in Pipe Flows Using Neural Networks
Bibliographic record
Abstract
The friction factors (f) for Newtonian, power law, Bingham plastic and Herschel-Bulkely fluids were predicted after developing and training four neural networks (NN). Three and four layer NN and Wardnet slab were used for f predictions. When average velocity (u), pipe diameter (D), fluid density and fluid viscosity were used for predicting f values for Newtonian fluids, average absolute error was only 0.00004 with standard deviation of 0.00050 and correlation coefficient (r) of 0.9981. When using flow behaviour index (n),u, D, density and consistency coefficient (k) as inputs of an NN for power law fluids, the average absolute error of predicting f was 0.0116 with r of 0.9998. For prediction of f using yield stress, u, D, density and plastic viscosity as inputs to an NN for Bingham plastic fluids, the average absolute error was 0.0044 with r of 0.9961. The average absolute error was 0.0169 with r of 0.9996 for the prediction of f taking n, yield stress, u, D, density and k as inputs to an NN for Herschel-Bulkely fluids. Inputs except n and density and output were transformed on a logarithmic base to 10 scale. Prediction using log f or extension of f limit reduced prediction errors.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| 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 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".