Rational approximation for solving an implicitly given Colebrook flow friction equation
| Autor: | Praks, Pavel, Brkić, Dejan |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Mathematics
Interdisciplinary Applications Engineering Civil approximations Logarithm General Mathematics 0207 environmental engineering Mathematics Applied Engineering Multidisciplinary 02 engineering and technology Wright Omega function 01 natural sciences 010305 fluids & plasmas pipe flow friction Approximation error 0103 physical sciences ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Computer Science (miscellaneous) Darcy friction factor formulae Applied mathematics Padé approximant Colebrook equation Colebrook–White experiment 020701 environmental engineering Engineering (miscellaneous) Mathematics Engineering Petroleum Transcendental function floating-point computations hydraulic resistance Engineering Mechanical Flow (mathematics) Symbolic regression symbolic regression Padé polynomials |
| Zdroj: | Scipedia Open Access Scipedia SL |
| Popis: | The empirical logarithmic Colebrook equation for hydraulic resistance in pipes implicitly considers the unknown flow friction factor. Its explicit approximations, used to avoid iterative computations, should be accurate but also computationally efficient. We present a rational approximate procedure that completely avoids the use of transcendental functions, such as logarithm or non-integer power, which require execution of the additional number of floating-point operations in computer processor units. Instead of these, we use only rational expressions that are executed directly in the processor unit. The rational approximation was found using a combination of a Pade approximant and artificial intelligence (symbolic regression). Numerical experiments in Matlab using 2 million quasi-Monte Carlo samples indicate that the relative error of this new rational approximation does not exceed 0.866%. Moreover, these numerical experiments show that the novel rational approximation is approximately two times faster than the exact solution given by the Wright omega function. Web of Science 8 1 art. no. 26 |
| Databáze: | OpenAIRE |
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