{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T21:42:07Z","timestamp":1772142127557,"version":"3.50.1"},"reference-count":48,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,19]],"date-time":"2022-01-19T00:00:00Z","timestamp":1642550400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002969","name":"Technology Agency of the Czech Republic","doi-asserted-by":"publisher","award":["CEET\u2014\"Center of Energy and Environmental Technologies\" TK03020027"],"award-info":[{"award-number":["CEET\u2014\"Center of Energy and Environmental Technologies\" TK03020027"]}],"id":[{"id":"10.13039\/501100002969","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The unknown friction factor from the implicit Colebrook equation cannot be expressed explicitly in an analytical way, and therefore to simplify the calculation, many explicit approximations can be used instead. The accuracy of such approximations should be evaluated only throughout the domain of interest in engineering practice where the number of test points can be chosen in many different ways, using uniform, quasi-uniform, random, and quasi-random patterns. To avoid picking points with undetected errors, a sufficient minimal number of such points should be chosen, and they should be distributed using proper patterns. A properly chosen pattern can minimize the required number of testing points that are sufficient to detect maximums of the error. The ability of the Sobol quasi-random vs. random distribution of testing points to capture the maximal relative error using a sufficiently small number of samples is evaluated. Sobol testing points that are quasi-randomly distributed can cover the domain of interest more evenly, avoiding large gaps. Sobol sequences are quasi-random and are always the same, which allows the exact repetition of scientific results.<\/jats:p>","DOI":"10.3390\/axioms11020036","type":"journal-article","created":{"date-parts":[[2022,1,19]],"date-time":"2022-01-19T08:20:57Z","timestamp":1642580457000},"page":"36","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Approximate Flow Friction Factor: Estimation of the Accuracy Using Sobol\u2019s Quasi-Random Sampling"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3913-7800","authenticated-orcid":false,"given":"Pavel","family":"Praks","sequence":"first","affiliation":[{"name":"IT4Innovations, VSB\u2013Technical University of Ostrava, 708 00 Ostrava-Poruba, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2502-0601","authenticated-orcid":false,"given":"Dejan","family":"Brki\u0107","sequence":"additional","affiliation":[{"name":"IT4Innovations, VSB\u2013Technical University of Ostrava, 708 00 Ostrava-Poruba, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1680\/ijoti.1939.13150","article-title":"Turbulent flow in pipes with particular reference to the transition region between the smooth and rough pipe laws","volume":"11","author":"Colebrook","year":"1939","journal-title":"J. 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