{"id":"https://openalex.org/W299809771","doi":null,"title":"Report on Investigation of Developed Turbulence","display_name":"Report on Investigation of Developed Turbulence","publication_year":1949,"publication_date":"1949-01-18","ids":{"openalex":"https://openalex.org/W299809771","mag":"299809771"},"language":"en","primary_location":{"id":"pmh:oai:UFDC:AA00006233_00001","doi":null,"is_oa":false,"landing_page_url":"http://ufdc.ufl.edu/AA00006233/00001","pdf_url":null,"source":{"id":"https://openalex.org/S4306400471","display_name":"University of Florida Digital Collections (University of Florida)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I33213144","host_organization_name":"University of Florida","host_organization_lineage":["https://openalex.org/I33213144"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"volume":null,"type":"article","indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044581007","display_name":"Ludwig Prandtl","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"L. Prandtl","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5044581007"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":37,"citation_normalized_percentile":{"value":0.08318099,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"5","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13951","display_name":"Fluid dynamics and aerodynamics studies","score":0.0024999999441206455,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12022","display_name":"Hydraulic flow and structures","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fully-developed-turbulence","display_name":"fully developed turbulence","score":0.8709999918937683},{"id":"https://openalex.org/keywords/pipe-flow","display_name":"pipe flow","score":0.7080000042915344},{"id":"https://openalex.org/keywords/smooth-tubes","display_name":"smooth tubes","score":0.6050000190734863},{"id":"https://openalex.org/keywords/friction-factor","display_name":"friction factor","score":0.6240000128746033},{"id":"https://openalex.org/keywords/reynolds-number","display_name":"Reynolds number","score":0.6340000033378601},{"id":"https://openalex.org/keywords/wall-friction","display_name":"wall friction","score":0.6970000267028809}],"concepts":[{"id":"https://openalex.org/C182748727","wikidata":"https://www.wikidata.org/wiki/Q178932","display_name":"Reynolds number","level":3,"score":0.6888495683670044},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.6395555734634399},{"id":"https://openalex.org/C87040749","wikidata":"https://www.wikidata.org/wiki/Q428971","display_name":"Power law","level":2,"score":0.5654126405715942},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.5278499126434326},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5241827368736267},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.5177285075187683},{"id":"https://openalex.org/C8673219","wikidata":"https://www.wikidata.org/wiki/Q6503510","display_name":"Law of the wall","level":4,"score":0.5009176731109619},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.452475905418396},{"id":"https://openalex.org/C94656876","wikidata":"https://www.wikidata.org/wiki/Q1695787","display_name":"Shear velocity","level":3,"score":0.4304421544075012},{"id":"https://openalex.org/C2986887940","wikidata":"https://www.wikidata.org/wiki/Q5503426","display_name":"Friction factor","level":4,"score":0.420046329498291},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3721905052661896},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.283025860786438},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14415323734283447},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:UFDC:AA00006233_00001","doi":null,"is_oa":false,"landing_page_url":"http://ufdc.ufl.edu/AA00006233/00001","pdf_url":null,"source":{"id":"https://openalex.org/S4306400471","display_name":"University of Florida Digital Collections (University of Florida)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I33213144","host_organization_name":"University of Florida","host_organization_lineage":["https://openalex.org/I33213144"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:casi.ntrs.nasa.gov:20050029454","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/2060/20050029454","pdf_url":null,"source":{"id":"https://openalex.org/S4377196257","display_name":"NASA STI Repository (National Aeronautics and Space Administration)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210124779","host_organization_name":"National Aeronautics and Space Administration","host_organization_lineage":["https://openalex.org/I4210124779"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"CASI","raw_type":"NACA-TM-1231"},{"id":"mag:299809771","doi":null,"is_oa":false,"landing_page_url":"https://digital.library.unt.edu/ark:/67531/metadc64715/m2/1/high_res_d/20050029454.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, justice, and strong institutions","score":0.5099999904632568}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2918335093","https://openalex.org/W84077846","https://openalex.org/W594950368","https://openalex.org/W2001051415","https://openalex.org/W1638056456","https://openalex.org/W1929763273","https://openalex.org/W241545936","https://openalex.org/W7139410241","https://openalex.org/W2133165935","https://openalex.org/W2051627471"],"abstract_inverted_index":{"The":[0],"recent":[1],"experiments":[2],"by":[3,24],"Jakob":[4],"and":[5,26],"Erk,":[6],"on":[7],"the":[8,36,43,47,60,63,86,97,102,106,109,112,115,121,125,137,169,177,187,196,207,218,221],"resistance":[9,87,158],"of":[10,46,85,99,114,124,171,176,184,211,220],"flowing":[11],"water":[12],"in":[13,18,111,118,174,194,203,209],"smooth":[14],"pipes,":[15],"which":[16,104,195],"are":[17,214],"good":[19],"agreement":[20],"with":[21,67],"earlier":[22],"measurements":[23],"Stenton":[25],"Pannell,":[27],"have":[28],"caused":[29],"me":[30],"to":[31,42,53,59,120,142,150],"change":[32],"my":[33],"opinion":[34],"that":[35,108,136,140,167,183,206],"empirical":[37,157],"Blasius":[38],"law":[39,101,170],"(resistance":[40],"proportional":[41],"7/4":[44],"power":[45],"mean":[48],"velocity)":[49],"was":[50],"applicable":[51],"up":[52],"arbitrarily":[54],"high":[55],"Reynolds":[56,69],"numbers.":[57],"According":[58],"new":[61],"tests":[62],"exponent":[64],"approaches":[65],"2":[66],"increasing":[68],"number,":[70],"where":[71],"it":[72,133],"remains":[73],"an":[74],"open":[75],"question":[76],"whether":[77],"or":[78,202],"not":[79,215],"a":[80,152,189,212],"specific":[81],"finite":[82],"limiting":[83],"value":[84],"factor":[88],"lambda":[89],"is":[90,134],"obtained":[91],"at":[92,186],"R":[93],"=":[94],"infinity.":[95],"With":[96],"collapse":[98],"Blasius'":[100],"requirements":[103],"produced":[105],"relation":[107],"velocity":[110,153,172],"proximity":[113,175,210],"wall":[116,126,178,213],"varied":[117],"proportion":[119],"7th":[122],"root":[123],"distance":[127,219],"must":[128],"also":[129],"become":[130],"void.":[131],"However,":[132],"found":[135,193],"fundamental":[138,161],"assumption":[139],"led":[141],"this":[143],"relationship":[144],"can":[145,163,191],"be":[146,164,192],"generalized":[147],"so":[148,165],"as":[149,179,181],"furnish":[151],"distribution":[154,173],"for":[155,168,182],"any":[156],"law.":[159],"These":[160],"assumptions":[162],"expressed":[166],"well":[180],"friction":[185],"wall,":[188],"form":[190],"pipe":[197],"diameter":[198],"no":[199],"longer":[200],"occurs,":[201],"other":[204],"words,":[205],"processes":[208],"dependent":[216],"upon":[217],"opposite":[222],"wall.":[223]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-10-01T08:54:57.152042","created_date":"2016-06-24T00:00:00"}