[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-565514-105":3,"detail-sidebar-cat-1-en-105":81,"doc-detail-565514-en":127},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","fluid-mechanics-5perdasdecarga","Fluid Mechanics - 5PerdasdeCarga","","Fluid mechanics discussion of turbulent pipe flow velocity profiles and friction behavior. Derives the outer turbulent layer velocity defect law and presents the power-law velocity profile with exponent tied to Reynolds number, including comparisons to laminar flow. Explains viscous sublayer relevance, how relative roughness affects the friction factor, and defines hydrodynamically rough versus smooth surfaces. Summarizes the dependence of Darcy friction factor on Reynolds number and relative roughness, leading to the Colebrook equation and the Moody chart for engineering use.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/template/","Template",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/template/general/","General",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/template/fluid-mechanics-5perdasdecarga/565514/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/fluid-mechanics-5perdasdecarga/565514.png","ImageObject",442,249,{"name":42,"@type":43},"Malam Tenang","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-27","2026-10-13",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",7,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is the velocity defect law in turbulent pipe flow?","Question",{"text":63,"@type":64},"The velocity defect law describes how the normalized velocity profile in the core region depends on distance from the centerline. It is independent of the fluid’s viscosity in that region because eddy motion dominates.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Why does the power-law velocity profile not work for wall shear stress?",{"text":68,"@type":64},"The power-law model implies an infinite velocity gradient at the wall, so it cannot provide a correct wall shear stress. It also fails to give a zero slope at the pipe centerline.",{"name":70,"@type":61,"acceptedAnswer":71},"How do Reynolds number and relative roughness affect the friction factor?",{"text":72,"@type":64},"In fully developed turbulent pipe flow, the friction factor depends on Reynolds number and the relative roughness e/D. Since the functional form is not obtained theoretically, results come from experiments and are summarized by the Colebrook equation and Moody chart.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},565514,1792123979,{"code":4,"msg":82,"data":83},"success",[84,89,94,99,104,109,114,119,124],{"id":85,"doc_module":22,"doc_module_name":25,"category_name":86,"show_sort_weight":87,"slug":88},11,"Presentations",90,"presentations",{"id":90,"doc_module":22,"doc_module_name":25,"category_name":91,"show_sort_weight":92,"slug":93},12,"Resumes",80,"resumes",{"id":95,"doc_module":22,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},14,"Invoices",70,"invoices",{"id":100,"doc_module":22,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},15,"Posters",60,"posters",{"id":105,"doc_module":22,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},16,"Social Media",50,"social-media",{"id":110,"doc_module":22,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},17,"Forms",40,"forms",{"id":115,"doc_module":22,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},18,"Letters",30,"letters",{"id":120,"doc_module":22,"doc_module_name":25,"category_name":121,"show_sort_weight":122,"slug":123},21,"Paper Templates",5,"papers-templates",{"id":125,"doc_module":22,"doc_module_name":25,"category_name":29,"show_sort_weight":4,"slug":126},158,"general-158",{"code":4,"msg":82,"data":128},{"doc_id":79,"user_id":129,"nickname":42,"user_avatar":130,"doc_module":22,"category_id":125,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":131,"file_id":132,"file_url":133,"file_type":134,"file_size":135,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":100,"language":136,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":137,"faqs":138,"seo_title":139,"seo_description":12,"update_tm":140,"read_time":122},962093532863,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","cen72367_ch08 .qxd  \n12/1/04  \n7:37  \nPM  \nPage  \n340  \n340  \nFLUID MECHANICS  \nFIGURE 8–26  \nPower-law velocity profiles for fully developed turbulent flow ina pipe for different exponents, and its comparison with the laminar velocity profile.  \nA good approximation for the outer turbulent layer of pipe flow can be obtained by evaluating the constant B in Eq. 8–46 from the requirement that maximum velocity in a pipe occurs at the centerline where r ! 0. Solving for B from Eq. 8–46 by setting y ! R & r ! R and u ! umax, and substituting it back into Eq. 8–46 together with k ! 0.4 gives  \nOuter turbulent layer:  \numaxu~~ ~~u ! 2.5 ln R~~ ~~R&~~ ~~r  \n(8–48)  \nThe deviation of velocity from the centerline value umax & u is called the velocity defect, and Eq. 8–48 is called the velocity defect law. This relation shows that the normalized velocity profile in the core region of turbulent flow in a pipe depends on the distance from the centerline and is independent of the viscosity of the fluid. This is not surprising since the eddy motion is dominant in this region, and the effect of fluid viscosity is negligible.  \nNumerous other empirical velocity profiles exist for turbulent pipe flow. Among those, the simplest and the best known is the power-law velocity profile expressed as  \nPower-law velocity profile: ~~ ~~uumax ! a~~ ~~yRb 1/n or ~~ ~~uumax ! a 1 & rRb 1/n (8–49) where the exponent n is a constant whose value depends on the Reynolds number. The value of n increases with increasing Reynolds number. The value n ! 7 generally approximates many flows in practice, giving rise to the term one-seventh power-law velocity profile.  \nVarious power-law velocity profiles are shown in Fig. 8–26 for n ! 6, 8, and 10 together with the velocity profile for fully developed laminar flow for comparison. Note that the turbulent velocity profile is fuller than the laminar one, and it becomes more flat as n (and thus the Reynolds number) increases. Also note that the power-law profile cannot be used to calculate wall shear stress since it gives a velocity gradient of infinity there, and it fails to give zero slope at the centerline. But these regions of discrepancy constitute a small portion of flow, and the power-law profile gives highly accurate results for turbulent flow through a pipe.  \nDespite the small thickness of the viscous sublayer (usually much less than 1 percent of the pipe diameter), the characteristics of the flow in this layer are very important since they set the stage for flow in the rest of the pipe. Any irregularity or roughness on the surface disturbs this layer and affects the flow. Therefore, unlike laminar flow, the friction factor in turbulent flow is a strong function of surface roughness.  \nIt should be kept in mind that roughness is a relative concept, and it has significance when its height e is comparable to the thickness of the laminar sublayer (which is a function of the Reynolds number) . All materials appear“rough” under a microscope with sufficient magnification. In fluid mechanics, a surface is characterized as being rough when the hills of roughness protrude out of the laminar sublayer. A surface is said to be smooth when the sublayer submerges the roughness elements. Glass and plastic surfaces are generally considered to be hydrodynamically smooth.  \nThe Moody Chart  \nThe friction factor in fully developed turbulent pipe flow depends on the Reynolds number and the relative roughness e/D, which is the ratio of the  \ncen72367_ch08 .qxd  \n12/1/04  \n7:37  \nPM  \nPage  \n341  \nmean height of roughness of the pipe to the pipe diameter. The functional form of this dependence cannot be obtained from a theoretical analysis, and all available results are obtained from painstaking experiments using artificially roughened surfaces (usually by gluing sand grainsof a known size on the inner surfaces of the pipes) . Most such experiments were conducted by Prandtl’sstudent J. Nikuradse in 1933, followed by the works of other","cbCaidMqvD5KTqhX","https://ap.wps.com/l/cbCaidMqvD5KTqhX","pdf",186795,"English","# Velocity profiles in turbulent pipe flow\n## Velocity defect law and outer turbulent layer\n## Power-law velocity profile and comparisons\n# Effect of surface roughness on friction factor\n## Hydrodynamically rough vs smooth surfaces\n## Colebrook equation and Moody chart","[{\"question\":\"What is the velocity defect law in turbulent pipe flow?\",\"answer\":\"The velocity defect law describes how the normalized velocity profile in the core region depends on distance from the centerline. It is independent of the fluid’s viscosity in that region because eddy motion dominates.\"},{\"question\":\"Why does the power-law velocity profile not work for wall shear stress?\",\"answer\":\"The power-law model implies an infinite velocity gradient at the wall, so it cannot provide a correct wall shear stress. It also fails to give a zero slope at the pipe centerline.\"},{\"question\":\"How do Reynolds number and relative roughness affect the friction factor?\",\"answer\":\"In fully developed turbulent pipe flow, the friction factor depends on Reynolds number and the relative roughness e/D. Since the functional form is not obtained theoretically, results come from experiments and are summarized by the Colebrook equation and Moody chart.\"}]","Fluid Mechanics - 5PerdasdeCarga | PDF",1791855662]