{"id":7,"date":"2026-10-08T16:58:45","date_gmt":"2026-10-08T16:58:45","guid":{"rendered":"https:\/\/marouane.site\/index.php\/lessons\/the-no-slip-condition\/"},"modified":"2026-10-08T16:58:45","modified_gmt":"2026-10-08T16:58:45","slug":"the-no-slip-condition","status":"publish","type":"ms_lesson","link":"https:\/\/marouane.site\/index.php\/lessons\/the-no-slip-condition\/","title":{"rendered":"01 \u00b7 What happens at the wall?"},"content":{"rendered":"<p class=\"wp-block-paragraph\">A fluid touching a solid surface is often modeled as having the same velocity as that surface. At a stationary wall, that means zero fluid velocity right at the wall. This is the no-slip condition.<\/p><div class=\"wp-block-group ms-callout is-layout-constrained wp-block-group-is-layout-constrained\"><h3 class=\"wp-block-heading\">Key idea<\/h3><p class=\"wp-block-paragraph\">No-slip describes the velocity at the boundary. It does not say that the entire fluid is stationary.<\/p><\/div><h2 class=\"wp-block-heading\">Understand the idea<\/h2><p class=\"wp-block-paragraph\">In a viscous fluid, adjacent layers exchange momentum. When a pressure difference drives flow through a pipe, the stationary wall restrains the nearby fluid. Farther from the wall, the fluid can move faster. The velocity gradient is associated with viscous shear stress.<\/p><h2 class=\"wp-block-heading\">Engineering example<\/h2><p class=\"wp-block-paragraph\">For a straight circular pipe with stationary walls, the axial velocity is zero at the radius R. In fully developed laminar flow, the maximum occurs on the centreline. A numerical model should impose the intended wall condition and resolve the nearby gradients adequately.<\/p><h2 class=\"wp-block-heading\">Checkpoint<\/h2><details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>Does no-slip imply zero wall shear stress?<\/summary><p class=\"wp-block-paragraph\">No. A zero velocity at the wall can coexist with a nonzero velocity gradient. For a Newtonian fluid in this simple shear setting, shear stress is proportional to dynamic viscosity times the velocity gradient.<\/p><\/details><h2 class=\"wp-block-heading\">Where the assumption needs care<\/h2><p class=\"wp-block-paragraph\">No-slip is a useful macroscopic continuum model for many ordinary liquid and gas flows. Rarefied gases and some micro-scale or specially treated interfaces may require different boundary models.<\/p><h2 class=\"wp-block-heading\">Next step<\/h2><p class=\"wp-block-paragraph\">Now connect what happens at a boundary to the mass flowing through a cross-section.<\/p>","protected":false},"excerpt":{"rendered":"<p>Distinguish the wall velocity from the velocity gradient, and see why the difference matters.<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"_ms_course_id":6,"_ms_order":10,"_ms_minutes":5,"_ms_level":"Foundation","_ms_classification":"","_ms_evidence":"","_ms_accent":"cyan","footnotes":""},"ms_topic":[2],"class_list":["post-7","ms_lesson","type-ms_lesson","status-publish","hentry","ms_topic-fluid-mechanics"],"_links":{"self":[{"href":"https:\/\/marouane.site\/index.php\/wp-json\/wp\/v2\/ms_lesson\/7","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/marouane.site\/index.php\/wp-json\/wp\/v2\/ms_lesson"}],"about":[{"href":"https:\/\/marouane.site\/index.php\/wp-json\/wp\/v2\/types\/ms_lesson"}],"version-history":[{"count":0,"href":"https:\/\/marouane.site\/index.php\/wp-json\/wp\/v2\/ms_lesson\/7\/revisions"}],"wp:attachment":[{"href":"https:\/\/marouane.site\/index.php\/wp-json\/wp\/v2\/media?parent=7"}],"wp:term":[{"taxonomy":"ms_topic","embeddable":true,"href":"https:\/\/marouane.site\/index.php\/wp-json\/wp\/v2\/ms_topic?post=7"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}