{"id":{"repo_id":"uab","oai_identifier":"oai:digitalcommons.library.uab.edu:etd-collection-8123"},"canonical_url":"https://search.dev.ndltd.org/etd/uab/oai:digitalcommons.library.uab.edu:etd-collection-8123","repository":{"repo_id":"uab","name":"University of Alabama Birmingham","base_url":"https://digitalcommons.library.uab.edu/do/oai/"},"display":{"title":"Boundary Layer Development in Laminar Swirl Flow Inside a Circular Pipe.","abstract":"Velocity distributions within the developing boundary layer of a swirling flow of an incompressible fluid in a circular pipe are investigated in this study. It is assumed that the intake conditions are such that the fluid, moving in the direction of the axis of the pipe, enters the pipe with an axial component which is practically constant over the whole cross section. A boundary layer initially of zero thickness is formed inside the pipe, and this layer increases in thickness downstream until its thickness becomes equal to the radius of the pipe. The solution for the boundary layer during the early stages of its development will be considered for three cases :1. When the pressure, axial velocity and tangential velocity immediately outside of the boundary-layer are constant ; 2. When the pressure varies in the axial direction in a prescribed manner and the tangential velocity outside the boundary-layer is constant ; 3. When the pressure and tangential velocity both vary along the cylinder axis in a prescribed manner. In case one, a numerical solution was obtained for small values of axial location z. In case two, a numerical solution was determined which used the transformation ∈= (∨Z / R2 Uo)1/2 for small values of z and ∈ , where ∈ is the transformation used in case two as a function of z; V is kinematic viscosity, z is any point along the pipe, R is the radius of the pipe, and Uo is constant velocity along the z axis. In case three, a numerical solution was investigated under the specific condition that V=V0+C∈ (where V is the swirling velocity along the z axis, V0 is the constant swirling velocity along the z axis, C is constant, and ∈ is the transformation function of z) for small values of z, using the transformation ∈ = (∨Z / R2 Uo)1/2 .","abstract_html":"Velocity distributions within the developing boundary layer of a swirling flow of an incompressible fluid in a circular pipe are investigated in this study. It is assumed that the intake conditions are such that the fluid, moving in the direction of the axis of the pipe, enters the pipe with an axial component which is practically constant over the whole cross section. A boundary layer initially of zero thickness is formed inside the pipe, and this layer increases in thickness downstream until its thickness becomes equal to the radius of the pipe. The solution for the boundary layer during the early stages of its development will be considered for three cases :1. When the pressure, axial velocity and tangential velocity immediately outside of the boundary-layer are constant ; 2. When the pressure varies in the axial direction in a prescribed manner and the tangential velocity outside the boundary-layer is constant ; 3. When the pressure and tangential velocity both vary along the cylinder axis in a prescribed manner. In case one, a numerical solution was obtained for small values of axial location z. In case two, a numerical solution was determined which used the transformation ∈= (∨Z / R2 Uo)1/2 for small values of z and ∈ , where ∈ is the transformation used in case two as a function of z; V is kinematic viscosity, z is any point along the pipe, R is the radius of the pipe, and Uo is constant velocity along the z axis. In case three, a numerical solution was investigated under the specific condition that V=V0+C∈ (where V is the swirling velocity along the z axis, V0 is the constant swirling velocity along the z axis, C is constant, and ∈ is the transformation function of z) for small values of z, using the transformation ∈ = (∨Z / R2 Uo)1/2 .","abstract_has_math":false,"creators":["Shodja, Mohssen"],"institution":null,"degree_name":null,"degree_level":"Thesis","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1983,"date_issued":"1983-01-01T08:00:00Z","date_published":"1983-01-01T08:00:00Z","updated_at":"2026-07-24T05:06:09Z","subjects":["Swirling flow","Velocity distributions","Cylinder axis","Numerical solution","Swirling velocity"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.library.uab.edu/etd-collection/7131","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Shodja, Mohssen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Swirling flow","Velocity distributions","Cylinder axis","Numerical solution","Swirling velocity"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.library.uab.edu/etd-collection/7131"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Velocity distributions within the developing boundary layer of a swirling flow of an incompressible fluid in a circular pipe are investigated in this study. It is assumed that the intake conditions are such that the fluid, moving in the direction of the axis of the pipe, enters the pipe with an axial component which is practically constant over the whole cross section. A boundary layer initially of zero thickness is formed inside the pipe, and this layer increases in thickness downstream until its thickness becomes equal to the radius of the pipe. The solution for the boundary layer during the early stages of its development will be considered for three cases :1. When the pressure, axial velocity and tangential velocity immediately outside of the boundary-layer are constant ; 2. When the pressure varies in the axial direction in a prescribed manner and the tangential velocity outside the boundary-layer is constant ; 3. When the pressure and tangential velocity both vary along the cylinder axis in a prescribed manner. In case one, a numerical solution was obtained for small values of axial location z. In case two, a numerical solution was determined which used the transformation ∈= (∨Z / R2 Uo)1/2 for small values of z and ∈ , where ∈ is the transformation used in case two as a function of z; V is kinematic viscosity, z is any point along the pipe, R is the radius of the pipe, and Uo is constant velocity along the z axis. In case three, a numerical solution was investigated under the specific condition that V=V0+C∈ (where V is the swirling velocity along the z axis, V0 is the constant swirling velocity along the z axis, C is constant, and ∈ is the transformation function of z) for small values of z, using the transformation ∈ = (∨Z / R2 Uo)1/2 ."]},{"key":"dc:title","label":"Title","values":["Boundary Layer Development in Laminar Swirl Flow Inside a Circular Pipe."]}]}],"canonical_facts":{"dc:creator":["Shodja, Mohssen"],"dc:description.abstract":["Velocity distributions within the developing boundary layer of a swirling flow of an incompressible fluid in a circular pipe are investigated in this study. It is assumed that the intake conditions are such that the fluid, moving in the direction of the axis of the pipe, enters the pipe with an axial component which is practically constant over the whole cross section. A boundary layer initially of zero thickness is formed inside the pipe, and this layer increases in thickness downstream until its thickness becomes equal to the radius of the pipe. The solution for the boundary layer during the early stages of its development will be considered for three cases :1. When the pressure, axial velocity and tangential velocity immediately outside of the boundary-layer are constant ; 2. When the pressure varies in the axial direction in a prescribed manner and the tangential velocity outside the boundary-layer is constant ; 3. When the pressure and tangential velocity both vary along the cylinder axis in a prescribed manner. In case one, a numerical solution was obtained for small values of axial location z. In case two, a numerical solution was determined which used the transformation ∈= (∨Z / R2 Uo)1/2 for small values of z and ∈ , where ∈ is the transformation used in case two as a function of z; V is kinematic viscosity, z is any point along the pipe, R is the radius of the pipe, and Uo is constant velocity along the z axis. In case three, a numerical solution was investigated under the specific condition that V=V0+C∈ (where V is the swirling velocity along the z axis, V0 is the constant swirling velocity along the z axis, C is constant, and ∈ is the transformation function of z) for small values of z, using the transformation ∈ = (∨Z / R2 Uo)1/2 ."],"dc:identifier":["https://digitalcommons.library.uab.edu/etd-collection/7131"],"dc:subject":["Swirling flow","Velocity distributions","Cylinder axis","Numerical solution","Swirling velocity"],"dc:title":["Boundary Layer Development in Laminar Swirl Flow Inside a Circular Pipe."],"thesis:degree_level":["Thesis"]},"updated_at":"2026-07-24T05:06:09Z"}