A boundary layer forms on a flat plate which is set parallel to an airstream, at standard sea level conditions, moving at 40m/s. (a) Sketch and label typical velocity profiles for the laminar and turbulent regions of the boundary layer. (b) Sketch the formation of a boundary layer on a flat plate, labelling the laminar region, the turbulent region, the laminar sub-layer and the transition point. (c) Calculate the distance from the leading edge to the transition point if the transition Reynolds number is 6 105. (d) By establishing whether the boundary layer is laminar or turbulent calculate the boundary layer general thickness, j, 0.85m from the leading edge. You may assume the boundary layer thicknesses are given by: For a laminar boundary layer, j = 5.48 Re0.5 For a turbulent boundary layer, j = 0.38 Re0.2 (e) Calculate the velocity at 4mm above the plate surface, 0.85m from the leading edge if the boundary layer profile can be described by: For a laminar boundary layer, m = 2 y j ? y j 2 For a turbulent boundary layer, m = y j 17 (f) Calculate the displacement and momentum thicknesses of the boundary layer at 0.85m from the leading edge and comment on their physical significance.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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A boundary layer forms on a flat plate which is set parallel to an airstream, at standard sea level conditions, moving at 40m/s. (a) Sketch and label typical velocity profiles for the laminar and turbulent regions of the boundary layer. (b) Sketch the formation of a boundary layer on a flat plate, labelling the laminar region, the turbulent region, the laminar sub-layer and the transition point. (c) Calculate the distance from the leading edge to the transition point if the transition Reynolds number is 6 105. (d) By establishing whether the boundary layer is laminar or turbulent calculate the boundary layer general thickness, j, 0.85m from the leading edge. You may assume the boundary layer thicknesses are given by: For a laminar boundary layer, j = 5.48 Re0.5 For a turbulent boundary layer, j = 0.38 Re0.2 (e) Calculate the velocity at 4mm above the plate surface, 0.85m from the leading edge if the boundary layer profile can be described by: For a laminar boundary layer, m = 2 y j ? y j 2 For a turbulent boundary layer, m = y j 17 (f) Calculate the displacement and momentum thicknesses of the boundary layer at 0.85m from the leading edge and comment on their physical significance.

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