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A dimensionless velocity profile, u= u/U = Co + C₁-C₂y, where, y =y/6, is proposed to approximate the laminar boundary layer solution for flow around a corner. The outer flow velocity can be expressed as, U = C²x, where, C, is constant. Boundary layer has the thickness of, 5, where, Co, C₁, and C₂, are the constants to be determined in order to match the boundary conditions in the boundary layer, including the no slip condition, match the outer flow velocity and zero shear stress at the edge of the boundary layer. Apart from that, an additional boundary condition is proposed. (0²u) U (du

A dimensionless velocity profile, u= u/U = Co + C₁-C₂y, where, y =y/6, is proposed to approximate the laminar boundary layer solution for flow around a corner. The outer flow velocity can be expressed as, U = C²x, where, C, is constant. Boundary layer has the thickness of, 5, where, Co, C₁, and C₂, are the constants to be determined in order to match the boundary conditions in the boundary layer, including the no slip condition, match the outer flow velocity and zero shear stress at the edge of the boundary layer. Apart from that, an additional boundary condition is proposed. (0²u) U (du

Elements Of Electromagnetics
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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e. b. C. d. a. EME3026 Question 2 A dimensionless velocity profile, u* = u/U = Co + C₁-C₂y, where, y = y/8, is proposed to approximate the laminar boundary layer solution for flow around a corner. The outer flow velocity can be expressed as, U = C²x, where, C, is constant. Boundary layer has the thickness of, 8, where, Co. C₁, and C₂, are the constants to be determined in order to match the boundary conditions in the boundary layer, including the no slip condition, match the outer flow velocity and zero shear stress at the edge of the boundary layer. Apart from that, an additional boundary condition is proposed. a²u dyz y=0 Given the fluid kinematic viscosity, v = 1.46 x 10-5 m²/s and the constant, C² = 0.09 s-¹. Validate the proposed additional boundary condition. FLUID DYNAMICS U (dU Find the velocity profile, u", by evaluating the constant, Co, C₁, and C₂. = --- Determine the displacement thickness and momentum thickness in term of boundary layer thickness. Show that the general momentum integral equation can be rewritten as, dom (do (26m + v) √u do dx √2Cx Calculate the boundary layer thickness. + X where, Sm, and, 8m, are the displacement and momentum thickness respectively. Tri 1, 2023/2024
Transcribed Image Text:e. b. C. d. a. EME3026 Question 2 A dimensionless velocity profile, u* = u/U = Co + C₁-C₂y, where, y = y/8, is proposed to approximate the laminar boundary layer solution for flow around a corner. The outer flow velocity can be expressed as, U = C²x, where, C, is constant. Boundary layer has the thickness of, 8, where, Co. C₁, and C₂, are the constants to be determined in order to match the boundary conditions in the boundary layer, including the no slip condition, match the outer flow velocity and zero shear stress at the edge of the boundary layer. Apart from that, an additional boundary condition is proposed. a²u dyz y=0 Given the fluid kinematic viscosity, v = 1.46 x 10-5 m²/s and the constant, C² = 0.09 s-¹. Validate the proposed additional boundary condition. FLUID DYNAMICS U (dU Find the velocity profile, u", by evaluating the constant, Co, C₁, and C₂. = --- Determine the displacement thickness and momentum thickness in term of boundary layer thickness. Show that the general momentum integral equation can be rewritten as, dom (do (26m + v) √u do dx √2Cx Calculate the boundary layer thickness. + X where, Sm, and, 8m, are the displacement and momentum thickness respectively. Tri 1, 2023/2024
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