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1. Consider the laminar boundary layer over a flat plate. Let 8(x) be the exact boundary layer thickness along the plate, where x is the distance from the leading edge of the flat plate. If we approximate the velocity profile by u/U = 2(y/5) - 2(y/8)³ + (y/8)4 for y≤ 8 and u = U for y > 8. (a) Show that this profile satisfies the appropriate boundary conditions; (b) Determine the boundary layer displacement thickness, 8* (x), momentum thickness 0(x), and the wall shear stress Tw in terms of 8(x) and μ and U if needed.

1. Consider the laminar boundary layer over a flat plate. Let 8(x) be the exact boundary layer thickness along the plate, where x is the distance from the leading edge of the flat plate. If we approximate the velocity profile by u/U = 2(y/5) - 2(y/8)³ + (y/8)4 for y≤ 8 and u = U for y > 8. (a) Show that this profile satisfies the appropriate boundary conditions; (b) Determine the boundary layer displacement thickness, 8* (x), momentum thickness 0(x), and the wall shear stress Tw in terms of 8(x) and μ and U if needed.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter5: Analysis Of Convection Heat Transfer
Section: Chapter Questions
Problem 5.26P
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1. Consider the laminar boundary layer over a flat plate. Let 8(x) be the exact boundary layer thickness along the plate, where x is the distance from the leading edge of the flat plate. If we approximate the velocity profile by u/U = 2(y/5) - 2(y/8)³ + (y/8)4 for y≤ 8 and u = U for y > 8. (a) Show that this profile satisfies the appropriate boundary conditions; (b) Determine the boundary layer displacement thickness, 8* (x), momentum thickness 0(x), and the wall shear stress Tw in terms of 8(x) and μ and U if needed.
Transcribed Image Text:1. Consider the laminar boundary layer over a flat plate. Let 8(x) be the exact boundary layer thickness along the plate, where x is the distance from the leading edge of the flat plate. If we approximate the velocity profile by u/U = 2(y/5) - 2(y/8)³ + (y/8)4 for y≤ 8 and u = U for y > 8. (a) Show that this profile satisfies the appropriate boundary conditions; (b) Determine the boundary layer displacement thickness, 8* (x), momentum thickness 0(x), and the wall shear stress Tw in terms of 8(x) and μ and U if needed.
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