2. You are working for a glider manufacturer and have been asked to analyse the laminar boundary layer at a certain point on the smooth wing. The velocity profile at this point, u(y), is given by: 2 3 U 2/4= 3 (-) ² - 2 (²) ³² + A (1) Us + B where 8 is the boundary-layer thickness and us is the velocity at the edge of the boundary layer. A and B are constants. a) Determine the values of A and B such that the primary boundary conditions for the velocity profile are satisfied. Is it necessary to apply any auxiliary boundary conditions? b) Evaluate the boundary-layer shape factor, H. c) At the point of separation, the wall shear stress goes from positive to negative. Thus, show that the boundary layer at this location is on the point of separating. d) Show that the pressure on the wing surface is increasing with downstream distance. Is this consistent with your calculations showing that the boundary layer is approaching separation? Explain your reasoning.
2. You are working for a glider manufacturer and have been asked to analyse the laminar boundary layer at a certain point on the smooth wing. The velocity profile at this point, u(y), is given by: 2 3 U 2/4= 3 (-) ² - 2 (²) ³² + A (1) Us + B where 8 is the boundary-layer thickness and us is the velocity at the edge of the boundary layer. A and B are constants. a) Determine the values of A and B such that the primary boundary conditions for the velocity profile are satisfied. Is it necessary to apply any auxiliary boundary conditions? b) Evaluate the boundary-layer shape factor, H. c) At the point of separation, the wall shear stress goes from positive to negative. Thus, show that the boundary layer at this location is on the point of separating. d) Show that the pressure on the wing surface is increasing with downstream distance. Is this consistent with your calculations showing that the boundary layer is approaching separation? Explain your reasoning.
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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Transcribed Image Text:2.
You are working for a glider manufacturer and have been asked to
analyse the laminar boundary layer at a certain point on the smooth
wing. The velocity profile at this point, u(y), is given by:
И
3
y
= 3 (²) ²³ - 2 ( ² ) ² + A ( ² ) + B
(15)
Us
where 8 is the boundary-layer thickness and us is the velocity at the
edge of the boundary layer. A and B are constants.
a) Determine the values of A and B such that the primary boundary
conditions for the velocity profile are satisfied. Is it necessary to apply
any auxiliary boundary conditions?
b) Evaluate the boundary-layer shape factor, H.
c) At the point of separation, the wall shear stress goes from positive to
negative. Thus, show that the boundary layer at this location is on the
point of separating.
d) Show that the pressure on the wing surface is increasing with
downstream distance. Is this consistent with your calculations showing
that the boundary layer is approaching separation? Explain your
reasoning.
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