16100lectre30_cj

16100lectre30_cj - 5 . 3 at 99 . ) ( = f : x V vx vx V vx V...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Solutions of the Laminar Boundary Layer Equations The boundary layer equations for incompressible steady flow, i.e., 2 2 0 y u dx dp y u v x u u y v x u e + = + = + µ ρ have been solved for a handful of important cases. We will look at the results for a flat plate and a family of solutions called Falkner-Skan Solutions. Flat Plate (Laminar): Blasius Solution For a flat plate, constant = p p e 0 = dx dp e Blasius was able to show that the boundary later equations could be rewritten to only depend on a parameter, vx V y 2 η and its derivatives The resulting solution has been tabulated and compared to experiments on the following page. Note: = = = = = V vx f V y u d df f f V y x u y w / 2 ) 0 ( where ) ( ) , ( 0 τ These values from the solution of ) ( f can be used to find: = V y x u y 99 . 0 ) , ( % 99 which at location δ Note: since ) ( set we , 0 x p p y p e = = , i.e. the boundary layer edge pressure.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Solutions of the Laminar Boundary Layer Equations 16.100 2002 2 From the table,
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 5 . 3 at 99 . ) ( = f : x V vx vx V vx V y 2 5 . 3 2 5 . 3 2 % 99 % 99 as grows layer boundary = = = Typically, this result is written non dimensionally as: x v x V x x x on based number s Reynold' where = Re Re . 5 % 99 We can also find: x w f x x V C x x Re 664 . 2 1 Re 664 . Re 7208 . 1 2 * = = = = Comment: At leading edge of a flat plate f C x gives this and ! In reality, the leading edge of an infinitely thin plate would have very large, but not infinite f C . The problem is that near the leading edge of a thin plate, the boundary layer equations are not correct and the Navier-Stokes equations are needed. Question: Why did the boundary layer approximation fail at x ?...
View Full Document

Page1 / 2

16100lectre30_cj - 5 . 3 at 99 . ) ( = f : x V vx vx V vx V...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online