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16100lectre25

# 16100lectre25 - grow with x The skin friction can be found...

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Falkner-Skan Flows For the family of flows, we assume that the edge velocity, is of the following form: ) ( x u e arbitrary constant = = K Kx x u m e ) ( The pressure can be calculated from the Bernoulli in the outer, inviscid flow: 1 2 2 2 . 2 1 = = = + m m e e e e e e x K dx dp dx du u dx dp const u p ρ i f 0 > m then < 0 dx dp e favorable pressure gradient i f 0 < m then > 0 dx dp e adverse pressure gradient These edge velocities result from the following inviscid flows: m m + 1 2 β y ) ( x u e y x π π β ) ( x u e 0 = x Flow around a corner (diffusion) Wedge flow 0 2 β 2 0

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Falkner-Skan Flows Some important cases: 0 , 0 = = m β : flat plat (Blasius) 1 , 1 = = m : plane stagnant point The boundary layer independent variable η from the Blasius solution generalizes to: vx x u m y e ) ( 2 1 + and ) ( ) ( ) , ( 1 m f x u y x u e = An interesting case in 1 , 1 = = m , i.e. stagnation point flow: ) ( x u e x x e K u = inviscid flow velocity increases away from stag. pt. at 0 = x y x x v K y 2 1 1 + = v K y = is independent of x Boundary layer at a stagnation point does not
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Unformatted text preview: grow with x ! The skin friction can be found from: ) ( ) ( 11 2 o f y d f d x u y u y e y w = = = ∂ ∂ = ∂ ∂ = µ τ 16.100 2002 2 Falkner-Skan Flows Since vx x u m y vx x u m y e e ) ( 2 1 ) ( 2 1 + = ∂ ∂ ⇒ + = η ⇒ ) ( ) ( 2 1 ) ( 11 o f vx x u m x u e e w + = µ τ tabulated The skin friction coefficient is normalized by ) ( 2 1 2 x u e ρ : ) ( ) ( 2 1 2 ) ( 2 1 ) ( 11 2 o f x x u v m x u x C e e w f + = ≡ ⇒ v x x u o f m C e x x f ) ( Re Re ) ( 2 1 2 11 ≡ + = Note: separation occurs when = f C which means . From the table, this occurs for ) ( 11 = o f 19884 . − = β ⇒ This is only an angle of 18 o ! 18 o 16.100 2002 3...
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16100lectre25 - grow with x The skin friction can be found...

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