FR - MAE130B Final Review Changzheng Huang Final Review 1....

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MAE130B Final Review Changzheng Huang
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Final review Changzheng Huang 2 Final Review 1. Ch 9. External Flow 2. Ch 11. Compressible Flow
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Final review Changzheng Huang 3 U D L θ x yp τ w U Given a pressure and shear stress distribution, compute drag and lift. ( ) ( ) () ( ) cos sin sin cos xw yw dF pdA dA dF pdA dA θ τθ = + =− + cos sin sin cos x wp f p f D dF p dA dA D D L dF p dA dA L L θτ == + = + = + = + ∫∫ (1) Ch 9. External Flow: lift and drag Drag parallel to free stream Lift perpendicular to free stream. 2 2 2 2 D L D C UA L C ρ = =
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Final review Changzheng Huang 4 y δ U ( ) 0.99 u U = y U y U * , δΘ Boundary layer thickness δ Boundary layer displacement thickness δ * Displaced mass = mass flow deficit () * 0 * 0 1 UU u d y u dy U ρδ ρ =− ⎛⎞ ⎜⎟ ⎝⎠ (1) Ch 9. External Flow: boundary layer thickness Boundary layer momentum thickness Θ Displaced momentum = momentum deficit 0 0 1 U U U u udy uu dy ρρ Θ=
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Final review Changzheng Huang 5 Boundary layer equation for a flat plate, U U P x y Boundary layer Outer flow x= 0 δ ( x ) (1) Ch 9. External Flow: Prandtle/Blasius boundary layer solution 2 2 0 uv xy uu u y ν ∂∂ += What are the boundary conditions? To seek a similarity solution, u y f U δ = How to estimate δ based on order of magnitude analysis? How to evaluate boundary layer thickness from Blasius solution?
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Final review Changzheng Huang 6 x (1) Plate width: b U U () w x τ 0 x dS ud S F ρ •= Vn v v y (2) h δ (x) u=u(y) Boundary layer edge Streamline Conservation of mass and x-momentum for steady flow, (1) (2) 0 0 x w dS
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FR - MAE130B Final Review Changzheng Huang Final Review 1....

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