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Unformatted text preview: 16.100 Homework Assignment # 8 Due: Monday, November 14, 9am Reading Assignment: No new reading. Relevant reading is same as from Homework #7. Anderson, 3 rd edition: Chapter 17, pages 787 – 801 Chapter 18, pages 803 – 810 Problem 1 In this problem, you will derive the 2D integral momentum equation for boundary layers. The start of this derivation is the incompressible, 2D boundary layer equations: (B) (A) = ∂ ∂ + ∂ ∂ ∂ ∂ + ∂ ∂ − = ∂ ∂ + ∂ ∂ y v x u y x p y u v x u u e τ ρ where is the pressure at the edge of the boundary layer and e p y u ∂ ∂ = µ τ . a) Assuming the flow outside of the boundary layer is inviscid, irrotational flow such that Bernoulli’s equation holds, show that Equation (A) can be manipulated to: (C) 1 y x u u y u v x u u e e ∂ ∂ + ∂ ∂ = ∂ ∂ + ∂ ∂ τ ρ b) Multiply Equation (B) by u and add to Equation (C). Then, integrate the resulting equation from to to find the boundary layer integral momentum equation:...
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 Fall '03
 willcox
 Dynamics, Aerodynamics, Airfoil, integral momentum equation

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