ps_8a - fixed but given by a kinematic condition in this...

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0 2 . 2 0 Problem Set 8A Name: ____________________ 1. Supplementary Problem P9 2. A two-dimensional hydrofoil is placed in a uniform stream of horizontal velocity U and density ρ . For this problem, assume steady potential flow. Γ Γ o o U U o o c 2 / (a) If the hydrofoil is designed to generate a constant circulation Γ = Γ o , calculate the lift on the wing (per unit span) L = L in open water. ow (b) If the hydrofoil now operates at a distance c 2 / above a horizontal bottom, calculate L = L for this near-bottom operation. b (c) For fixed hydrofoil geometry and orientation, the circulation generated is actually not
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Unformatted text preview: fixed but given by a kinematic condition, in this case, that the vertical velocity at a distance c 2 / directly behind the vortex has to be V − = α U o . Γ U o c 2 / U o o U Γ c c o U 2 / 2 / 2 (i) Calculate the lift L ow and the lift coefficient C ( ≡ L 5 . 0 /( U c ) , for the hydrofoil in L o ow open water in terms of , U o and c. (ii) Again, this hydrofoil operates at a distance c 2 / over the bottom. Obtain L and C b L b in this case. (iii) Calculate the ratio C L b / C L in terms of . What is this value for = ? 1 . 0 ow...
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