65_add_Added Masses of Ship Structures.pdf - 2.4 Added Masses of a Duplicated Shipframe Contour Moving in Unlimited Fluid 53 Using the formula(2.14 we

65_add_Added Masses of Ship Structures.pdf - 2.4 Added...

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2.4 Added Masses of a Duplicated Shipframe Contour Moving in Unlimited Fluid 53 Using the formula ( 2.14 ) we get (up to an arbitrary additive constant) the condition ψ = U y z U z y ω 2 ( y 2 + z 2 ) , (2.15) to be fulfilled on the contour. Taking into account ( 2.15 ) one represents the function w(τ) in the form w(τ) = U y w 2 (τ) + U z w 3 (τ) + ωw 4 (τ), where the functions w 2 (τ) , w 3 (τ) and w 4 (τ) are determined by geometric prop- erties (i.e. the shape) of the contour only; these functions characterize the per- turbed potential flow of the fluid under the motion of the contour with unit ve- locities along the axes Oy , Oz and under rotation, respectively. The functions w k (τ) = ϕ k (τ) + k (τ) are regular outside of the contour and vanish at infinity. On the contour C their imaginary parts, according to ( 2.15 ), satisfy the conditions ψ 2 | C = z ; ψ 3 | C = − y ; ψ 4 | C = − 1 2 ( y 2 + z 2 ) . (2.16) To find the potential of the fluid around contour C in the τ -plane it is sufficient to find the function τ = y + iz = f (ζ), (2.17)
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