摩擦抵抗に対するForm Effect(2) : 波動現象の影響(昭和25年11月造船協会秋季講演会)
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概要
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1. When the curvature of the surface of a ship is everywhere small, the following equation of motion is obtained, assuming that within the boundary layer, the pressure does not vary in the normal direction to the surface. u ∂u/∂x=-1/ρ ∂p/∂x+X+ν ∂^2u/∂y^2 (1) The X-axis is in the direction of stream line, the y-axis in the direction of surface normal, u the velocity of the stream, p the pressure of the fluid at y=δ (δ=the thickness of boundary layer) and X is x-component of gravity. ρ & v is the density and the kinematic viscosity of the fluid respectively. Take ζ-axis in the direction vertically upwards, the following well-known relations are obtained. p=const-ρV^2/z-ρgζ X=-g ∂ζ/δx where V=[u]_<y=δ> and g is the acceleration of gravity. The equation (1) is then transformed into the form u・∂u/∂x=∂/∂x (V^2/z)+ν ∂^2u/∂y^2 (5) Therefore, if the distribution of fluid velocity, and the form of stream lines are known for potential flow, the solution of 2-dimensional cases will readily give the distribution of tangential stress etc. along stream lines. The equation (5) also show that the effects of gravity come in evidence in the form of dynamic pressure only. 2. According to above mentioned idea, a calculation of boundary layer thickness at free surface was worked out. The result show good proximity to experimental values. Corresponding to the velocity increases & decreases at wave surface, the thickness of boundary layer has thin & thick values, the rate of growth of layer fluctuates about some positive values. 3. Assuming the variation of fluid velocity in the vertical direction, the distribution of tangential stresses, the frictional resistance etc. were calculated about a cylinder of parabolic waterline (L/B=16.5). The frictional resistance along a stream line has a tendency to increase near the free suaface and the total frictional resistance is about 4% greater than that calculated on the basis of Froudes method.
- 社団法人日本船舶海洋工学会の論文
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