回転体を過ぎる軸対称の流れに関する1つの近似法則

概要

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The velocity distribution over a body of revolution of arbitrary shape moving in an infinite mass of incompressible inviscid fluid is considered. The equation of motion is written in the form: ∂F/∂z=ψ/2y^2, where F = Φ+ iΨ/y, z = x + iy, in which Φ is the velocity potential, and Ψ the stream function. Based on the consideration that F → U(3z + z)/4 as z → ∞ and Ψ ≒0 near the surface of the body, the equation is approximately integrated in the form: F = U(3z + z)/4 + g(z) as z → ∞ = f(z) near the body, where f(z) and q(z) are analytic functions. From the condition that the above two forms for F should connect smoothly with each other, f(z) and g(z) are determined explicitly in terms of the transformation function which maps the outside region of the meridian section of the body onto the outside region of the unit circle. Hence an approximate rule is obtained which states that the velocity induced on the surface of a body of revolution moving parallel to its axis in an infinite mass of incompressible perfect fluid is equal to half that for a cylinder of the same cross section moving with the same velocity perpendicular to its axis. By comparing the results of application of the rule to the case of ellipsoids of revolution with known exact results, it is found that the rule is especially accurate for bodies with nearly spherical shape.
宇宙航空研究開発機構の論文
1953-12-21