流体運動における応力と変位との関係

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概要

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• Conclusions obtained from solutions of Navier-Stokes' equations which are accepted generally to hold in fluid motion lead to various hydrodynamical paradoces. In order to avoid the defects the author proposes a generalized relation between stress and displacement, introducing new functions of space coordinates and time μ_1 (x, y, t) and μ_2 (x, y, t). The equations derived from the new relation are solved for the case of a plate placed parallel to the flow. Examining numerical results obtained from these solutions, the author get the following conclusions. 1) The relation which is adopted in the derivation of Navier-Stokes' equations is true only in a limited part of boundary layer and at very low velocity. μ_1 differs from unity and varies widely as velocity increases. 2) Laminar and turbulent flow are distinguished by behevier of μ_1 (x, y, t) along the direction of flow. In laminar flow μ_1 (x, y, t) decrease, and in turbulent flow increases as x increases. In a transient flow μ_1 (x, y, t) becomes constant for all x. 3) The law of similarity is effected by a characteristic number K. The curve which is considered as typical one for frictional resistane of a plate must be observed from the author's point of view. Points obtained by Blasius' experiment correspond to the author's results for L = 0.5 and show a good agreement. At all the author's solutions give a good agreement with experiments, can explain detailed mechanism of the flow in boundary layer and remove hydrodynamical paradoces previously encountered in the solutions of Navier-Stokes' equations.

• 明治大学の論文

著者

• 片岡 正治

  明治大学

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