Reynolds' law of similitude

Japanese: レーノルズの相似則 - レーノルズのそうじそく（英語表記）Reynolds’ law of similitude

This law of similarity governs flows without free surfaces where compressibility can be ignored. It is also called the law of mechanical similarity. It was discovered by O. Reynolds. It states that geometrically similar flows (for example, flows in circular pipes or objects of similar shape placed in a flow) are also mechanically similar if _the Reynolds number Re is the same. In this case, not only the flow pattern but also the pressure distribution will match perfectly if written in a dimensionless form (non-dimensional form). In other words, the pressure coefficient, obtained by dividing pressure p by 1/2ρ U ² ( _ρ is the density of the fluid and U is the flow velocity), is a function only of Re and the position coordinate X / L , which is non-dimensionalized by the characteristic length L.

Source: Heibonsha World Encyclopedia, 2nd Edition Information

Japanese:

圧縮性を無視できる自由表面のない流れを支配する相似則。力学的相似則ともいう。O.レーノルズが見いだした。幾何学的に相似な流れ(例えば形が相似な物体が流れの中におかれた場合や円管内の流れなど)は，レーノルズ数R_eが同一であれば力学的にも相似であるというもの。このとき，流れのパターンばかりでなく，圧力分布なども次元のない形(無次元形)で書けば完全に一致する。すなわち，圧力pを1/2ρU²(ρは流体の密度，Uは流速)で割った圧力係数，は，R_eと，代表長さLで無次元化した位置座標X/Lだけの関数である。

出典　株式会社平凡社世界大百科事典第２版について　情報

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