Any quantity observed physically has dimensions. However, when these quantities are multiplied or divided, a simple dimensionless number is sometimes obtained. This is called a dimensionless number. The simplest dimensionless number is the ratio of the length and width of a rectangle. In general, ratios are dimensionless numbers. The Mach number is the ratio of the speed of an object to the speed of sound, so it is also a dimensionless number. There are also dimensionless numbers that are not simply ratios. A typical example is the Reynolds number. The Reynolds number is the product of speed U (m/s) and length L (m) divided by the kinetic viscosity ν (m2/s), and is indeed a dimensionless number. Source: Heibonsha World Encyclopedia, 2nd Edition Information |
物理的に観測される量は必ず次元をもっている。しかしこれらの量を掛けたり割ったりすると無次元の単なる数が得られることがある。これを無次元数という。最も簡単な無次元数は長方形の縦,横の長さの比である。一般に比は無次元数である。マッハ数は物体の速度と音速の比であるから無次元数である。単なる比ではない無次元数もある。その代表的なものはレーノルズ数である。レーノルズ数は速度U(m/s)と長さL(m)の積を動粘度ν(m2/s)で割ったものであって,確かに無次元数である。
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