By Harold A. Simon
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Sample text
There is a clear advantage in avoiding such constants by using consistent units. The square foot as a unit of area is said to be consistent with the foot as a unit of length and K = 1. The unit of area is now called a derived unit. M, L, and T are called fundamental units or dimensions. Notice that it would have been equally logical to take area as a fundamental unit with the unit of length derived from it. Other derived units occurring in mechanics, based on mass, length, and time as fundamental, are given below.
The Reynolds number may be shown to represent the ratio of inertial force to viscous force. The force coefficient expresses the ratio of the force exerted to the inertial force. Second, even though the result expressed is universal, so one unique curve of C against Re for a particular body might be expected regardless of the units commonly employed by the experimenter, certain pitfalls must be guarded against. It is common, for example, to define force coefficients as (F/(l/2)pl/ 2 / 2 ), but this is not always true.
But a dependent variable will be a function of independent variables and parameters. In the case of a body immersed in a flowing fluid, the density, viscosity, overall drag force, and body dimensions may be parameters, while the local pressure, velocity, coordinates, and time would be variables. The results from dimensional analysis are more specific if the problem can be phrased in terms of parameters only. If there are only a few independent parameters, dimensional analysis can lead to a complete determination of the form of the required relationship down to a numerical constant which must be obtained by other methods.