## Numerical Values

Ordinarily, any numerical quantities that appear in equations that have a theoretical basis (such as that for ke above) are dimensionless and hence ''universal.'' However, many valuable engineering relations have an empirical rather than a theoretical basis, in which case this conclusion does not always hold. For example, a very useful expression for the (dimensionless) friction loss coefficient (Kf) for valves and fittings is

Here, NRe is the Reynolds number,* which is dimensionless, as are Kf and the constants K1 and Ki. However, the term ID is the internal diameter of

* We use the recommended notation of the AIChE for dimensionless groups that are named after their originator, i.e., a capital N with a subscript identifying the person the group is named for. However, a number of dimensionless quantities that are identified by other symbols; see, for example, Section IV.

the fitting, with dimensions of length. By the ''fruit salad'' law, the constant Kd in the term Kd/ID must also have dimensions of length and so is not independent of scale, i.e., its magnitude is defined only in specific units. In fact, its value is normally given in units of in., so ID must also be measured in inches for this value to be valid. If ID were to be measured in centimeters, for example, the value of Kd would be 2.54 times as large, because (1 in.)(2.54 cm/in.) = 2.54 cm.

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