[VIM3] 1.12 coherent derived unit

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derived unit that, for a given system of quantities and for a chosen set of base units, is a product of powers of base units with no other proportionality factor than one


NOTE 1 A power of a base unit is the base unit raised to an exponent.

NOTE 2 Coherence can be determined only with respect to a particular system of quantities and a given set of base units.

EXAMPLES If the metre, the second, and the mole are base units, the metre per second is the coherent derived unit of velocity when velocity is defined by the quantity equationv = dr/dt, and the mole per cubic metre is the coherent derived unit of amount-of-substance concentration when amount-of-substance concentration is defined by the quantity equation c = n/V. The kilometre per hour and the knot, given as examples of derived units in 1.11, are not coherent derived units in such a system of quantities.

NOTE 3 A derived unit can be coherent with respect to one system of quantities but not to another.

EXAMPLE The centimetre per second is the coherent derived unit of speed in a CGS system of units but is not a coherent derived unit in the SI.

NOTE 4 The coherent derived unit for every derived quantity of dimension one in a given system of units is the number one, symbol 1. The name and symbol of the measurement unit one are generally not indicated.



2 Measurement