2.9 DIMENSIONAL FORMULAE AND DIMENSIONAL EQUATIONS

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The expression which shows how and which of the base quantities represent the dimensions of a physical quantity is called the dimensional formula of the given physical quantity. For example, the dimensional formula of the volume is [M^0 L^3 T^0 ], and that of speed or velocity is [M^0 L T^−1]. Similarly, [M^0 L T^−2] is the dimensional formula of acceleration and [M L^−3 T^0] that of mass density.

An equation obtained by equating a physical quantity with its dimensional formula is called the dimensional equation of the physical quantity. Thus, the dimensional equations are the equations, which represent the dimensions of a physical quantity in terms of the base quantities. For example, the dimensional equations of volume [V], speed [v], force [F ] and mass density [ρ] may be expressed as


[V] = [M^0 L^3 T^0]


[v] = [M^0 L T^−1]


[F] = [M L T^−2]


[ρ] = [M L^−3 T0]

The dimensional equation can be obtained from the equation representing the relations between the physical quantities. The dimensional formulae of a large number and wide variety of physical quantities, derived from the equations representing the relationships among other physical quantities and expressed in terms of base quantities are given in Appendix 9 for your guidance and ready reference.