Course Physics1

The dimensional analysis is a theoretical tool for interpreting problems based on the dimensions of the physical quantities involved: length, time, mass, etc. Dimensional analysis makes it possible to^[1]

• Determine the unit of a physical quantity based on the essential units (meter, second, kilogram, etc.)

• Research into the nature of physical quantities

• Search for the homogeneity and the validity of physical laws

Any derived quantity X can be expressed as a function of the fundamental quantities (Length, Mass, Time, Current intensity, etc.) according to the expression^[2]

$X=L^a\mathrm{.}{M}^b\mathrm{.}{T}^c\mathrm{.}{A}^d\mathrm{.}{\mathrm{\theta }}^e\mathrm{.}{N}^f\mathrm{.}{C}^j$

This expression is the “Equation of dimensions” of the quantity X

With:

a, b, c, d, e, f and j are real numbers

L, M, T, A, θ, N and C are the dimensions of length, mass, time, electric current, temperature,  amount of substance and luminous intensity, respectively.