Dimensional Analysis

In dimensional analysis, mass, length, and time are termed fundamental dimensions, and physical quantities in mechanics can be expressed in terms of fundamental dimensions.

For instance, consider a ball being hit by an object; the force applied is calculated as the product of mass and acceleration, where acceleration is denoted as a change in velocity over time, while velocity is the distance over time.

Consider a kinematic equation, where u is the initial velocity, a is the acceleration having unit meter per second squared, t is the time, and v is the final velocity.

If the powers of the fundamental dimensions on both sides of the equation are identical, it is called dimensional homogeneity.

Dimensional analysis methods include Rayleigh's method and Buckingham's pi theorem.

Rayleigh's method determines the expression for a variable, which depends on a maximum of three or four independent variables.

Buckingham's pi theorem states that if n is the total number of variables in a dimensionally homogeneous equation containing m fundamental dimensions, they may be grouped into (n-m) dimensionless terms.