To convert units between different systems

To check the validity of an equation

To derive new equations from existing ones

To determine the physical properties of a fluid

A theorem that states that any physical quantity can be expressed as a function of a certain number of dimensionless parameters

A theorem that states that the number of dimensionless parameters in a physical problem is equal to the number of independent variables minus the number of fundamental dimensions

A theorem that states that the dimensions of a physical quantity are determined by the dimensions of its constituent variables

A theorem that states that the units of a physical quantity are determined by the units of its constituent variables

Mass, length, and time

Mass, force, and acceleration

Mass, velocity, and displacement

Mass, energy, and momentum

$\frac{L}{T}$

$\frac{M}{LT}$

$\frac{L^2}{T^2}$

$\frac{ML}{T^2}$

$\frac{L}{T^2}$

$\frac{M}{LT}$

$\frac{L^2}{T^2}$

$\frac{ML}{T^2}$

$\frac{M}{LT^2}$

$\frac{ML}{T^2}$

$\frac{L^2}{T^2}$

$\frac{ML^2}{T^2}$

$\frac{M}{L^2T^2}$

$\frac{ML}{T^2}$

$\frac{L^2}{T^2}$

$\frac{ML^2}{T^2}$

$\frac{ML^2}{T^2}$

$\frac{ML}{T^2}$

$\frac{L^2}{T^2}$

$\frac{M}{L^2T^2}$

$\frac{ML^2}{T^3}$

$\frac{ML}{T^2}$

$\frac{L^2}{T^2}$

$\frac{M}{L^2T^2}$

$\frac{M}{L^3}$

$\frac{L^3}{M}$

$\frac{L}{T^2}$

$\frac{M}{L^2T^2}$

$\frac{L^2}{T}$

$\frac{ML}{T}$

$\frac{L^2}{T^2}$

$\frac{ML^2}{T^2}$

$\frac{ML}{T}$

$\frac{ML^2}{T}$

$\frac{L^2}{T^2}$

$\frac{ML^2}{T^2}$

$\frac{M}{L^2}$

$\frac{ML}{T}$

$\frac{L^2}{T^2}$

$\frac{ML^2}{T^2}$

$\frac{ML}{T^3K}$

$\frac{ML^2}{T^3K}$

$\frac{L^2}{T^3K}$

$\frac{ML^2}{T^2K}$

$\frac{ML}{T^3K}$

$\frac{ML^2}{T^3K}$

$\frac{L^2}{T^3K}$

$\frac{ML^2}{T^2K}$