Homogeneous Equations

homogenoues_equation.jpg

The example problem examines how to ensure that the dimensions used for a straight line curve fit to experimental data are homogeneous (have the same dimensions).

By Quartl (Own work) [CC-BY-SA-3.0], via Wikimedia Commons

In the context of Dimensional Analysis, a homogeneous equation is one that has homogeneous (the same) dimensions for all components that add together.


All components of an equation that add together must have the same units.  For example, before a force of 10 lb can be added to a force of 10 Newton, the forces must be converted to a single force unit.  An equation is homogeneous when all parts of an equation that add together have the same dimensions.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Learning Objectives:

Learn the definition of a homogeneous equation in the context of dimensional analysis.

Learn how to ensure that an equation has homogeneous dimensions.