dimensional homogeneity
we all Know from grade school that apples and oranges do not add. But we somehow manage to do it (by mistake, of course). In engineering, all equation must be dimensionally homogeneous. That is, every term in an equation must have the same unit (fig. 1-11). If, at some stage of an analysis, we find ourselves in a position to add two quantities that have different units, it is a clear indication that we have made an error at an earlier stage. So checking dimensions can serve as a valuable tool to spot errors.
We all know from experience that units can give terrible headaches if they are not used carefully in solving a problem. However, with some attention and skill, units can be used to our advantage. They can be used to check formulas; they can even be used to derive formulas, as explained in the following example.