What Is A Dimensionally Homogeneous Equation?
In the post, Solving Equations with Maple, I noted the Manning equation for flow in an open channel was only valid when used with US Customary units. The units on the left side of the equation were cubic feet per second. The units on the right hand side were feet raised to the 8/3 power. Units are hidden in the constant, 1.486.
When the units on the two sides are not the same, the equations is said to be not dimensionally homogeneous. Such an equation can only be used with the units for which it was derived.
When the units on the two sides of an equation are the same, the equation is said to be dimensionally homogeneous. Such an equation can be used with any system of units.