Consistency in equations means the units in formulae have to be the same on both sides. For example
distance=speedXtime
m=m/s*s=m so the units on both sides are the same
The equation distance=speed/time is not possible because the units on both sides are not the same.
distance=speed/time
m=m/s/s=m/s
2Some equations can be written down with this in mind.
For instance Reynolds number, important in studies of fluid motion, could be written in many different ways, but only equations of the form R=U*x*
/
are homogeneous.
U=speed in m/s
x=distance in m
=density in kg/m
3=viscosity in Nsm
-2=kgms
-2sm
-2=kgm
-1s
-1Sometimes it is necessary to change units to the standard units of mass (kg), length (m) and time (seconds) and temperature (K) as I did above to write N as kgms
-2 to make the equations homogeneous but this is also consistent.