Homogeneity

[astarmathsandphysics]

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/s²

Some 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/m³
=viscosity in Nsm^-2=kgms^-2sm^-2=kgm^-1s^-1

Sometimes 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.

[sweetsh]

Now i'm figuring it out!!
Thanks astar

[nid404]

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/s²

Some 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/m³
=viscosity in Nsm^-2=kgms^-2sm^-2=kgm^-1s^-1

Sometimes 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.

Thanks astar That will definitely help

[slvri]

hey thanks astar.........i was studying homogenity in school 2day as well

[sweetsh]

I dont like it, wasnt getting it properly until I asked astar and he made me understand