IGCSE/GCSE/O & A Level/IB/University Student Forum

Qualification => Subject Doubts => GCE AS & A2 Level => Sciences => Topic started by: astarmathsandphysics on September 07, 2009, 03:01:24 pm

Title: Homogeneity
Post by: astarmathsandphysics on September 07, 2009, 03:01:24 pm: 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* $\rho$ / $\mu$ are homogeneous.

U=speed in m/s
x=distance in m
$\rho$ =density in kg/m³
$\mu$ =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.
Title: Re: Homogeneity
Post by: sweetsh on September 07, 2009, 03:03:32 pm: Now i'm figuring it out!!
Thanks astar
Title: Re: Homogeneity
Post by: nid404 on September 07, 2009, 03:58:33 pm: Quote from: astarmathsandphysics on September 07, 2009, 03:01:24 pm
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* $\rho$ / $\mu$ are homogeneous.

U=speed in m/s
x=distance in m
$\rho$ =density in kg/m³
$\mu$ =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
Title: Re: Homogeneity
Post by: slvri on September 07, 2009, 04:06:45 pm: hey thanks astar.........i was studying homogenity in school 2day as well
Title: Re: Homogeneity
Post by: sweetsh on September 07, 2009, 04:08:35 pm: I dont like it, wasnt getting it properly until I asked astar and he made me understand