# dimensional analysis for metric conversions

• May 8th 2013, 11:09 AM
dwinns17
dimensional analysis for metric conversions
I need to learn how to solve metric conversions through dimensional analysis. Can someone please help any info would be greatly appreciated.
• May 8th 2013, 11:35 AM
topsquark
Re: dimensional analysis for metric conversions
Do you mean something like 100 m = ? ft or something like finding the unit of a quantity by using an equation? (Such as F = Gm_1*m_2/r^2, and find the unit for G)? Or is it something else?

-Dan
• May 8th 2013, 11:45 AM
Shakarri
Re: dimensional analysis for metric conversions
I think I know what you are asking but I might be wrong. I think the best way to explain is with an example.

We want a formula to describe how long it takes a ripple moving through a liquid to die down.
We assume that the time taken is a function of the fluid's density $\rho$, viscosity $\eta$ and the speed of sound in the fluid $v$

Assume that the formula is in the form
$t=\rho^a\cdot \eta^b\cdot v^c$

Examining the units of each quantity
$t: s$
$\rho: kg m^{-3}$
$\eta: Ns^{-1}= kgms^{-3}$
$v: ms^{-1}$

The formula must be such that the units are balanced
$t=\rho^a\cdot \eta^b\cdot v^c$
$s=(kg m^{-3})^a\cdot (kgms^{-3})^b\cdot (ms^{-1})^c$

$s^1=kg^am^{-3a}kg^bm^bs^{-3b}m^cs^{-c}$

The indexes on the units must match up
seconds, $1=-3b-c$
meters, $-3a+b+c=0$
kilograms, $a+b=0$

If you solve this set of equations you find that b=1, c=-4, a=-1.
So we know the equation must be
$t=\rho^{-1}\cdot \eta^1\cdot v^{-4}$
• May 8th 2013, 12:56 PM
Hartlw
Re: dimensional analysis for metric conversions
convert m/sec2 to ft/hr2

1 meter = 3.28 ft
1 hr =60 sec

(m/sec2)(3.28ft/m)(60sec/hr)2 = 11822ft/hr2

That's the pattern for any unit conversion, if that's what you are asking.