I need to learn how to solve metric conversions through dimensional analysis. Can someone please help any info would be greatly appreciated.

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- May 8th 2013, 11:09 AMdwinns17dimensional 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 AMtopsquarkRe: 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 AMShakarriRe: 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 $\displaystyle \rho$, viscosity $\displaystyle \eta$ and the speed of sound in the fluid $\displaystyle v$

Assume that the formula is in the form

$\displaystyle t=\rho^a\cdot \eta^b\cdot v^c$

Examining the units of each quantity

$\displaystyle t: s$

$\displaystyle \rho: kg m^{-3}$

$\displaystyle \eta: Ns^{-1}= kgms^{-3}$

$\displaystyle v: ms^{-1}$

The formula must be such that the units are balanced

$\displaystyle t=\rho^a\cdot \eta^b\cdot v^c$

$\displaystyle s=(kg m^{-3})^a\cdot (kgms^{-3})^b\cdot (ms^{-1})^c$

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

The indexes on the units must match up

seconds, $\displaystyle 1=-3b-c$

meters, $\displaystyle -3a+b+c=0$

kilograms, $\displaystyle a+b=0$

If you solve this set of equations you find that b=1, c=-4, a=-1.

So we know the equation must be

$\displaystyle t=\rho^{-1}\cdot \eta^1\cdot v^{-4}$ - May 8th 2013, 12:56 PMHartlwRe: dimensional analysis for metric conversions
convert m/sec

^{2}to ft/hr^{2}

1 meter = 3.28 ft

1 hr =60 sec

(m/sec^{2})(3.28ft/m)(60sec/hr)^{2}= 11822ft/hr^{2}

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