Results 1 to 4 of 4
Like Tree5Thanks
  • 1 Post By topsquark
  • 2 Post By Shakarri
  • 2 Post By Hartlw

Math Help - dimensional analysis for metric conversions

  1. #1
    Newbie
    Joined
    May 2013
    From
    joliet
    Posts
    1

    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.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,962
    Thanks
    349
    Awards
    1

    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
    Thanks from MarkFL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Oct 2012
    From
    Ireland
    Posts
    597
    Thanks
    165

    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}
    Thanks from Hartlw and topsquark
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Aug 2010
    Posts
    961
    Thanks
    98

    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.
    Thanks from topsquark and Shakarri
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. dimensional analysis
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: April 22nd 2012, 06:02 PM
  2. [SOLVED] Compact set in metric space (finite and infinite dimensional)
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: May 30th 2011, 12:38 PM
  3. Dimensional Analysis
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: February 7th 2011, 05:54 PM
  4. dimensional analysis help?
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: August 20th 2010, 08:37 PM
  5. Dimensional Analysis
    Posted in the Advanced Applied Math Forum
    Replies: 4
    Last Post: August 2nd 2008, 06:59 AM

Search Tags


/mathhelpforum @mathhelpforum