Cancelling out units in an equation

  1. Apr 16, 2011 #1
    Hi i have done all the work for this problem calculating viscosity and i come to the last part where i need to manipulate and cancel out units to come to a final solution. The equation works out as

    viscosity = 0.0042m^2 x 9.8m/s/s x 11,401.4kg/m^3 all divided by 1.034466m/s

    viscosity is measured in Pascals/sec

    can someone help me with the last step with the units

  2. jcsd
  3. Apr 16, 2011 #2


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    I usually start by drawing a long horizontal line and writing all the units in the denominator or numerator as appropriate. Thereby, dividing by a/b means writing b "above" and a "below" (as dividing by a/b means multiplying by b/a).

    In this case, going through them one by one, you'd get

    [tex]\frac{m^2}{1} \times \frac{m}{s \times s} \times \frac{kg}{m^3} \times \frac{s}{m}[/tex]
    If you write this in a single fraction, and take the similar units together, you get
    [tex]\frac{m^3 \, s \, kg}{s^2 \, m^4}[/tex]
    which is straightforward to simplify.

    Now to check that this is indeed Pa/s, it is easiest to convert Pascals into kg/m/s. Personally, I find it easiest to remember that pressure is force per unit area, and Newton's law is F = ma, so
    [tex][Pa] = \frac{[F]}{[A]} = \frac{[m] [a]}{[A]} = \frac{kg \times m/s^2}{m^2} = \frac{kg \times m}{s^2 \times m^2}[/tex]
  4. Apr 16, 2011 #3


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    welcome to pf!

    hi andrew! welcome to pf! :smile:

    (try using the X2 icon just above the Reply box :wink:)
    nooo :redface: … viscosity is measured in Pascal.sec :wink:
  5. Apr 16, 2011 #4
    thanks - my final units are 453 kg/sm. any chance on helping me how to get this into pascals which are measured in mPa s?
  6. Apr 16, 2011 #5


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    Pa.s = force.time/area = mass.time.acceleration/area

    = mass.time.distance/time2.area :wink:
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