1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper

    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


    User Avatar
    Science Advisor
    Homework Helper

    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


    User Avatar
    Science Advisor
    Homework Helper

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

    = mass.time.distance/time2.area :wink:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook