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Units of viscosity

  1. Mar 2, 2015 #1
    I don't understand units associated with kinematic viscosity.

    Let's recap dynamic viscosity (η):

    η = Shear stress (τ) / rate of shear strain (m/s)/m)

    η = F/A / (velocity (m/s) / gap distance (m))

    η = Force( N) / Area (m2) / (velocity (m/s) / gap distance (m))

    Stress (F/A) is pressure, Newtons per metre squared, so unit is Pascals. When you cancel the two m's out in the divisor, you are left with:

    η = N/m2 or Pascals / s (Pascal Seconds).

    The equation to convert dynamic viscosity to kinematic velocity is:

    ν = η / ρ

    ν = η N m-2 s / ρ Kg m-3

    I get this. The numerator is saying Newtons per square meter (pressure in Pascals) per second (Pascal seconds) and the divisor is saying Kg per cubic metre)

    Since 1 Kg = N m-1 s2, this simplifies to dimesions of m2 s-1

    I don't get how things simplify.

    I know that the Stoke is the unit, and it's a unit of position and time.

    Last edited: Mar 2, 2015
  2. jcsd
  3. Mar 2, 2015 #2
    1 stoke is 1 centimeter squared per second. I'm having difficulty in conceptualising what that means.

    Velocity is metres per second.

    Acceleration is meters per second per second.

    ν = η / ρ is relating shear characteristics (dynamic viscosity) to fluid acceleration (mass density).

    Still trying to conceptualise the stoke as a dimension.

    The SI unit of kinematic viscosity is m2/s.

    The cgs physical unit for kinematic viscosity is the stoke.
    Last edited: Mar 2, 2015
  4. Mar 2, 2015 #3
    Actually, right now I could do to concentrate on using the formula correctly.

    ν = η / ρ

    The answer needs to be in centistokes.

    How the heck to get centistokes.

    An oil might have a dynamic viscosity of 0.25 Pascal Seconds.

    The oil might have a mas of 900Kg per cubic meter.

    Okay, ν = η / ρ = 0.250 / 900 = 0.00027.

    The answer is wrong for centistokes. 270 or 27 might be about right. I must figure out why I'm not getting the right answer.

    I think the numerator might be 106 larger than it should be.

    Stokes are in CGS units. Might be a clue.
    Last edited: Mar 2, 2015
  5. Mar 2, 2015 #4

    Andy Resnick

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    It is a little tricky, to be sure- viscosity can be thought of as 'diffusion of momentum':

    http://www.quora.com/How-is-viscosity-the-diffusion-of-momentum [Broken]

    As a practical matter, I find it best to consistently simplify the units into MLT (rather than Pa, N, kg, etc...) to make sure everything works out.
    Last edited by a moderator: May 7, 2017
  6. Mar 2, 2015 #5
    ν = η / ρ

    Before I go to bed:

    For centistokes.

    I think η needs to be in centipoise (1 cP = 0.001 Pa second) and ρ in g /cm-3.

    Where η is 0.25 Pacal seconds, and ρ 900 Kg / m-3, I think the answer should be 27 centistokes.
    Last edited: Mar 2, 2015
  7. Mar 2, 2015 #6
    OK. I'm going to do this in cgs units, which are the units that I like to work with. I leave it up to you to convert to metric.

    Force: ##dynes=\frac{gm-cm}{sec^2}##

    Stress and Pressure: ##\frac{dynes}{cm^2}=\frac{gm}{cm-sec^2}##

    Velocity: ##\frac{cm}{sec}##

    Velocity gradient: ##\frac{cm}{sec-cm}=\frac{1}{sec}##

    Dynamic Viscosity: ##Poise=\frac{dynes}{cm^2-sec}=\frac{gm}{cm-sec}##

    Dynamic Viscosity: ##centipoise = 0.01 Poise##

    Density: ##\frac{gm}{cm^3}##

    Kinematic Viscosity: ##Stokes = \frac{Poise-cm^3}{gm}=\frac{dynes-cm}{gm-sec}=\frac{cm^2}{sec}##

    Kinematic Viscosity: ##centistokes=0.01Stokes##

    Hope this helps.

  8. Mar 3, 2015 #7
    Let me see if I can get this.

    Up till now, all my physics calculations are worked out using SI units. That means I'm entering meters, Kg and seconds. I do this for working out dynamic viscosity η.

    But, now I've come across a formula to work out centistokes (a unit of kinematic viscosity) from dynamic viscosity and mass, which is a unit worked out using cgs units.

    Therefore I must make changes when using the equation ν = η / ρ.

    Lets take ρ, mass first. 900Kg per m-3 in SI units is 900. So, what's that in cgs? 1 x cm-3 is 106 times smaller than m-3. So, in cgs 900Kg becomes 9 x 10-4Kg. Were still in Kg, so, to show in grams we must multiply by 103. So, our figure should be 0.9g cm-3

    Correct I think so far.
  9. Mar 3, 2015 #8
    The issue now is what units should be being used for η.

    I believe it is true, that the dynamic viscosity for engine oil will be in the tenths of a Pascal-second range.

    To work out kinetic viscosity in stokes we would enter the POISE for η. A poise is 0.1 Pascal-second.

    But, we need to work with centistokes. So, we need to be working in centipoise that is 1 x 10-2 of a Poise (cP).

    1 cP is therefore 10-3 times a Pascal second.

    Going back to our original equation: ν = η / ρ = 0.250 / 900 = 0.00027.

    η should be in cP therefore 250. ρ should be in g / cm-3 therefore 0.9.

    ν = η / ρ = 250 / 0.9 = 277.7 centistokes (kinetic viscosity).

    I think that is correct.

    So, if you get η in Pascal-seconds, from earlier calculations, you have to multiply η by 1000, when using the formula to obtain centistiokes.
    Last edited: Mar 3, 2015
  10. Mar 3, 2015 #9
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