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© The scientific sentence. 2010

ThomasStormer viscometer
1. Dynamic viscosity: ThomasStormer viscometer:
The viscosity is the fluid resistance to shear or flow
The Tomas Stormer apparatus mesures a dynamic viscosity of a liquid as oil.
The shear stress on the surface of the rotor is proportional to:
 The viscosity μ of the liquid, and
 The rotation speed of the rotor.
Hence:
σ = k μ ω
If S is the wetted surface area of the rotor, and F is the tangential force on the
edge of the rotor, we can write:
F = σ S
The related torque is τ = F x r_{rotor}
r_{rotor} is the radius of rotor.
We neglect frictions in the system to write that the power exerted on the rotor is
equal to the power supplied by the weight W in order to move this weight
of a distance L = v x t.
We have:
L = 2 x π x r_{axis}
Then
v = L/t = 2 x π x r_{axis} x n_{axis}/t (1)
n_{axis} is the number of rotations made by the axis.
Since the power of the falling weight and the power dissipated over the
rotor by viscous steress are equal, we can write:
Power_{fluide} = Power_{weight}; that is:
τ ω = W x v
W is the weight of the falling body.
In other hand: ω = 2π x r_{rotor} x n_{rotor}/t (2)
The relationships (1) et (2) give:
2 x π x r_{axis} x n_{axis}/v = 2π x r_{rotor} x n_{rotor}/ω
Or:
r_{rotor} x n_{rotor}/ω = r_{axis} x n_{axis}/v
Then:
μ k = σ/ω = F/S/ω = τ / r_{rotor}/S/ω =
W x v/ω /S/ r_{axis} x n_{axis}/v/ =
W /ω /S/ r_{axis} x n_{axis} /n_{rotor}/r_{rotor}
We define the constant K of the viscometer as:
C = (W x r_{axis} x n_{axis})/(r_{rotor} n_{axis} x S x k)
Forethermore:
μ = C x W / ω
In the SI system the dynamic viscosity unit is N.s/m2 = Pa.s = kg/m.s where
In the metric CGS system, the unit is g/cm.s = dyne.s/cm2 = poise (p) = 1/10 Pa.s = 100 cP
Pa is the Pascal and cP is the centiPoise.
Water at 20 ^{o}C has a dynamic viscosity of one (1) centiPoise.
2. Kinematic viscosity:
Kinematic viscosity is, by definition, the ratio of absolute or dynamic viscosity
to density:
ν = μ /ρ
where ν = kinematic viscosity, μ = absolute or dynamic viscosity, and ρ = density
In the SI system, the unit is m2/s
In the CGS system, the unit is the Stoke (St) where 1 St = 104 m2/s
We use also the Centistoke (cSt) = 1/100 St where
The kinematic viscosity of water at 20 ^{o}C is 1.0 cSt.
3. Measurement:
For a fluid liquid, we use communly the Oswald apparatus tp mesure the viscosity.
We set the following relationship:
μ = k ρ t
where k is a constant callibration of the apparatus, &pho; density and t the time spent by the fluid
to live a part "1" of the cappilary viscometer.
According to a known value of the kinematic viscosity of a certain fluid, we just make the
ratio μ /μ_{known}= k &pho; t1 / k &pho;_{known} t2; and measuring the times
t1 and t2 to have the value of μ
μ = μ_{known} ρ t1 / ρ_{known} t2
We have also for the kinematic viscosity:
ν = ν_{known} t1 / t2
We use also Saybolt, Engler, or Brookfield viscosimeters depending on circumstances.

