Brookfield Viscometer Assignment
Introduction
The Brookfield viscometer works by rotating a cylindrical spindle of known surface area
in a fluid, and finding the torque on the spindle. Viscosity is then found through the
relationship:



Figure 1- This is very similar design to our viscometer. The only significant difference is the speed
control. Ours is on the side and operates in stepped increments of 6, 12, 30 and 60 RPM. From
Brookfield’s “Solution to Sticky Problems”
Where  is the viscosity in poise,  is the shear stress in dynes / cm2, and  is the rate of
shear (sec-1). The full scale torque of our LVF model viscometer is 673.7 dyne-cm;
torque is linear with the scale reading. A material requiring a shear stress of 1 dyne per
cm2 to produce a shear rate of one reciprocal second has a viscosity of 1 poise (100cp).
Theory
Newtonian fluids such as light oils have a viscosity that is constant with shear rate.
Bingham fluids have a constant viscosity, but require a certain “yield-stress” (o) in order
to initiate shear (movement):
   o  
Power Law fluids are either pseoudoplastic (shear thinning) or dilatant (shear
thickening). These fluids obey the model:
  k n
Where k is the “consistency index” and n is positive for dilatant fluids and negative for
pseudoplastics (note that for n = 1, k reduces to the Newtonian viscosity).
A power law fluid that has a yield stress is also called a “Herschel Bulkley” fluid, and
follows:
   o  k n
For cylindrical spindles, the area can be computed as R2L. Torque is computed as the
force acting on the outer surface of the spindle times the radius (“lever arm”). Therefore,
the following relationships hold:
Shear
-1
Rate (sec )
2Rc2 Rb2
  2 2
)
x ( Rc  Rb2
Shear Stress (dynes/cm2)  
Viscosity

M
2Rb2 L


Definitions:  = angular velocity of
spindle (rad/sec)
Rc = radius of container
(cm)
Rb = radius of spindle
(cm)
x = radius at which
shear rate is being
measured
M = torque input by
instrument
L = effective length of
spindle
Standard Operating Procedure
1) Level the viscometer using the bolts on the legs of the instrument.
2) Insert the spindle guard.
3) Insert the spindle by very carefully holding the viscometer side and screwing the
spindle in a counterclockwise direction (“left handed threads”).
4) Carefully lower the viscometer into the solution to be measured using the
mounting nut on the viscometer handle. Insert up to the insertion marking on the
spindle.
5) Check to make sure the viscometer is still level
6) Turn the viscometer on and set to the desired speed (the combination of spindle
and speed should not cause the torque reading to exceed 100%).
7) Wait several rotations for the reading to stabilize and mark the torque by pressing
down on the clutch lever.
8) Turn off the motor when the needle is in front of the view window and read the
scale.
9) Calculate torque by multiplying the factor found on the card by the unit. Use the
“LV” and the appropriate spindle number. Spindle numbers are stamped on the
top of the shaft.
10) Clean up and unplug viscometer after use.
Experiments
I-Effect of Temperature on Vegetable Oil
Following the SOP and using spindle#1, measure the viscosity of the Crisco Canola Oil
at several different temperatures. Start at room temperature and use the water bath to
hear the solution, periodically taking measurements. Measure the viscosity at all 4
speeds if possible.
II-Non-Newtonian Fluid (ketchup)
Following the SOP and using spindle#4, measure the viscosity of the ketchup at all 4
speeds (room temperature).
Analysis
I- Effect of Temperature on Vegatable Oil
1) At a given temperature, are all of the viscosity readings approximately the same
for each speed? What does this tell you about the nature of the fluid?
2) Plot temperature versus viscosity. Does viscosity increase or decrease? How do
these values compare to accepted values for similar oils?
3) Check to see if the viscosity of the oil follows the temperature dependence given
in the Brookfield “Solutions to Sticky Problems” .pdf file and determine
coefficients A and B in equation 15 on page 26.
4) For the lowest temperature, calculate the torque (scale reading/100 x 637.7), the
shear stress and the shear rate. Do this for all 4 speeds. Plot shear rate versus
shear stress. Find the slope of the resultant line. Is the slope within a 95%
confidence interval of the values you calculated using the factors from the card?
II- Ketchup Viscosity
1) Plot rotational speed of the stirrer vs. viscosity. What does the data indicate about
the nature of the fluid? See if a power function (insert trendline) fits the data.
2) Plot rotational speed of the stirrer vs. viscosity on a log-log plot. What does this
(along with #1) tell you about the fluid properties?
3) Use linear regression of the data from #2 to find the intercept at zero RPM. This
is the dynamic yield torque.
4) Ketchup often doesn’t flow unless you bang on the bottom of the bottle. What
does this tell you about the fluid? Construct a plot that allows you to determine
the yield stress.
Table 1Spindle Dimensions-
Diameter (cm)
Effective Length (cm)
Spindle #1
1.884
0.32
Spindle #4
6.51
3.101