Mer331 Lab – Week 2 - Viscosity
Background: Viscosity

A fluid is a state of matter that does not permanently
resist shear and the resistance to deformation (shear
stress) is a function of the rate of deformation (shear
rate)

Rheology = science of deformation

Viscometry = measurement of rheological properties
 Viscosity is the property of a fluid that resists
deformation:
molasses vs water,
 molasses in January vs molasses in July.


Newton Law of Viscosity (for Newtonian fluids)
Background: Viscosity
Shear Thickening
Shear stress as a function of deformation
Background
Oobleck: shear thickening
http://io9.com/5715076/non+newtonian-fluids-theweirdest-liquids-youve-ever-seen
http://en.wikipedia.org/wiki/Bartholome
w_and_the_Oobleck
http://www.youtube.com/watch?v=yHlAcASsf6U
Background
Ketchup, Toothpaste: shear thinning
Leaping Shampoo!
Versluis M, Blom C, Meer D, Weele K, Lohse D (2006) Leaping Shampoo and the Stable
Kaye Effect. Journal of Statistical Mechanics: Theory and Experiment 2006P07007.
http://www.youtube.com/watch?v=GX4_3cV_3Mw
Background: Viscosity Units
Absolute (or Dynamic) Viscosity, 
Units:
1 Poise = 1 g/(cm sec)
1 Pa sec = 1 kg/(m sec) = 1 N sec/m2
1 Poise = 100 cP = 0.1 Pa sec
Kinematic Viscosity:  = /ρ
Units:
1 stoke = 1 cm2/sec = 0.0001 m2/sec
Techniques for Measuring Viscosity




Capillary Viscometers
Rotary Viscometers
Falling “Object” Viscometers
And many others….
Capillary Viscometers

Capillary Viscometers
Measure the flow rate of a fixed volume of
fluid through a small orifice
 From laminar flow theory we can relate the
flow rate, pressure drop to viscosity

 = K*time
K is a calibration constant
Time is measured in seconds
 is given in cSt
Rotary Viscometers

Use the torque on a rotating shaft to
measure a fluids resistance to flow
 = F * torque
F is a calibration constant which you
look up in the instrument manual
Falling “Object” Viscometers


Apply F=ma
At terminal speed a=0
FG = FB + FD
FB= Buoyancy
FD =Drag
FG = mg = rpD3g/6
FB = rfluidpD3g/6
The drag on a sphere depends
on the flow field:
….
FG = Weight
Falling “Object” Viscometers
The drag on a sphere depends on the flow field:
Reynold’s Number:
rVD
Re =

For Stokes Flow: Re < 0.1
F
Drag
Therefore:

gD2
=
rB  r f
18V
3pDV
=
Re

Restrictions: terminal velocity, Re < 0.1
Gilmont Viscometer
 = Kt(rball-rfluid)
K = 35
Rball,ss = 8.02 (gm/ml)
Rball,glass = 2.53 (gm/ml)
 in Cp
t in minutes
Lab Write Up
You will write a full lab report. Review the information on the
course webpage:
http://engineering.union.edu/~andersoa/mer331/MELabReports.htm
Include detailed information on the uncertainty analysis:
 Table of uncertainty values for each thing you measure
(i.e. mass, volume etc).
 Report all data with an uncertainty value
 Include (hand written) derivation of uncertainty equations
with a sample calculation in an appendix.
 See handout on lab report expectations.