[chemistrymonkey]

In this experiment the mixtures from Experiment 3 will be used to determine the viscosity of a
mixture as a function of mole fraction of ethanol. It is a general property of
uids (liquids and
gases) that an applied shearing force that produces
ow in the
uid is resisted by a force that
is proportional to the gradient of
ow velocity in the
uid. This is the phenomenon known as
viscosity.
Figure 1: Laminar Flow.
Consider two parallel plates of areas A, at distance D apart, as in Fig. 1. It is convenient to imagine
that D is small in comparison with any dimension of the plates in order to avoid edge eects. Let
there be a uniform
uid substance between the two plates. If one of the plates is held at rest
while the other moves with uniform velocity v0 in a direction parallel to its own plane, under ideal
conditions the
uid undergoes a pure shearing motion and a
ow velocity gradient of magnitude
v0=D exists throughout the
uid. This is the simplest example of laminar
ow, or pure viscous

ow, which takes place under such conditions that the inertia of the
uid plays no signicant role
in determining the nature of the
uid motion. The most important of these conditions is that the

ow velocities be small. In laminar
ow in a system with stationary solid boundaries, the paths of
innitesimal mass elements of the
uid do not cross any of an innite family of stationary laminar
surfaces that may be dened in the system. In the simple example above, these laminar surfaces
are planes parallel to the plates. When
uid velocities become high, the
ow becomes turbulent
and the momentum of the
uid carries it across such laminar surfaces so that eddies or vortices
form.
In the above example, with laminar
ow the force f resisting the relative motion of the plates is
proportional to the areas A and to the velocity gradient v0=D:
f = A
v0
D
(1)
The constant of proportionality  is called the coecient of viscosity of the
uid, or simply the
2
viscosity of the
uid. A convenient unit for viscosity is the poise, which is the cps unit equivalent
to 10��1 N s m��2 = 10��1 Pa s.
1.1 Theory
The theory behind Poiseuille's law allows us to apply the parallel plate theory to a long cylindrical
capillary tube, such as the one we will use in this experiment. The theory is discussed tersely on
pages 129-132 of the text, but the only the results are given here. Specically, the volume rate of

ow past a certain point (volume per unit time) is given by
dV
dt
=
r4(p1 �� p2)
8L
(2)
where p1 and p2 are the pressures at the inlet and outlet of the tube and L is the length of the
tube. In practice a viscometer of a type similar to that shown in Fig. 2 is used. Since (p1 �� p2) is
proportional to the density , it can be shown that, for a given total volume of liquid,
Figure 2: Viscometer


= Bt (3)
where t is the time required for the upper meniscus to fall from the upper to the lower ducial
mark and B is an apparatus constant that must be determined through calibration with a liquid
of known viscosity. In our case, this will be pure cyclohexane.
For a liquid mixture, the relative viscosities can therefore be determined from
r =

0
=
t
t00
(4)
where the \0" subscript identies one of the pure liquids, which we will take to be cyclohexane.
3
1.2 Experimental
We will use Eqn. 4 to determine the viscosity of ethanol/water mixtures to pure ethanol for dierent
volume fractions of ethanol. Using 10 mL volumetric
asks and two 2 mL volumetric pipettes, make
up the following mixtures of ethanol and water:
Solution Number mL ethanol mL water
1 0 10
2 2 8
3 4 6
4 6 4
5 2 2
6 0 10
Clean the viscosimeter with water/acetone and dry with air. Immerse the viscosimeter in at 25
water bath. Using a 10 mL pipette, transfer the liquid from one of the solutions to the viscosimeter.
Rinse the pipette with acetone/water and dry.
Using a pipette bulb to draw solution up to a point well above the upper ducial mark. Release the
suction and measure the
ow time between the upper and lower marks with a stopwatch of timer.
Obatin two or more additional runs with the same lling of the viscosimeter. Three runs agreeing
within about 1 percent should suce.
Each time the discoimeter is emptied, rinse it throughly with distilled water and acetone and dry.
1.3 Calculations
Using Eqn. 4, calculate the relative velocity at each volume fraction. Use the information provided
in the lab manual posted on Moodle to get the errors in the volume measurements and propagate
errors.
4

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