Advanced Program
Department of Oil Refining and Petrochemistry
HUMG
ECH 155A, 2015

Viscosity Lab
Goals of the Laboratory
Determine the specific weight and the viscosity of two liquids at room temperature. Determine a relationship between the coefficient of drag and the Reynolds number. Compare your findings to established literature values and relationships.

Theoretical Background
Consider a sphere with diameter d and specific weight (s, falling at a constant velocity V through a liquid with viscosity (, specific weight (l, and density (. The forces acting on the sphere are shown in Figure 1.




















One expression for the drag force can be derived from Stoke’s Law and is valid only for small Reynolds number [1]:

𝐹
𝐷=3𝜋𝜇𝑉𝑑 (1)

The drag force on a sphere may also be calculated by:

(2)
Where Ap is the projected area of the sphere and CDis the coefficient of drag. This general equation for the drag force comes from the definition of the friction factor and Friction force, Fk, which may be arbitrarily expressed as the product of a characteristic area A, a characteristic kinetic energy per unit volume K, and a dimensionless quality f, known as the friction factor

(3)

In analyzing the phenomena of a settling sphere in an infinite fluid, once the sphere has reached terminal velocity,
, according to Newton’s Second Law.


(3)

After some algebraic manipulation, the following expression for μ in terms of (s, (l, d, and V can be obtained.

(4)

The previous expression is valid for a sphere falling in an infinite fluid or far from a wall. The fluid can be considered “infinite” (an error of less than 5%) when
. Otherwise theproximity of the wall and its effect on the spheremay be significant. There is a rich literature on the “wall effect” and many empirical relations are available to correct for this effect [2-3].An early correction was proposed by Ladenburg in 1907 [3]

for
(5)
Improved corrections include that proposed by Francis in 1933 [3]


for
(6)
A further search of more recent literature and investigation of “wall effects” is highly suggested.

Experimental Apparatus

Two liquids of different viscosity: glycerin and paraffin.
Two transparent vertical tubes or graduated cylinders.
Tweezers.
Thermometer, micrometer.
Spheres of variable diameter and density.

Experimental Procedure

Record the temperature of the liquids (use the ambient temperature if the liquids have been in the room for a long period of time).
Use the viscometer to determine the viscosity of the various fluids.
Use the settling sphere method to determine the viscosity of the various fluids. Start by selecting a sphere.
Weigh each sphere and measure its diameter with a micrometer (to account for out-of-round conditions, take several measurements at various diameters and average the result, you could obtain the weight of multiple spheres to get a better measure of the density). Calculate the specific weight of the sphere. NOTE: if the specific weight of the sphere is not greater than that of the fluid, it will float and not fall.
Measure and record the inside diameter of the tubes.
Place the sphere at the surface of the liquid using the tweezers and measure and record the vertical fall distance as a function of time.
REPEAT STEP 6 many, many times with spheres of different sizes and DIFFERENT SPECIFIC WEIGHTS – the more the better. When all spheres have been measured, retrieve the spheres and clean the thoroughly with soap and water. Dry spheres completely with paper towels. Spheres can be re-used during the experiment.

HINT: Plots of CD vs. Reynolds number are widely available in the literature. A photocopy of such a graph would be a useful means to rapidly plot your data points DURING THE LABORATORY TIME to (1) compare and (2) see what sort of range of date one might want to collect as one carries out this experiment.

Data Analysis

In this experiment, after measuring the terminal velocity of spheres falling through a fluid, determine the viscosity of the two liquids using the settling sphere measurements. Based on the data, determine the coefficient of drag and the Reynolds number and show this relationship.

In your memo consider the following points as part of the data analysis and discussion of results.

Part 1: Viscosity
Describe the quality of the settling sphere method by comparisons with the known fluid viscosities. How do wall effects impact your experimental determination of viscosity? Is all your data appropriate for viscosity determination, why or why not?
Wall effects can substantial reduce the observed terminal velocity. Justify your methodology for determining the terminal velocity.
Compare your calculated values of viscosity with an authoritative source.
What is the impact of temperature