Falling Ball Viscometry Lab #1

Chase Hilderbrand

Joanna Nicholson

Eddwie Perez

September 11, 2015

Professor: Dr. Danvers Johnson

CWR3201C

INTRODUCTION

The objective of the viscometry lab is to use a falling ball viscometer to determine the

viscosity of a fluid. The viscosity of a fluid is a quantification of its resistance to deformation by

various stresses. This is accomplished by measuring the velocity of a ball bearing, of known

diameter, travelling through the unknown fluid. In order to calculate the results, one must assume

that the ball had reached terminal velocity, and was not affected by turbulence until the bottom of

the tube. The velocities were calculated using marked points on the tube, before the bottom. As

well, there is an assumption made that Stokes’ Law is valid, and that minor temperature changes

throughout the fluid make extremely minor differences and can be ignored.

THEORY

Once a sphere falling through a fluid has reached terminal velocity, it is in equilibrium. The

Force of Gravity (FG) is therefore equal to the Resistive Force (FR).

FG = FR (1)

The Force due to gravity is a function of Volume (V), Density (ρ), and gravity (g):

𝐅G = (Vball)(ρball)(g) = 𝟒

𝟑(𝛑)(𝐫2)(𝛒ball)(𝐠) (2)

The Resistive Force is a function of the Viscosity (µ), and our measured velocity v):

FR = 6πµrv (3)

By substituting Equation 2, and 3 into Equation 1, we can derive a function for viscosity:

µ = 1/18(ρball – ρfluid)(g)(D)2

v (4)

To find Kinematic Viscosity, (ν):

ν = µ

𝛒 (5)

The Reynolds Number, (Re) is used to describe the relationship of the kinematic forces to

viscous forces. It is a ratio that describes the way in which the ball reacts to the viscosity of the

fluid. A low Reynolds number indicates a laminar flow.

Re = 𝛒𝐯𝐃

µ

EXPERIMENTAL PROCEDURES

1. Measure the diameter of the available balls and weigh them. Record the diameter and weight.

2. Determine a distance from the surface of the liquid at which the ball reaches terminal velocity by

doing a dry run; dropping the ball and looking for the instant the ball starts to drop at a continuous rate.

3. Once the distance from the surface where terminal velocity begins is established, determine a

distance below the point where terminal velocity is reached that is relatively far from the bottom of

the tube.

4. Mark two points, one below the location at which terminal velocity is initially reached and the

other above the point chosen in step 3. Record the distance between these two points.

5. Using the balls that were measured in step 1 drop one ball in the liquid. Start the timer at P1 and

stop the timer at P2. Record the time.

6. Repeat step 5 three more times with the remaining balls measured in step 1.

RESULTS

Equation 4 was used with the mean data from the above to get a value for viscosity, 0.694 P

and a kinematic viscosity of 5.60E-4 m2/s was also calculated.

µ = (𝟏

𝟏𝟖) × (𝝆ball-𝝆gly )

𝒌𝒈

𝒎𝟑×𝟗. 𝟖𝟏𝟎

𝒎

𝒔𝟐∗ (

𝟗.𝟖𝟗

𝟏𝟎𝟎𝟎) 2𝒎𝟐 ×

𝟏

𝟎.𝟒𝟕𝟏

𝒎

𝒔= 𝟎. 𝟕𝟔𝟐𝑷

DISCUSSION

The calculated kinematic viscosity was compared to the values in Figure 1 (Munson et al.

2009). An assumption was made that the temperature of the viscometer was approximately 21.0

°C. In comparing the calculated value of dynamic viscosity the value was close to that of glycerin

and suggests that the liquid in the viscometer was likely glycerin. As well, it could be observed that

the sphere fell more slowly than it would in water, and in fact, the dynamic viscosity value was

Ball

diameter

(D) in

(mm)

Drop

time (t)

in (s)

Drop

distance

s (mm)

Rate of

fall v=s/t

(mm/s)

Re

Mass

of ball

(g)

ρ ball

(kg/m3)

Viscosity

(µ) in

(Ns/m2)

Kinematic

Viscosity

(v) in

(m2 /s)

Test 1 9.89 2.12 1000 471.70 7.65 4.05 7995.88 0.7624 0.00061

Test 2 9.88 1.84 1000 543.48 10.08 4.08 8055.11 0.6661 0.00053

Test 3 9.89 1.91 1000 523.56 9.40 4.06 8015.63 0.6889 0.00055

Test 4 9.88 1.91 1000 523.56 9.38 4.07 8035.37 0.6895 0.00055

Test 5 9.89 1.84 1000 543.48 10.12 4.06 8015.63 0.6636 0.00053

Mean 9.89 1.92 1000 521.16 9.32 4.06 8023.52 0.6941 0.00056

Standard

Deviation 0.001 0.018 0.00 2.94 0.15 0.16 22.500 0.46 0.00003

FLUID: Glycerine

Table 1. Falling Ball Data

greater than that of water; 762E-3 vs 1.002E-3 (water). The only notably erroneous measurement

was the time needed for the ball to travel 1000 mm on the first trial; there seems to be a delay as

compared to the other values. However, the overall standard deviation is only 2.94 and does not

severely alter the calculated viscosities.

CONCLUSIONS

The fluid in the viscometer was determined to be that of glycerin based on an assumption of a

consistent temperature of the viscometer and fluid and that the terminal velocity was established

far enough from the bottom and wall of the tube to prevent any turbulent interference. The largest

variance in the data was a delay in time to fall, although it was not very relevant to the final

calculations.

Figure 1

Works Cited

Munson, B. R., Young, D. F., Okiishi, T. H., Huebsch, W. W. (2009). Fundamentals of Fluid

Mechanics, Wiley, Hoboken, NJ, Appendix B. pg. 714.