Hanoi University of Mining and Geology, HUMG
Chemical Engineering Laboratory, ECH 155A
Advanced Program
Viscosity Laboratory Experiment

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Figure1
I-Summary of the experiment

The experiment were carried out with a settling sphere viscometer to determine a glycerin viscosity , find drag coefficient of a sphere and determine a relationship between the coefficient of drag and the Reynolds number. Compare your findings to established literature values and relationship. Using the method, the viscosity of glycerin was = 0.659±0.565 (Kg.m-1.s-1); CD=(25.1±1.2)Re-1.24±0.12 ; CD dependence on Re. Comparing with the viscosity in the theoretical, two value almost the same, the measurement could acceptable.
II- Theory
Process experiment
A settling sphere viscometer, as shown in figure 1.We prepare a column contain glycerin solution and the sphere of steel, glass and decline with different size, weight. Weigh each sphere and measure its diameter. Repeat this step four times with each sphere to restrict the error. In this work, the viscosity of glycerin was determined using a fluid column of diameter 15 cm and measuring the settling time of various spheres (diameter from 3 mm to 6mm) with densities ranging from 1.212544 to 1.2149 g/cm3. We drop the sphere into the solution. Using the mobile phone to count the time when a sphere go away surface to time when a sphere touch the bottom of column. The distance we choose was 31cm. Wall effects were negligible because diameter of a sphere is smaller than 0.1 diameter of the column d<0.1D.
Equation
At terminal velocity, according to Newton’s Second Law

: FB -FG+ FD =0 (1)
For Re<<1: FD= .
The drag force on a sphere may also be calculated by:
FD = CD d2 𝜋
8 (2)
From (1)(2) we have the coefficient of drag: CD
4∆𝛾 𝑑
3.
In fluid mechanics: Re= d.V∞/𝜗 and 𝜇∆𝛾d2
18V

III- Result and discussion
Viscosity (figure2).
µexp= 0.659±0.056 (kg.m-1.s-1)
.F= 0.454 ±0.010 (kg.m-1.s-1)
ρl=1.215±0.001(g.cm-3)
µc.f= 0.552±0.006 (kg.m-1.s-1)
Table1: The error of the viscosity
 
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%

Intercept
66.32567248
399.5105376
0.166017
0.876197
-1042.89
1175.545
-1042.89
1175.545

Variable
6.594017762
0.564932272
11.67223
0.000308
5.025514
8.162521
5.025514
8.162521


As you can see in the result, the viscosity that we got from settling sphere method greater than value from Cannon-Fenske method because we got error on it .we did the settling sphere experiment in different time, the viscosity is sensitive with the temperature, so the temperature changes cause the viscosity changes. Another reason is that the fluid wasn’t pure. We got the density of the glycerin in the glass that was less than the pure glycerin because there was water content in the glass so we also had error on the density of the glycerin.
Coefficient of drag (figure3)
CD=(25.1±1.2)Re-1.24±0.12
Table 2: The error of the drag coefficient.
 
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%

Intercept
3.22198
0.22516
14.30941
0.00014
2.59682
3.84713
2.59682
3.84713

Variable
-1.24478
0.12094
-10.29222
0.00050
-1.58057
-0.90898
-1.58057
-0.90898


Theoretically , we have : Cd= 24/Re. In the experiment, we have CD=(25.1±1.2)Re-1.24±0.12. .We had error because the Stoke’s Law only apply with Re<1. Some of reasons are the measurement time and diameter had error so the velocity wasn’t completely correct and the road of sphere drop wasn’t vertical.
Conclusion: The accuracy of sphere settling method is quite good.
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