Viscosity Laboratory Experiment






By Phạm Thị Nga
For
Prof.Tonya Kuhl





ECH: Chemical Engineering Laboratory
Group #4
Phạm Thị Nga, Trần Thị Huyền, Trần Duy Hưng and Trần Hà My

Experiment Performed: April 7,2015
Report Submitted: April 14,2015



Summary
Determing unkown viscosity’s fluids is really important in industry. In this experiment, we use settling sphere method to find out the viscosity of grycerine and the relationship between drag coefficient and Reynolds number. The results were µ= 0.6626 ± 0.0321 kg/(m.s);
𝐶
𝐷=(-1.2542±0.1147) x
𝑅𝑒
26.3±1.2339. The density of Grycerine was also determinded by Cannon-Fenske viscometer with value of 1213.893±0.99 kg
𝑚
3. These results show that this method is simple and accuracy.
Theory
In this work, spheres with different sizes d and weights m was dropped through a column of Grycerine with a constant velocity V. We measured time when the spheres went from 10cm to 34cm. The forces acting on the spheres are shown in figure 1.
/
Figure 1. Schematic of the settling sphere viscometer in this experiment
The drag force derived from Stoke’s law (Re<<1):
𝐹
𝑑=3𝜋𝜇𝑉𝑑 Or:
𝐹
𝑑
𝐶
𝑑
𝜋
8
𝜌
𝑉
2
𝑑
2

According to Newton’s second law:
𝐹
𝐹
𝑑
𝐹
𝑏
𝐹
𝑔=0
After some algebraic manipulation, the following expression for µ can be obtained: 𝜇
𝑑
2
𝛾
𝑠
𝛾
𝑙
18 
𝑉 => 18
𝑉
𝜇
𝑑
2
𝛾
1
𝛾
2
) (equation 1)
The work will also determine the relationship between
𝐶
𝑑 𝑎𝑛𝑑 𝑅𝑒 using :

𝐶
𝑑=𝑎
𝑅𝑒
𝑛 => log
𝐶
𝑑)=𝑛𝑙𝑜𝑔
𝑅𝑒+log⁡(𝑎) (equation 2) The stoke’law
𝐶
𝑑
24
𝑅𝑒

Results and discussion
From equation (1) and data measured in Lab, we can draw a plot that show the viscosity of grycerine and its error:
/
Figure 2. Plot of equation (1)
Table 1. Data analysis and error of Grycerine’s viscosity
 
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95,0%
Upper 95,0%

Intercept
0,035619
0,039313
0,906014
0,416169
-0,07353
0,14477
-0,07353
0,14477

X Variable 1
0,662647
0,032154
20,60875
3,27E-05
0,573374
0,751919
0,573374
0,751919



𝜇
𝑒𝑥𝑝= 0.6626 ± 0.0321 kg/(m.s)

𝜇
𝐶𝐹=0.5517±0.0468 kg/(m.s)

𝜌
𝐺𝑟𝑦𝑐𝑒𝑟𝑖𝑛𝑒= 1213.893 ±0.99 kg
𝑚
3

𝜇
𝑒𝑥𝑝 >
𝜇
𝐶𝐹 because: (+) the wall affects the spheres (+) Time to measure
𝜇
𝑒𝑥𝑝 is different from time to measure
𝜇
𝐶𝐹 ( we measured
𝜇
𝑒𝑥𝑝 on April 7 and another group measured
𝜇
𝐶𝐹 the day after). Therefore, Grycerine absorbed more water and became lower viscosity. (+) We (group 4) did experiments with the left column but they measured
𝜇
𝐶𝐹 with the right column (+) random error
From equation (2) and data, we can plot :
/
Figure 2. Plot of equation 2
Table 2. Data analysis and error of Cd and Re
 
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95,0%
Upper 95,0%

Intercept
1,420092
0,091267
15,55968
9,96E-05
1,166693
1,673491
1,166693
1,673491

X Variable 1
-1,25424
0,114717
-10,9333
0,000397
-1,57274
-0,93573
-1,57274
-0,93573



𝐶
𝐷=(-1.2542±0.1147) x
𝑅𝑒
26.3±1.2339
( equation 3) / Figure 3. Plot of equation 3
As you can see that the experimental results is not fit the theorical model much because of some reason I’ve mentioned above. Our experiments wasn’t really good.