CDB 2052

CHEMICAL ENGINEERING LABORATORY 1

Sept 2015

Experiment : 2-Viscosity Measurement

Group : 13

Group Members : Mohd Hafiz bin Mohd Nor 19992

Nurfatien binti Bacho 20005

Tracy Chua Peng Ling 20443

Vegenes A/L Venkatasal Rao 19867

Lab Instructor : Claudya Debbie

Date of Experiment : 26th November 2015

1

ABSTRACT

Viscosity is a property arising from collisions between neighboring particles in a fluid that are moving at different velocities. Due to internal friction among their particles, liquids and gases have different viscosities. Hence, the experiment was conducted to measure the viscosity of the fluid in different conditions.

The main objectives of this experiment is to determine the relationship between the viscosities of pure liquid substance with the temperature and to evaluate the effect of mixture of liquids to the viscosity. Liquids and gases have different viscosities due to the internal friction among the particles which are also dependent on their structure and temperature. Therefore, this experiment is conducted to measure the viscosity of the fluid in different conditions.

In order to measure the viscosity of Newtonian fluid, the Höppler principle of falling ball was used by recording the time taken for the specific ball to fall through the a sample-filled tube under the influenced of gravity.

This experiment is divided to two parts. The first part is to investigate the between viscosities of pure liquid substance with temperature. The temperature was varied between 40°C, 45°C, 50°C, 55°C and 60°C for two balls which are Boron Silicate Glass (ball 1) and Nickel-Iron (ball 3). For each ball, two type of liquids was used that are water and methanol. It can be observed that ball 1 took longer time to reach the bottom line than ball 3. Meanwhile, the second part is to determine the effect of mixture liquids to the viscosity. The temperature is kept constant at 60°C and only one type of ball was used that is ball 1. The concentration of mixture is varied by 0%, 25%, 50%, 75% and 100% water and the rest is methanol. It is assumed that pure substance has a lower dynamic viscosity than its mixture. The viscosity is calculated based on the volume ratio of water and methanol.

In short, the main factor that affects viscosity of pure fluid is temperature while the mixture of pure solution gives out different values of dynamic viscosity.

2

LITERATURE REVIEW

Fluid Mechanics is the study of forces and motion in fluids and it is among the important component in our daily lives. The significance of fluid mechanics can be grasp through the importance it brings in our daily lives which include the air that human breathe, drinking water, human body internal environment which include blood circulation and etc (Nevers,1991). As the fluids come in two types; liquid and gases, the properties of fluid need to be taken into consideration. The behaviour of fluid in flow is mostly related to two intrinsic physical properties which is density and viscosity. The properties of density are the measure of the ‘heaviness’ of a fluid. However, this properties are not sufficient enough to characterize how fluids behave as certain fluid (e.g. oil and water) have approximately the same value of density-approximately 900-1000kg/m3 but behave differently when flowing. This is where viscosity takes charge to differentiate the fluids.

According to Never (1991), viscosity is defined as ‘measure of resistance to flow’. In other words, viscosity is the measure of the thickness of the liquid, a property that resist the force tending to cause the fluid to flow. Due to internal friction among their particles, liquid and gases have different viscosities. A fluid with large viscosity resists motion because its molecular makeup gives it a lot of internal friction. A fluid with low viscosity flows easily because its molecular makeup results in very little friction when it is in motion.

Newton’s law of viscosity states that the shear stress is linearly proportional to the velocity gradient and demonstrated using the following equation

τ = μ dvdy

………………..(1)

From the Newton Laws of viscosity, the following equation can also be used to demonstrate the definition of viscosity

μ = τ

dV /dy………………..(2)

where μ = dynamic viscosity

τ=shear stress

The value of viscosity varies with the types of fluid; Newtonian fluid or Non-Newtonian fluid, timeand it is highly dependent on temperature (Munson,Young,Okiishi & Huebsch, 2009).

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Figure 1 : viscosity depend on the types of fluid

A number of methods are used to measure the viscosity of fluids. This are typically based on one of three phenomena—a moving surface in contact with a fluid, an object moving through a fluid, and fluid flowing through a resistive component. These phenomena utilize three major viscometers in the industry, i.e., a rotating viscometer, a falling-ball viscometer, and a capillary viscometer.

In this experiment, the existence and nature of viscosity can be demonstrated using The Höppler principle. This method is discovered by Fritz Höppler in 1932 and the method is named after him. The principles is used to measure the viscosity of Newtonian fluids. The viscosity can be experimentally determined by measuring the rate of a fall of a ball in a tube filled with liquid to be investigated.

Under Hoppler principle, the falling time of a ball of known diameter and density through a close to vertical glass tube of known diameter and length, filled with the fluid to be tested. The viscosity of the sample liquid is related to the time it takes for the ball to pass a distance between two specified lines on the cylindrical tube. The average time of three tests is taken and the result is converted into a viscosity value using a simple formula

When the sphere moves through the liquid, it is affected by the gravity, buoyancy and frictional forces: Gravity as downward force, buoyancy and friction as the upward forces

W=mg=Vρsg=4/3πr3 ρsg………………..(3)

ρs :density of sphere

g: gravitational acceleration

V: volume of ball

r: radius of ball.

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The viscosity measurement are used and apply in the industry to enhance the research and optimize the production of the desired product. Among the industry that are familiar with this concept are food industries, petroleum industries, concrete industries, cosmetics industries and etc.

One of the industries that performed the concept of viscosity is the petroleum refining facilities. This industry manufacture a wide variety of fuel and lubrication products. In order to ensure exact product specifications, accurate viscosity measurements are needed (Hart Scientific).

Jenton writes that Viscosity also plays a very prominent role in the petroleum industry. The viscosity of a crude oil affects our ability to pump it out of the ground; the viscosity and volatility of a fuel affect how easy it is to atomize in the fuel injector; the viscosity of a lubricant affects its ability to protect an engine. The application of viscosity in petroleum industries is further supported by CSC Scientific Company,InC(2014) who states that viscosity measurements project the effectiveness of lubricating oil and determines design elements of pipeline.

5

METHODOLOGY

In experiment 2: Viscosity Measurement, there are two parts of experiments that were conducted, which are part 2(a) and part 2(b). Experiment of 2(a) aimed to determine the relationship between viscosities of pure liquid substance with temperature.

In experiment 2(a), the relationship between the viscosities of the pure liquid substance with temperature using the Höppler principle of falling ball were studied. During the conduct of experiment 2(a), a minimum of 5 temperature readings were obtained which are 40 C, 45 C, 50 C, 55 C and 60 C .The temperature were regulated accordingly through ̊� ̊� ̊� ̊� ̊� the water bath provided. A liquid sample, which is distilled water, is used for the experiment and its density is determined using available data. A glass sphere with a diameter of 15.810mm is selected, named Ball 1 and metal sphere with a diameter of 15.639mm is selected and named Ball 3. A viscometer tube is fill with the water and regulated to temperature of 40 C. The glass ball 1 is placed into the tube and a stopper is secured to the ̊� tube. The time taken for Ball 1 to fall from one ring mark to another is recorded with a stopwatch. Ball 1 is substituted with Ball 3 and the time for the movement of the ball from one ring to another is recorded. The steps are repeated using temperatures of 45 C, 50 C, ̊� ̊� 55 C and 60 C. The whole experiment is then repeated again using methanol instead of ̊� ̊� distilled water. The corresponding viscosity of the liquid samples are determined. The results are then compared with the theoretical value. Discussion were made using the data given.

Experiment 2(b) aimed to evaluate the effect of mixture of liquids to the viscosity. The relationship between the concentrations of the pure liquid substance with viscosity using the Höppler principle of falling ball is studied. In the experiment, a minimum of 5 different concentrations of liquid mixtures consisting of pure water and methanol are prepared. A volume-to-volume ration (v/v %) is used. The variation of the concentration of both distilled water and methanol are determined accordingly. Glass Ball 1, is selected for the experiment. The temperature were regulated to 40 C through the water bath provided. ̊� Liquid mixture of concentration ratio of water to methanol is 1.0:0.0 is fill into the viscometer. Ball 1 is placed into the tube and a stopper is secured to the tube. The time taken for Ball 1 to fall from one ring mark to another is recorded with a stopwatch. The steps are repeated with liquid mixtures of different concentration with the ration of water to methanol being 0.75:0.25, 0.50:0.50, 0.25:0.75 and 0.0:1.0. The corresponding viscosity of the liquid samples are determined. Discussion were made using the data given.

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Flowchart for Experiment 2(a):

7

Flowchart for Experiment 2(b):

8

RESULTS AND DISCUSSION

Experiment 2A: Determination of relationship between viscosities of pure liquid substance with temperature

Tabulated Data

1) Ball 1 (Glass)

Type of ball : Boron Silicate Glass

Diameter of the ball, D (mm) : 15.810

Mass of the ball, m (g) : 4.594

Density of the ball, p (g/cm3) : 2.2200

Ball Constant Forward, K (mPa.cm3/g) : 0.00861

Ball Constant Forward, K (mPa.cm3/g) : 0.00872

Viscosity Range (mPa.s) : 0.5 – 7x104

Type of Solution: Water

No.

Temperature, T (˚c)Time (s)

Distance, s (mm) K (mpa.cm3/g)t1 t2 t3 Avg

1 40 33.12 33.04 33.19 33.11667 100 0.008612 45 29.38 29.5 29.22 29.36667 100 0.008613 50 26.56 26.53 26.49 26.52667 100 0.008614 55 24.41 24.39 24.4 24.4 100 0.008615 60 23.59 23.2 23.97 23.58667 100 0.00861

Table 1 : Raw data for water using glass ball

Temperature, T (˚c)

Density ps (g/cm3)

Density pl (g/cm3)

Experimental Viscosity η

(mPa.s)

Theoretical Viscosity η (mPa.s)

Percentage Difference (%)

40 2.22 1 0.34786409 0.653 0.4672831745 2.22 1 0.30847334 0.596 0.48242728250 2.22 1 0.278641412 0.547 0.49060070955 2.22 1 0.25630248 0.504 0.49146333360 2.22 1 0.247759064 0.467 0.469466672

Table 2 : Manipulated data for water using glass ball

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Type of Solution: Methanol

No.

Temperature, T (˚c)Time (s)

Distance, s (mm) K (mpa.cm3/g)t1 t2 t3 Avg

1 40 21.39 21.02 21.79 21.4 100 0.008612 45 17.96 17.45 18.34 17.91667 100 0.008613 50 16.41 16.35 16.47 16.41 100 0.008614 55 15.43 15.44 15.42 15.43 100 0.008615 60 14.37 14.33 14.42 14.37333 100 0.00861

Table 3 : Raw data for methanol using glass ball

Temperature, T (˚c)

Density ps (g/cm3)

Density pl (g/cm3)

Experimental Viscosity η (mPa.s)

Theoretical Viscosity η (mPa.s)

Percentage Difference (%)

40 2.22 0.792 0.263114712 0.446 0.410056745 2.22 0.792 0.22028685 0.4201 0.47563234950 2.22 0.792 0.201762263 0.3942 0.48817284955 2.22 0.792 0.189713084 0.3726 0.49083981660 2.22 0.792 0.176721283 0.351 0.496520561

Table 4 : Raw data for methanol using glass ball

2) Ball 3 (Steel)

Type of ball : Nickel Iron Alloy

Diameter of the ball, D (mm) : 15.639

Mass of the ball, m (g) : 16.277

Density of the ball, p (g/cm3) : 8.1268

Ball Constant Forward, K (mPa.cm3/g) : 0.0723

Ball Constant Forward, K (mPa.cm3/g) : 0.0722

Viscosity Range (mPa.s) : 0.5 – 7x104

Type of Solution: Water

No.

Temperature, T (˚c)Time (s)

Distance, s (mm) K (mpa.cm3/g)t1 t2 t3 Avg

1 40 1.66 1.66 1.67 1.663333 100 0.07232 45 1.47 1.51 1.45 1.476667 100 0.07233 50 1.39 1.38 1.38 1.383333 100 0.07234 55 1.5 1.51 1.46 1.49 100 0.07235 60 1.41 1.42 1.41 1.413333 100 0.0723

Table 5 : Raw data for water using steel ball

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Temperature, T (˚c)

Density ps (g/cm3)

Density pl (g/cm3)

Experimental Viscosity η (mPa.s)

Theoretical Viscosity η (mPa.s)

Percentage Difference (%)

40 8.1268 1 0.857061841 0.653 0.31249899145 8.1268 1 0.760878548 0.596 0.2766418650 8.1268 1 0.712786902 0.547 0.30308391655 8.1268 1 0.767748784 0.504 0.52331107960 8.1268 1 0.728244931 0.467 0.559410988

Table 6 : Manipulated data for water using steel ball

Type of Solution: Methanol

No.

Temperature, T (˚c)Time (s)

Distance, s (mm) K (mpa.cm3/g)t1 t2 t3 Avg

1 40 1.53 1.51 1.56 1.533333 100 0.07232 45 1.28 1.28 1.27 1.276667 100 0.07233 50 1.31 1.3 1.32 1.31 100 0.07234 55 1.32 1.35 1.33 1.333333 100 0.07235 60 1.22 1.24 1.23 1.23 100 0.0723

Table 7 : Raw data for methanol using steel ball

Temperature, T (˚c)

Density ps (g/cm3)

Density pl (g/cm3)

Experimental Viscosity η (mPa.s)

Theoretical Viscosity η (mPa.s)

Percentage Difference (%)

40 8.1268 1 0.790077048 0.446 0.77147320245 8.1268 1 0.65782502 0.4201 0.56587722150 8.1268 1 0.675000608 0.3942 0.71233031155 8.1268 1 0.68702352 0.3726 0.84386344660 8.1268 1 0.633779197 0.351 0.805638738

Table 8 : Manipulated data for methanol using steel ball

30 35 40 45 50 55 60 650

0.10.20.30.40.50.60.70.80.9

Graph of Dynamic Viscosity of Water vs Temperature

Ball 1 (Glass) Linear (Ball 1 (Glass))Ball 3 (Steel) Linear (Ball 3 (Steel))Linear (Ball 3 (Steel))

Temperature, T (˚c)

Dyna

mic

Vis

cosi

ty (m

Pa.s

)

11

Figure 1: Graph of dynamic viscosity of water vs temperature by using Ball 1 and Ball 3.

30 35 40 45 50 55 60 650

0.10.20.30.40.50.60.70.80.9

Graph of Dynamic Viscosity of Water vs Temperature

Ball 1 (Glass) Linear (Ball 1 (Glass))Linear (Ball 1 (Glass)) Ball 3 (Steel)Linear (Ball 3 (Steel)) Linear (Ball 3 (Steel))Theoretical Value

Temperature, T (˚c)

Dyna

mic

Vis

cosi

ty (m

Pa.s

)

Figure 2: Graph of dynamic viscosity of water vs temperature by using Ball 1 and Ball 3 with comparison with the theoretical value.

30 35 40 45 50 55 60 650

0.10.20.30.40.50.60.70.80.9

Graph of Dynamic Viscosity of Methanol vs Temperature

Ball 1 (Glass) Linear (Ball 1 (Glass))Linear (Ball 1 (Glass)) Ball 3 (Steel)Linear (Ball 3 (Steel)) Linear (Ball 3 (Steel))

Temperature, T (˚c)

Dyna

mic

Vis

cosi

ty (m

Pa.s

)

Figure 3: Graph of dynamic viscosity of methanol vs temperature by using Ball 1 and Ball 3

12

30 35 40 45 50 55 60 650

0.10.20.30.40.50.60.70.80.9

Graph of Dynamic Viscosity of Methanol vs Temperature

Ball 1 (Glass) Linear (Ball 1 (Glass))Linear (Ball 1 (Glass)) Ball 3 (Steel)Linear (Ball 3 (Steel)) Linear (Ball 3 (Steel))Theoretical Value

Temperature, T (˚c)

Dyna

mic

Vis

cosi

ty (m

Pa.s

)

Figure 4: Graph of dynamic viscosity of water vs temperature by using Ball 1 and Ball 3 with comparison with theoretical value.

For this experiment 2(a), there are two materials of ball which is boron silicate glass and also nickel iron alloy. The boron silicate glass has a diameter of 15.810 mm while the nickel iron alloy has a diameter of 15.639 mm. The glass ball is then inserted into Hoppler Viscometer and then the reading for time taken for the ball to pass through 100mm is noted. The variable is the temperature at which we start at 40 ˚C till 60 ˚C with 5 ˚C intervals. The experiment is repeated for steel ball to replace the glass ball. The pure liquid that was used for this experiment was water and methanol. The results obtain from this experiment is then tabulated in the table.

The time taken for this readings were taken 3 times to make it an average so that we can minimize the error in our results. This will also help to minimize the human reaction time error.

From the results, it is clear that the time taken for the ball to pass through 100mm for steel ball takes less time compared to the glass ball. Besides that, it shows that the average time taken for both sphere decreases as the temperature increases. The equation that is used to calculate the dynamic viscosity is as follows:

𝜂=𝐾𝑡(𝜌𝑠−𝜌𝐿)

The experiment data is compared to the theoretical value to have the percentage error which is obtained from Table A-9 (Properties of Saturated Water) which is attached in the appendix and graph are plotted for a better view. Based on the graph, as the temperature increases, it is observed that there is a steady declining rate in the theoretical as well as experimental graph.

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The reason why the viscosity decreases as the temperature increases is that when the liquid is heated, the attractive binding force between water molecules decreases. Referring to the percentage error, in this experiment, we have percentage of below 1%. This shows that the experiment have a very low error which is in acceptable range. But then. Due to some reasons, there is few errors that exist.

Firstly, parallax error which can be caused by incorrect eye level’s position while observing the spherical ball to fall. Next, time reaction error where u start the stopwatch late. This errors can be reduced by taking 3 readings. Some errors are unavoidable such as systematic error for the temperature reading given by the equipment. The readings also fluctuates a lot. Thus, to conclude this part of experiment, as the temperature increases, the viscosity decreases.

Experiment 2b: Evaluating the effect of mixture of liquids to the viscosity

Specification of Glass ball 1:

Material of Ball 1: Glass

Diameter of Ball 1 (mm) : 15.810 mm

Mass of Ball 1,(g) : 4.594 g

Density of Ball 1 (g/cm3) : 2.2200 g/cm3

Ball Constant Forward, K (mPa cm3/g) : 0.00861 mPa cm3/g∙ ∙

Ball Constant Reverse, K (mPa cm3/g) : 0.00872 mPa cm3/g∙ ∙

Volume (ml) Ratio Time taken for ball to move from one ring mark to another (s)Water

Methanol Water Methanol

Reading 1(s)

Reading 2 (s)

Reading 3 (s) Average Reading (s)

40 0 1.0 0.0 23.58 23.60 23.59 23.59

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30 10 0.75 0.25 35.12 35.17 35.16 35.1520 20 0.50 0.50 32.48 32.53 32.50 32.5010 30 0.25 0.75 25.47 25.50 25.50 25.500 40 0.0 1.0 14.35 14.37 14.38 14.37

Table 2(b)(i): Raw data of mixture with different concentrations at 40 C ̊�

Table 2(b)(ii): Calculated data on the concentration of methanol and dynamic viscosity

Specification of pure substances:

Water MethanolMolar mass 18.02 g/mol 32.04 g/molDensity 0.9921 g/m3 769600 g/m3

Dynamic Viscosity

0.653 x 10-3 kg/m s∙

4.460 x 10-4 kg/m s∙

In Part B of the experiment the objective is to study the effect of concentration of liquid mixtures to the viscosity by using the HÖppler principle of falling ball. In this experiment, five different concentration of mixture are prepared. The mixture consist of pure substances which are, pure water and methanol. A glass sphere ball with diameter of 15.639mm is selected to conduct the experiments. The bath water is regulated to a temperature of 40 C ̊� and the viscometer is filled with pure water. Glass ball is then inserted into the viscometer and time taken for the ball to move from one mark ring to another is recorded. The procedure is then repeated by replacing water with mixture of different concentrations.

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Volume (ml) Concentration of Theoretical DynamicExperimental Dynamic

Water Methanol

methanol (mol/dm3) Viscosity, μ (mPa s)∙ Viscosity, η (mPa s)∙

Percentage error (%)

40 0 0 0.653 0.2494 61.8130 10 6.005 0.6013 0.3884 35.420 20 12.01 0.5495 0.3747 31.8110 30 18.015 0.4978 0.3062 38.490 40 24.02 0.446 0.1795 59.75

0 6.005 12.01 18.015 24.020

0.1

0.2

0.3

0.4

0.5

0.6

0.70.653

0.60130.5495

0.49780.446

0.2494

0.3884 0.37470.3062

0.1795

f(x) = − 0.05175 x + 0.70477

f(x) = − 0.0222 x + 0.36624

Theoretical Dynamic Viscosity, μ (mPa s)∙Linear (Theoretical Dynamic Viscosity, μ (mPa s))∙Experimental Dynamic Viscosity, η (mPa s)∙Linear (Experimental Dynamic Viscosity, η (mPa s))∙

The concentration of metanol

Dyna

mic

Visc

osity

Graph 5: Graph of dynamic viscosity VS concentration of methanol at 40 °C

The graph above shows that as methanol concentration increases, the dynamic viscosity calculated at 40 C increases. However, when the liquid mixtures reach a certain ̊� concentrations where the ratio of water to methanol is 0.75:0.25 , the dynamic viscosity is decreasing along with increasing of the mixture concentrations. Theoretically, the mixture of water and methanol should have a higher dynamic viscosity than pure liquid substance because the intermolecular forces of the liquid molecules are strongly interacting with each other. From this, it can be concluded that the results obtained from this experiment does not follow the theory. Besides, the highest percentage difference of theoretical and experimental dynamic viscosity is 61.81%. These are due to the errors found in the experiment that interfere with the accuracy of the data.

Errors

During experiment, a few errors are being observed causing inaccuracy in the data collected:

1. Parallax error. This error due to observer’s incorrect eye level’s position while observing the transition of the ball from one marked ring to another.

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2. Human error may occur during the starting and the stopping of stopwatch. Slow reaction time will cause the time recorded to differ from the actual time of experiment, thus affecting the result.

3. Temperature. The temperature of liquid in Höppler viscometer is not kept constant thus affecting the experiment result.

Recommendations

1. Observer needs to place the eye level at angle of 90˚ perpendicular to the marked ring on the viscometer to avoid parallax error.

2. Three readings of time taken for the ball to fall from one marked ring to another are taken and

the average is obtained to improve the accuracy of the results.

3. The temperature of the liquid should be left to stabilize to obtain a constant temperature before conducting the experiment.

CONCLUSION

As the conclusion, we are able to determine the viscosity of pure water, pure methanol and the mixture of both liquids using the Höppler Method. The dynamic viscosity for each sample is calculated using the time recorded and the data is tabulated and then presented in graphical form.

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For the first part of the experiment, we can relate the viscosities of pure substances and its temperature based on the graph plotted. The time taken for the ball to reach the bottom line is shorter when the temperature is higher for both substances. From the graph, the increase in temperature reduces the dynamic viscosity of both water and methanol. The different material balls with almost the same diameter do not significantly affect the dynamic viscosity of the fluid samples used. The experimental values are not approximately the same to the theoretical values as the might be some errors when the experiment is conducted.

For the second part, we want to evaluate the effect of mixture of water and methanol to the dynamic viscosity. From the graph made, it indicated that pure substances has lower dynamic viscosity if compared to their mixtures as longer time is needed for the ball to fall when mixtures is used.

However, the might be some error while conducting the experiment. For example, the existence of air bubble inside the tube affects the time taken for the ball to fall, as well as the accuracy of taking the reading from where the ball should fall with the time of manually pushing the stopwatch. The parallax error might occurs also when observing the ball to start falling and when it reached the bottom line. Despite the errors, it is still concluded that the hypothesis is accepted.

Conducting this experiment has deepened our understanding regarding the viscosity of fluids and the factors affecting it. It is a useful information especially to transport fluids through pipe over long distances as part of our field of work. Changing climates and different temperatures should be considered because it will affect the viscosity and rate flow of fluids.

REFERENCES

Abdullah, M.Z. (2015). CDB 2052 CHEMICAL ENGINEERING LABORATORY 1 LABORATARY MODULE. Universiti Teknologi PETRONAS

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Cengel, Y. A. and Cimbala, J. M.(2006). Fluid Mechanics: Fundamentals & Application, Pennsylvania USA: McGraw-Hill.

CSC Scientific Company,InC. 2014. Viscosity, Testing the flow ability of liquids product. Retrieved from http://www.cscscientific.com/viscosity

Department of Energy Technology. SOP for Falling Ball Viscometer. Retrieved 18 October 2015 fromhttps://www.kth.se/polopoly_fs/1.291037!/ Menu/general/column-content/attachment/KTH-SOP-H%C3%B6pplerVisc-NanoHex-%20Final.pdf

Geankoplis, C. J. (2003). Transport Process and Unit Operations. 4th ed., New Jersey: Prentice Hall. Green, D. W. & Perry, R. H. (2008).

Jenton International UK. Viscosity Contol Application. Retrieved from http://www.viscositycontrol.co.uk/viscosity%20applications.html

Hart Scientific, Determination of Kinematics Viscosity, Industries Performing Kinematic Viscosity Testing Retrieved from http://www.mbelectronique.fr/Oil%20&%20Gas%20-%20Kinematic%20Viscosity.pdf

http://classroom.synonym.com/changing-temperature-affect-viscosity-surface-tension-liquid-16797.html

http://www.columbia.edu/itc/ldeo/lackner/E4900/Themelis3.pdf

Perry’s Chemical Engineers’ Handbook. United State : McGraw Hill.

White, F. M., Fluid Mechanics, 5th Ed., McGraw-Hill, 2005.

APPENDICES

Calculations (2a)

19

Average time taken, t = t 1+t 2+t 3

3

Percentage error (%) = (theory−experimental)

experimental×100

Density of water (ρ) & Theoretical dynamic viscosity (μ) at different temperatures are obtained from Appendix I (Property Tables and Charts).

Specification of Glass ball 1:

Material of Ball 1: Glass

Diameter of Ball 1 (mm) : 15.810 mm

Mass of Ball 1,(g) : 4.594 g

Calculations (2b)

Calculation for theoretical dynamic viscosity for ratio of water against methanol (0.75 : 0.25) :

μ = (μ of water at 40 °C)(ratio of water) + (μ of Methanol at 40 °C)(ratio of Methanol)

= (0.653 × 10-3 )(0.75) + (4.460 × 10−4 )(0.25) = 6.0125 x 10-4 𝑘𝑔/𝑚 ∙ 𝑠 = 0.6013 𝑚𝑃𝑎 ∙ 𝑠

Calculation for experimental dynamic viscosity, η for ration of water against methanol (0.75:0.25) :

Total volume of solution = 40 𝑚𝐿 × 0.001𝑑𝑚3 /1 𝑚𝐿

= 0.04 𝑑𝑚3

Mole of Methanol = 𝜌𝑉 /𝑀= 10mL×(0.001dm3/1mL)×(769600g /1m 3)×( 0.001m 3

1dm3)

32.04 g /mol

= 0.2402 𝑚𝑜l

Concentration of Methanol

= 0.2402mol0.04dm 3

= 6.005 𝑚𝑜𝑙/𝑑𝑚3

Density of mixture, ρL

20

= (0 .7696 gcm 3)(10 cm3)+(0.9921 gcm3)(30 cm3)

40cm 3

= 0.9365 𝑔/𝑐𝑚3

Experimental dynamic viscosity, η

= 𝐾𝑡(𝜌𝑠 − 𝜌𝐿 )

= (0.00861 𝑚𝑃𝑎 ∙ 𝑐𝑚3 ) (35.15 𝑠)(2.2200 − 0.9365)𝑔/𝑐𝑚3

= 0.3884 𝑚𝑃𝑎 s∙

Percentage error for ratio for ratio water towards methanol ( 0.75: 0.25)

Percentage Error

= | Theoretical−ExperimentalTheoretical

Theoritical | × 100%

= | 0.6013−0.3884

0.6013| × 100% = 35.40 %

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Appendix: Table A-9 : Properties of Saturated Water

22

Appendix 2 : Properties of Liquids

23