Science Investigative Project: June 2011

Experiment 2b – Finding a mixture between honey and water with a viscosity of 10

Aim of experiment: To find a mixture with a viscosity of 10 by mixing honey and water in different percentages.

Hypothesis:

Let the amount the viscosity of the 100ml mixture increases by, with every replacement of 1ml of water with 1ml of honey, be x.

x = 0.01(Viscosity of honey – Viscosity of water)

= 0.01(40.2402 – 1.004)

= 0.01 x 39.238

= 0.39238 cSt

If x = 0.39238 is accurate,

The percentage of honey in the mixture

= (10 – 1.004) ÷ 0.39238

= 8.996 ÷ 0.39238

= 22.92675468%

= 23% (Round off to whole no.)

The percentage of water in mixture

= 100 – 23

= 77%

Therefore, if the viscosities of water and honey are accurate, the mixture should consist of 23% honey and 77% water to achieve a viscosity of 10.

Materials Needed:

- 1 Zahn cup set-up (From experiment 1)

- 1 measuring cup (100ml)

- 1 measuring cup (44ml)

- 1 stopwatch (times up to milliseconds)

- 1 bottle of honey

- 1 calculator

- 1 mixing spoon

- 1 thermometer

Experiment Procedure:

1. Measure 23ml of honey into the measuring cup (100ml).

2. Measure 77ml of water into the same measuring cup.

3. Mix it well.

4. Allow the mixture to reach the temperature of the air-conditioned room (20ºC).

5. Use the thermometer to check the temperature of the mixture.

6. Pour the mixture into the Zahn Cup and start the stopwatch at the same time.

7. Stop the stopwatch when the continuous flow of honey water is broken.

8. Take down the timing up to milliseconds.

9. Repeat steps 1-8 4 times more for more accurate results.

10. Using the formula [1.1(time taken for liquid to flow from orifice – 29)], calculate the viscosity of the mixture based on the 5 timings.

11. Calculate the average viscosity of the 5 values.

*Note: If percentages do not result in the expected viscosity of 10 cSt, re-conduct the experiment and increase or decrease the percentage of honey by 1% each time till viscosity is close to 10 cSt.

Independent Variable: (only is hypothesis is false) Percentage of honey in mixture.

Constant Variables:

1. Amount of mixture poured into Zahn Cup.

2. Size of orifice of Zahn Cup.

3. Temperature of mixture

Dependent Variable: Time taken for the continuous flow of honey water through the orifice to stop.

Results:

Liquid	Time	Viscosity
Honey Water	38.05	9.955
23% Honey	38.04	9.944
77% Water	38.56	10.516
	38.72	10.692
	37.45	9.295
	Average Viscosity	10.0844

Data Analysis:

A mixture of 23% honey and 77% water has a measured average viscosity of 10.0844 cSt. This is very close to my intended 10 cSt.

Conclusion:

To obtain a liquid with a viscosity of 10 cSt, I have to create a mixture with 23% honey and 77% water. This conclusion is valid only with the following assumptions:

1. The mixture was mixed well and the honey was not clumped together.

2. Human error of starting and stopping the stopwatch was minimal.

Experiment 2a – Finding the viscosity of honey

Type of honey used: SUPERBEE PURE AUSTRALIAN HONEY

Aim of experiment: To find the viscosity of honey at 20ºC using Zahn Cup.

Hypothesis: Honey is a very thick liquid, thus its viscosity should be high.

Materials needed:

- 1 Zahn cup set-up (From experiment 1)

- 1 measuring cup (44ml)

- 1 stopwatch (times up to milliseconds)

- 1 bottle of honey

- 1 calculator

Experiment Procedure:

1. Measure 44ml of honey using the measuring cup.

2. Allow the honey to reach the temperature of the air-conditioned room (20ºC).

3. Use the thermometer to check the temperature of the honey.

4. Pour the honey into the Zahn Cup and start the stopwatch at the same time.

5. Stop the stopwatch when the continuous flow of honey is broken.

6. Take down the timing up to milliseconds.

7. Repeat steps 1-6 4 times more for more accurate results.

8. Using the formula [1.1(time taken for water to flow from orifice – 29)], calculate the viscosity of honey based on the 5 timings.

9. Calculate the average viscosity of the 5 values.

Independent Variable: -NA-

Constant Variables:

1. Amount of honey poured into the Zahn Cup.

2. Size of orifice of Zahn Cup.

3. Temperature of honey.

Dependent Variable: Time taken for the continuous flow of honey through the orifice to stop.

Results:

Liquid	Time	Viscosity
Honey (20ºC)	65.76	40.436
	65.72	40.392
	65.31	39.941
	65.23	39.853
	65.89	40.579
	Average Viscosity	40.2402

Data Analysis:

From this experiment, I measured an average viscosity of honey: 40.2402 cSt.

Conclusion:

I conclude that the viscosity of honey is 40.2402 cSt. This conclusion is valid only with the assumption that human error in starting and stopping the stopwatch is minimal.

Experiment 1 - Does DIY Zahn Cup work?

Temperature - t - (^oC)	Dynamic Viscosity - µ - (N s/m²) x 10^-3	Kinematic Viscosity - ν - (m²/s) x 10^-6
0	1.787	1.787
5	1.519	1.519
10	1.307	1.307
20	1.002	1.004
30	0.798	0.801
40	0.653	0.658
50	0.547	0.553
60	0.467	0.475
70	0.404	0.413
80	0.355	0.365
90	0.315	0.326
100	0.282	0.294

Aim of Experiment: To find out if my DIY Zahn Cup #1 is able to measure viscosity of liquids accurately by trying it with water at 20ºC, which has a viscosity of 1.004 cSt. (Based on background research.)

Hypothesis: I should be able to calculate a viscosity of about 1.004 cSt if I keep the size of the orifice as close to the actual Zahn Cup as possible.

Materials needed:

- 2 styrofoam cups

- 1 transparent plastic container

- 1 measuring cup (44ml)

- 1 screwdriver

- 1 sheet of cardboard

- 1 ruler

- 1 pair of scissors

- 1 mathematical compass

- 1 stopwatch (times up to milliseconds)

- 1 string

- 1 calculator

Set-up:

Making cup holder

1. Using a piece of string, measure the circumference of the middle of the styrofoam cup by measuring the length of the string using a ruler.

2. Calculate the radius of the middle of the styrofoam cup using the circumference. (Circumference ÷ π ÷ 2)

3. Draw a circle with the calculated radius on the cardboard sheet using the compass.

4. Cup out the circle.

5. Measure the diameter of the transparent plastic container and make sure the cardboard sheet is larger than the diameter.

Making Zahn Cup # 1

1. Using a ruler, mark out a circle with diameter of 2mm [0.078 inch = 0.19812cm = 1.9812mm = 2mm (rounded off to nearest whole number)] on one of the styrofoam cups.

2. Using the screwdriver, poke the marked circle out to create a hole. Keep as close to the marking as possible.

3. Measure the diameter of the hole with the ruler to check if it is accurate. Re-do set-up if diameter of hole is more than 0.5mm off.

Experiment Set-up:

1. Place the cup holder on top of the transparent plastic container. (At the centre).

2. Place the Zahn Cup # 1 into the cup holder.

Experiment Procedure:

1. Using the measuring cup, measure 44ml of water.

2. Allow the water to reach the temperature of the air-conditioned room. (20ºC)

3. Use the thermometer to check the temperature of the water.

4. Pour the water into the Zahn Cup and start the stopwatch at the same time.

5. Stop the stopwatch when the continuous flow of water is broken.

6. Take down the timing up to milliseconds.

7. Repeat steps 1-6 4 times more for more accurate results.

8. Using the formula [1.1(time taken for water to flow from orifice – 29)], calculate the viscosity of water based on the 5 timings.

9. Calculate the average viscosity of the 5 values.

10. Check against the actual viscosity of water (1.004 cSt).

*Note: Should experiment fail (measured viscosity is more than 0.01 off the actual viscosity), repeat experiment once more, or check the orifice size of the Zahn Cup again.

Independent Variable: -NA-

Constant Variables:

1. Amount of water poured into Zahn Cup.

2. Size of orifice of Zahn Cup.

3. Temperature of water.

Dependent Variable: Time taken for the continuous flow of water through the orifice to stop.

Results:

Liquid (44ml)	Time (s)	Viscosity (cSt)
Water (20ºC)	29.84	0.924
	29.97	1.067
	29.98	1.078
	29.96	1.056
	29.82	0.902
	Average Viscosity	1.0054

Data Analysis:

From this experiment, I measured an average viscosity of water: 1.0054 cSt. The measured viscosity is only 0.0014 off from the actual viscosity. This margin of error may be due to human error made when starting and stopping the stopwatch.

Conclusion:

I conclude that the DIY Zahn Cup is effective in measuring viscosity of liquids as the measured viscosity of water is very close to the actual viscosity. This conclusion is valid only with the following assumptions:

1. The Zahn Cup will work as well with other types of liquid, and not only for water.

2. Human error in starting and stopping the stopwatch is minimal.

Summary of Research on Viscosity

What is viscosity?

Viscosity is a measure of the resistance of a liquid to flow.

Viscosity (represented by the symbol η) is the ratio of the shear stress (F/A) to the velocity gradient (Δv_x/Δz or dv_x/dz) in a fluid.

η =

⎛
⎝

⎞
⎠

⎛
⎝

Δv_x

⎞
⎠

η =

⎛
⎝

⎞
⎠

⎛
⎝

dv_x

⎞
⎠

Δz

F = Force applied

A = Cross-sectional area of material perpendicular to the force applied

v = velocity

z = distance

What is kinematic viscosity?

Kinematic viscosity is when viscosity is measured by timing the flow of a fixed volume of liquid from a viscosity measuring cup. (Zahn cups) The SI Unit for kinematic viscosity is Centistokes (cSt).

What are Zahn Cups?

Zahn cups are cups used to measure kinematic viscosity of liquids. They are 5 types of Zahn Cups, meant for different range of viscosities. They differ only in the size of the orifice (hole).

Catalog No.	Cup No.	Orifice, inch	Liquid type	Zahn range, seconds (250°C)	Range, Centistokes
3410-01	1	0.078	Very thin	45-80	18-56
3401-02	2	0.108	Thin	25-80	40-230
3401-03	3	0.148	Medium	20-75	150-790
3401-04	4	0.168	Heavy-thick	20-80	220-1100
3401-05	5	0.208	Very heavy-thick	20-75	460-1725+

In my experiment, I will most probably only be making use of Zahn Cup #1 as I only need to measure viscosities of up to 30. Zahn cups measure viscosity by measuring the time taken for 44ml of liquid to flow from the cups.

GENERAL FORMULA

V= K (T – C)

where: V is Kinematic Viscosity (cSt)

T is Efflux time (Zahn seconds)

K + C are constants ( Ref. # 1)

SPECIFIC FORMULAS

Zahn cup # Formula “T range seconds”

1 V = 1.1 ( T-29) 45-80

2 V = 3.5 (T-14) 25-80

3 V= 11.7 (T-7.5) 20-75

4 V= 14.8 (T-5) 20-80

5 V= 23 (T-0) 20-75

What is drag?

Drag, in fluid dynamics, refers to forces that oppose the relative motion of an object through a fluid (a liquid or gas). Drag forces depend on velocity.

STOKE'S GREAT LAW OF DRAG

If

r = the radius of a sphere in cm d₁ = the density of the sphere in g/cm³ d₂ = the density of the fluid in g/cm³ g = the local gravitational acceleration in cm/S² c = the Viscosity of the fluid in Poise v = the terminal velocity in cm/S

Then

$v = \frac{2r^2g\left(d_1 - d_2 \right)}{9c}$

From this, I can derive that the more viscous the fluid, the smaller the terminal velocity. Thus, I can form an hypothesis for my experiment (how does viscosity affect the movement of a pendulum in terms of speed?): The higher the viscosity of the liquid, the slower the pendulum will travel, therefore, the longer the time taken for one oscillation.