VISCOSITY MEASUREMENT USING FALLING BALL VISCOMETER

During our discussion on previous post “Hydraulic Fluid”, I have promised to create one post for understanding the concept of viscosity measurement with the help of viscometer technology. 

Let us understand how we can measure viscosity of a fluid, i have decided to produce one live experiment report for better understanding the concept of measurement of viscosity . 

Let’s start!!!

Let us think we have to measure the viscosity of glycerin with the help of falling viscometer technology. We will start to understand the viscosity measurement with following basic points.

1. Concept & Theory
2. Apparatus 
3. Experimental procedure
4. Result and Analysis 
5. Conclusion 

Sphere	D (m)	W (N)	T (s)	U (m/s)	Re	C	µ1 ( Pa. S)
1	0.0043688	0.00341	4.06	0.0750	0.444	54	0.9292
2	0.0043688	0.00341	4.19	0.0727	0.417	57.53	0.9590
3	0.0043688	0.00341	3.88	0.07855	0.487	49.31	0.8881
4	0.0043688	0.00341	4.00	0.0762	0.46	52.40	0.91552
5	0.0043688	0.00341	4.07	0.07488	0.44	54.26	0.93154
6	0.0043688	0.00341	4.00	0.0762	0.46	52.40	0.91552
7	0.0043688	0.00341	4.13	0.0738	0.429	55.86	0.94527
8	0.0043688	0.00341	3.87	0.078759	0.489	49	0.88576
9	0.0043688	0.00341	3.94	0.07736	0.472	50.84	0.90178
10	0.0043688	0.00341	4.00	0.0762	0.46	52.40	0.91552
11	0.0043688	0.00341	4.03	0.0756			0.92239
12	0.0043688	0.00341	3.97	0.07677			0.90865
13	0.0043688	0.00341	3.90	0.07815			0.89263
14	0.0043688	0.00341	4.09	0.07452			0.93612
15	0.0043688	0.00341	4.06	0.07507			0.92925
16	0.0043688	0.00341	4.09	0.07452			0.93612
17	0.0043688	0.00341	3.75	0.08128			0.8583
18	0.0043688	0.00341	3.87	0.78759			0.88576
19	0.0043688	0.00341	3.84	0.079375			0.87899
20	0.0043688	0.00341	3.97	0.07677			0.90865

Concept & Theory

When a body falls in a liquid due to gravity,' it accelerates until the weight of the body is equivalent to the drag force and buoyancy and the velocity of the body at this point is known as terminal velocity. We may determine the viscosity of the liquid by determining the terminal velocity of object or sphere in that liquid.

Let us understand, with the help of free body diagram, drag force, buoyancy force and weight of object or sphere during falling in liquid.

When this sphere will achieve its terminal velocity, we will have following force balanced equation

∑ F = 0

W= F_D + F_B

Where,

W= weight of sphere = Ƴ_S. V

F_D = drag force

F_B= Buoyancy force

Drag force:-

F_D= (Cρ₁U² A) / 2

Where,

C = drag coefficient

ρ₁= density of liquid (kg/m³)

U= terminal velocity of sphere (m/s)

A = (πD²/4)

In case of creeping flow

Drag co-efficient, C = 24/ Re

Where, Re= Reynolds number = ρ₁UD/µ₁

Where, D = Sphere diameter

µ₁= Liquid Dynamic viscosity

ρ₁= density of liquid

But we must be aware that for creep flow, Re<1

As per the Archimedes principle,

The force of buoyancy of a submerged body will be equivalent to the weight of the liquid which is displaced by the body.

Let us consider about the buoyancy force

F_B= Ƴ₁. V

Ƴ₁= Liquid specific weight

V= Volume of sphere

After solving above equation, we will have the final result as mentioned below for dynamic viscosity.

µ₁= (Ƴ_S- Ƴ₁). D²/ (18 U)

Apparatus

We have used following mentioned apparatus

1. Stop watch
2. Thermometer
3. Glycerol
4. Needle-nose pliers or tweezers
5. Scale of 1 Foot
6. 1000 ml graduated cylinder
7. Micrometer or vernier caliper
8. Electronic scale
9. Copper plated steel spheres (BB s)
10. Masking tape
11. Ring stand

Experimental procedure

We may briefly describe the procedure as mentioned below

• Measure the diameter with micrometer or vernier of 20 sphere and consider the average value for each sphere.
• Measure the weight of those 20 spheres of steel and consider the average value of weight of each sphere.
• Filling of graduate cylinder with glycerol and must assure that there will not be any entry of air bubbles.
• Now we will locate one masking tape piece on the cylinder approximate 100 mm below the glycerol surface and must be noted that the other piece i. e second piece should be about 305 mm lower than the first piece.
• Saturate the thermometer in the glycerol and must assure that temperature might be measured any time during experiment.
• Hold one sphere, with the help of pillers, approximate 25 mm lower the glycerol surface in the center of the cylinder. Now release the sphere.
• Measure the time with the help of stop watch that sphere takes to fall 305 mm as marked by the pieces of masking tape.
• Repeating the last two steps.
• Use the equation and determine the viscosity.

Result & Discussion

Some important point 

1.   1 Pa. s = 1000 CP

2.   Possible source of experimental error.There will be some error in measuring the time.There is also possibility in measuring the diameter of sphere

3.   Wall effect will have a retarding effect over the terminal velocity due to Presence of wall

Wall effect is normally indicated in terms of wall factor.

4.   Accuracy of the experiment could be improved by correct measurement of diameter of sphere and measurement of duration of time to fall the sphere by a distance as specified in experiment.

5.   Glycerol is Newtonian fluid

Conclusion

We have concluded the following points after studying this blog

• let us consider about the result that we have secured from our experiment. We have secured dynamic viscosity 912.20 Centi-poise (it's average value) 
• Objective of this blog is to secure the value of dynamic viscosity by falling ball viscometer technique.
• Glycerol is Newtonian fluid Wall effect will have a retarding effect over the terminal velocity due to presence of wall 
• Wall effect is normally indicated in terms of wall factor 
• Possible source of experimental error
• There will be some error in measuring the time
• There is also possibility in measuring the diameter of sphere

Accuracy of this report could be improved by correct measurement of diameter of sphere and measurement of duration of time to fall the sphere by a distance as specified in experiment.

Let us move towards new post.

The various components of Hydraulic system”

Keep reading...