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Viscosity in Fluids (Theoretical & Experimental approach)

By: Rahim HASSANZADEH

Faculty of Mechanical Engineering Cukurova University

Adana-Turkey 2010

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Introduction All fluids offer resistance to any force tending to cause one layer to move

over another. Viscosity is the fluid property responsible for this resistance.

Since relative motion between layers requires the application of shearing

forces, that is, forces parallel to the surfaces over which they act, the

resisting forces must be in exactly the opposite direction to the applied

shear forces and so they too are parallel to the surfaces.

It is a matter of common experience that, under particular conditions,

one fluid offers greater resistance to flow than another. Such liquids as

tar, treacle and glycerine cannot be rapidly poured or easily stirred, and

are commonly spoken of as thick; on the other hand, so-called thin liquids

such as water, petrol and paraffin flow much more readily. (Lubricating

oils with small viscosity are sometimes referred to as light, and those with

large viscosity as heavy; but viscosity is not related to density.)

Gases as well as liquids have viscosity, although the viscosity of gases is

less evident in everyday life.

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Table2-1:Units of dynamic viscosity

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Kinematic viscosity and its units

In fluid dynamics, many problems involving viscosity are concerned

with the magnitude of the viscous forces compared with the magnitude

of the inertia forces, that is, those forces causing acceleration of particles

of the fluid. Since the viscous forces are proportional to the dynamic

viscosity µ and the inertia forces are proportional to the density ρ , the

ratioρµ is frequently involved. The ratio of dynamic viscosity to density

is known as the kinematic viscosity and is denoted by the symbol υ so that:

ρµυ =

Table2-2:Units of kinematic viscosity

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Figure 2.2 Variation of shear stress and velocity gradient (deformation rate) for Newtonian and non-Newtonian fluids.

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In Newtonian fluids the variation between shear stress and velocity

gradient is linear.

y

u

∂∂= µτ

But in non-Newtonian fluids it is non-linear.

n

y

uK

∂∂=τ

in which K is the consistency index and n is the flow behavior index.

n<1 : pseudoplastic fluids (examples: gelatin, milk, blood, liquid cement)

n>1: dilatant fluids (examples: concentrated solution of sugar in water)

n=1:(and µ=k ) Newtonian fluids.

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The causes of viscosity

i) Liquids : In a liquid, the viscosity is due to cohesive forces.

ii) Gases : In a gas, it is due to collisions of molecules.

Effects of temperature and pressure on the dynamic viscosity :

i) Temperature effects : In a liquid cohesive forces decrease with

increasing of temperature . So, when temperature of a liquid increases ,

its dynamic viscosity decreases. On the other hand, In a gas accidents

and collisions between molecules increase with increasing of

temperature. So, when temperature of a gas increases , its dynamic

viscosity increases.

ii) Pressure effects: T he dynamic viscosity of fluids consist of liquids and

gases changes marginally with pressure , therefore, the variation of

dynamic viscosity with pressure is generally neglected in most

engineering applications.

Note: The kinematic viscosity of a gas depends to pressure because its

density changes with pressure changing strongly.

≠≠

)(

)(

pf

pfLiquids

υµ

=≠

)(

)(

pf

pfGases

υµ

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APPARATUS

The basic of the measurement of the shear stress with rotational

viscosimeter depends up on the principle of measurement of the shear

stresses and velocity gradient by creating a Couette flow. This principle

is shown schematically in figure 3a. Couette flow which has a maximum

velocity of wR is given in figure 3b. The indicator capable of rotating

240o is a measure for the moment effecting on the piston.

The period number of piston can be adjusted by turning the

adjusting lever clockwise or in opposite direction.

The water necessary for the temperature-controlled vessel is

provided by a water bath attached on the experimental set up.

Motor

P

S A

T.C.V.

P : Piston

S : Cylinder A: fluid which will be measured

T.C.V: Temperature controlled vessel

Figure 2-3a.Schematic diagram of the measurement technique.

Pump

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The water cycle between the constant temperature-container and water

bath is supplied by a pump behind the panel of experimental set up.

PERFORMING THE EXPERIMENT

It is essential to obey the following procedure.

a) The water level in the temperature controlled vessel and water

bath should be checked. If there is lacking water, water should be added.

b) The plug of the experiment set up should be connected to the city

network (220 volt, 50 Hz) and the main switch should be on. It must be

controlled that the circulation between the temperature controlled vessel

and water bath is continuous. If there is no water circulation, the air

bubbles in the system should be released.

c) The appropriate cylinders and pistons must be chosen from Table

2-3 for the measured fluid.

Cylinder Piston

Figure 2-3b.Velocity gradient between Piston-Cylinder

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Table 2-3. Choosing the appropriate cylinder and pistons for experimental fluids.

Name of

Cylinder

Name of

Piston

Shear Stress (N/m2) Velocity

Gradient (1/s)

Dynamic Viscosity

(cp)

N1 5……………………50 49.6……….496 10………….….1000 N

N2 5.6………………….56 18.8……….188 30..……………3000

M1 19…………………190 19.0……….190 100……….….10000 M

M2 26…………………260 8.56……….85.6 3000…………30000

H1 83…………………830 8.28……….82.8 10000………100000 H

H2 150……….……...1500 5.0………...50.0 25000………250000

d) Amount of liquid which has been determined at table 2-4 should

be put into the cylinder. The piston, cylinder and the temperature-

controlled vessel should be mounted to the experiment set up.

Table 2-4. Amount of liquid put in the cylinders

Name of Cylinder

N M H

Name of Piston N1 N2 M1 M2 H1 H2

Amount (cm3)%±±±±5 13.5 18 7.5 10.5 3.0 4.5

e) Thermometer must be connected to temperature-controlled vessel

and the thermometer of water bath must be adjusted to the temperature

which will be measured. By turning the speed lever, position of velocity

which is required must be chosen and experimental set up can be turned

on.

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NOTE : While the velocity is changed, the experiment should be

stopped.

f) The values on the indicator should be read after 10 or 20 sec.

Starting the experiment to run. If any value can not be read from the

indicator, it means that the chosen piston or cylinder isn’t suitable for

liquid whose viscosity is measured. In this case, you should continue

with (c).

g) Dynamic viscosity should be calculated using table 2-5 and

eq.2.3; Here, (skt) is indicated value by system.

µµµµ = K N αααα (Pa.sn= kg/ms) (2-3)

Table 2-5. Determining the coefficient K, N and Z

N velocity factor for velocity gradient Name of

Cylinder

Name of

Piston K (Pa.s/skt) Z (Pa/skt)

10 4 2 1

N1 0.99 10-3 0.491 49.6 124 248 496 N

N2 2.84 10-3 0.533 18.8 47 94 188

M1 9.40 10-3 1.786 19.0 47.5 95 190 M

M2 2.745 10-2 2.349 8.56 21.4 42.8 85.6

H1 8.197 10-2 6.787 8.28 20.7 41.4 82.8 H

H2 22.779 10-2 11.390 5.0 12.5 25 50

ττττ = Z αααα (Pa) (2-4)

Shear stress must be calculated with the help of table 2-5 and eq.2.4.

h) After finishing the experiments, temperature controlled vessel,

cylinder and piston must be disassembled from the experimental set up.

After the experiment set must be dried with soft cloth or pressured air.

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i) All buttons on apparatus and the main switch are to turn off and

plug of apparatus is to be disconnected from the socket.

EXPERIMENT REPORT

5.1. Evaluation

a) Determine the experimental results calculate the required values from

table 2-6.

Table 2-6. Sample of utilizing of experimental results.

Kind of

Fluid

Name of

Cylinder

Name

of

Piston

K

(Pas/skt) Z

(Pa/skt) N

du/dy

1/s

T

(°°°°C)

αααα

(skt)

µµµµ

(Pas)

ττττ

Pa

b) Draw the relationship between dynamic viscosity-temperature of

measured fluid on the diagram.

c) Draw the relationship between shear stress-velocity gradient of

measured fluid on the diagram.

Discussions

a) Is the measurement fluid in accordance with Newton’s shear stress

law?

b) How is the variation between viscosity and temperature? Why?

c) Consider Figure 2-3b ,with implementation of suitable coordinates

,calculate the variation of velocity gradient and sheer stress

magnitude.