VISCOSITY

YEDİTEPE UNIVERSITY DEPARTMENT OF

MECHANICAL ENGINEERING

1

YEDITEPE UNIVERSITY ENGINEERING FACULTY

MECHANICAL ENGINEERING LABORATORY

1. OBJECTIVE

To calibrate the system with a known viscosity.

To measure fluid viscosity and observing the difference between Newtonian and non-

Newtonian fluids.

2. EQUIPMENT

Capillary tube

Multimeter

Pressure Sensor

Compressor

Thermometer

Beaker

Pressure Tank

Stop-watch

Water container (the cup that capillary tube is connected)

Electronic balance

Power Supply

2

3. PROCEDURE

Figure 1: Schematic diagram of the test setup

3.1 Calibration of the capillary tube

1. Fill the beaker with tap water and measure its temperature by using a thermometer.

2. Poor the tap water into the water tank and close the lid of the capillary tube.

3. The beaker is weight.

4. Prepare the stop-watch and place the beaker under the capillary tube.

5. Measure the initial height of the fluid (H1) and record it.

6. Simultaneously open the lid of the capillary tube and start the stop-watch.

Water

Tank

Cappilary

Tube

3

7. When water level drops to a specific height (do not allow the water completely flow

through the tank stop the experiment before it completely finishes) stop the stop-watch

and measure the final height of the fluid. Record the height and time measured by the

stop-watch.

8. Weigh the beaker (this time with the water in it!) and determine the mass of the water by

subtracting the empty weight of the beaker measured in the step 3. Than record it.

9. Repeat steps 2 times.

10. Use measurements to calculate capillary tube diameter according to Eq. 4.4 via the

computer software and compare result with the known value.

3.2 Measuring the viscosity of the water and peach juice

1. Fill the beaker with tap water and measure its temperature by using a thermometer.

2. Poor the tap water into the water tank and close the lid of the capillary tube.

3. The beaker is weight.

4. Check that valve 1 is open and valve 2 is closed shown in Fig 1.

5. Fill the pressure vessel with pressurized air from the compressor until the pressure in the

compressor air tank reaches to 0.2 bars (run the compressor until this moment than stop

it).

6. After stopping the compressor you will see that the pressure is balanced between

compressor and pressure vessel and the final value will be 0.4 bars.

7. Prepare the stop-watch and place the beaker under the capillary tube.

8. Measure the initial height of the fluid (H1) and record it.

9. Open the valve 2 and valve 3 shown in Fig. 1.

10. Measure the ampere (A1) from the multimeter and record it.

11. Simultaneously open the lid of the capillary tube and start the stop-watch.

12. When water level drops to a specific height (do not allow the water completely flow

through the tank stop the experiment before it completely finishes) stop the stop-watch

and measure the final height of the fluid (H2) and the final ampere (A2). Record the

height and time measured by the stop-watch.

4

13. Weigh the beaker (this time with the water in it!) and determine the mass of the water by

subtracting the empty weight of the beaker measured in the step 3. Than record it.

14. Repeat steps 2 times.

15. Use measurements to calculate viscosity of the fluid by using Equation 4.2 and compare

the results by known value.

16. Repeat all steps for peach juice

4. THEORY

A fluid has an ability to flow by changing positions of its molecules with respect to

another. As expected this ability to flow is different for different fluids. As an example from real

life: if you poor a cup of water and honey on a surface it is seen that water flows easier than the

honey. This is because viscous effects on honey are much bigger than viscous effects on water.

There two related measures of fluid viscosity. These are known as the dynamic (absolute)

viscosity and the kinematic viscosity. Dynamic viscosity, μ, is the measure of the internal

resistance. It is the tangential force per unit area that required for the movement of the fluid layer

with respect to the neighboring one at unit displacement for a unit velocity. Kinematic viscosity,

υ, is the ratio of the dynamic viscosity to density of the fluid. No force is applied in this quantity.

It is expressed as υ = μ/ρ. Velocity gradient and stresses effecting on the fluid flowing in the pipe

is given in Fig. 2

Figure 2: Velocity is zero on the wall of the pipe as no slip condition states. Also it is seen that velocity

increases as y reaches to the middle of the pipe and gets its highest value.

5

2.1. Newtonian and Non-Newtonian fluids

When shear stress applied, viscosity of some fluid change. These types of fluids are

called as Non-Newtonian fluids. Non-Newtonian fluids can be categorized as shear-thinning and

shear thickening. Fluids that have no change in their viscosity by an applied shear stress are

called as Newtonian fluids. As an example mixing the fluid by a spoon or applying pressure on

the fluid creates shear stress on the fluid.

Shear thinning:

Shear thinning liquids have macromolecules or particles. And these molecules are

randomly stayed together under no flow. But at large shear stress levels they start to orient

themselves to the flow and their molecules rotate become parallel to the flow. Shear thinning

liquids’ viscosity decreases as the shear force increases.

Shear thickening:

Shear thickening liquids usually have solid particle suspensions. At low shear the fluid

layers act like a thin film layer to the relative motion and viscosity is low too. Contrary to shear

thinning liquids when the shear stress is increased the particle to particle contact and friction

appears. Thus the viscosity of shear thickening liquids increases as the shear force increases.

Figure 3: Viscosity vs. Shear Rate

6

2.2 Reynolds Number

In fluid mechanics Reynolds number, which is a dimensionless number, shows the

behavior of the flow. It is literarily the ratio of internal forces to viscous forces. Also it refers to

the flow situations, relative motion of the fluid, in various conditions. Reynolds number is given

as the following;

(4.1)

Where;

Re Reynolds number

ρ Fluid density

L Characteristic length

u Velocity of the fluid

μ Viscosity of the fluid

The flow type of the fluid should be known to make further calculations for the fluid viscosity.

For a flow through a pipe, the flow is

Laminar when Re < 2300

Transient when 2300 < Re < 4000

Turbulent when Re > 4000

2.3 Equations for Calculations

The viscosity of the fluid is calculated by using equation which is given below. This

equation is used only for the laminar flow condition.

7

( )

( ) {( )

} (4.2)

Where;

ρ Fluid density

L Length of the capillary tube (thickness of the connection member is included)

Mass flow rate

g Gravitational acceleration

Pt Applied pressure

Pa Atmospheric pressure

D Diameter of the capillary tube

Ht Average of the initial height and the final height of the fluid (

)

α2 Kinetic energy correction factor for fully developed laminar flow

Kent Entrance loss

Output of the pressure sensor is milliampere which is 4-20mA.Range of the pressure sensor is 0-

10psi (0-0.69bar). The applied pressure is obtained from equation which is given below;

( ) (4.3)

Pt Applied pressure

Aave Average milliampere which is read from multimeter (

)

8

The diameter of the capillary tube is calculated by doing algebraic arrangements to above

equation as follows.

(

( )

( ) ( ( )))

(4.4)

Take Kent, α2 and μ (water) as following for the calculations.

Kent=0.24

α2 =2

μ water = 0.0010449 (

)

Shear stress on the pipe wall can be found by using equation 4.5.

(4.5)

The following “Figure 4” is the graph of the (

) - ( )for ketchup. The coefficient of

x in the graph (can be denoted as n) is found as 0.3089. The reason of taking the logarithm of the

“ ” and “

” is very important.

If

n<1 the fluid is Non-Newtonian

n>1 the fluid is Newtonian

Where;

V Fluid velocity

D Diameter of the capillary tube

9

Figure 4: The slope of the line on the ( ) and (

) plot shows if the fluid is shear thinning

or shear thickening.

5. ANALYSIS AND DISCUSSION

1. Give a sample calculation of the diameter, the viscosity, and the wall shear stress.

2. Show the variations of the (

) (in x axis) - ( ) (in y axis) for each fluid in

the different graphs and comment the graph.

3. Discuss how the viscosity changes with τ wall.