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Fluid Mechanics Lab, Experiment #1

LAB 2 – VISCOSITY

The most familiar property of a fluid is the viscosity. The viscosity is responsible for drag on

aerospace vehicles, friction in pipes, and the destabilization/stabilization of some laminar flows.

Viscosity is a fluid property subject to changes in temperature and pressure. The viscosity

of a liquid decreases with increasing temperature while the viscosity of a gas increases with

increasing temperature. It is sufficient to recognize that viscous effects originate at the molecular

level. In the presence of a velocity gradient normal to the mean flow, momentum exchange

between adjacent fluid lamina result in a net decrease of momentum – fluid friction. This

phenomenon occurs at the microscopic level and should not be confused with momentum transfer

in turbulence, which occurs at the macroscopic level.

Popular science characterizes the viscosity of a fluid by the degree of “thickness” or

“resistance” to flow. Water drains out of a sink much faster than an equivalent volume of molasses.

In fact, this observation has been exploited by the petroleum industry as a means to quantify

viscosity. For example, SAE 30 motor oil means that it took 30 seconds for a given quantity of

the oil at a specified temperature to drain from a container (the container in this case is more

appropriately a “Saybolt viscometer”). However, this is an oversimplification as viscosity does

not have the units of seconds.

Viscosity is better defined as that property which relates an applied strain rate to the

resulting shear stress and vice versa. It is usually beyond the scope of an undergraduate fluid

mechanics course to develop a general relation between stress and strain since this requires the use

of tensor analysis. However, students should recognize that a linear relation between stress and

strain is a special case in fluid mechanics. In general, the relation between stress and strain in a

fluid is written as

= f ( )

(1)

where is the shear stress and is the strain rate. There is not an a priori reason to suppose a

linear relationship. In fact, viscosity may be a function of strain rate itself.

©Department of Aerospace, Physics and Space Sciences

Florida Institute of Technology

Fluid Mechanics Lab, Experiment #1

Effects of Temperature

Gases: Viscosity increases with increasing temperature as seen in Sutherland’s formula:

=

b T

1+ S T

b = 1.458 x 10-6

(2)

kg

(3)

ms K

where µ is the coefficient of absolute viscosity, T is in K(elvin), and S = 110.4K.

Liquids: Viscosity decreases with increasing temperature

= Ae

B

T

For water, A = -1.94

(4)

B = -4.80 [F.M. White, 1994]

A Newtonian fluid is defined as a substance in which the shear stress in linearly

proportional to the strain rate. Consider the flow between parallel plates as shown in Figure 1. A

parcel of fluid is strained by the moving upper plate; hence, shear stresses are produced. For a

Newtonian fluid, the relation between shear and stress reduces to

=

du

dy

du

where dy is twice the strain rate, 2 .

(5)

du

Note that this special geometry results in a linear velocity distribution; hence, dy is constant. The

deformation of a fluid parcel is represented by element A which, as it moves to the right, deforms

to element B in Figure 1. This deformation is associated with the strain rate.

©Department of Aerospace, Physics and Space Sciences

Florida Institute of Technology

Fluid Mechanics Lab, Experiment #1

Figure 1. Strain in a fluid due to a moving boundary.

Non-Newtonian fluids may also be characterized by their stress-strain behavior. Table 1 contains

a description of various rheological classifications, and Figure 2 contains a comparative plot of

stress versus strain rate for a variety of rheological classifications.

RHEOLOGICAL CLASSIFICATION

Classification

Characteristics

Newtonian:

Stress is linearly proportional to strain.

Bingham Plastic:

Yield—Newtonian; stress is linearly proportional

to strain after initial applied yield strain.

Dilatant:

Stress increases with increasing strain rate.

Pseudo Plastic:

Stress decreases with increasing strain rate.

Rheopectic*:

Stress increases with time – constant strain rate.

Thixotropic*:

Stress decreases with time – constant strain rate.

*not shown in plot

Table 1. Rheological Classification

©Department of Aerospace, Physics and Space Sciences

Florida Institute of Technology

Fluid Mechanics Lab, Experiment #1

Figure 2. Stress-strain behavior for various fluids.

Given an unknown fluid, the above classifications could be determined by imposing a strain rate

and qualitatively sensing the resistance (stress). Slowly pouring the fluid out of a cup would

simulate a relatively low strain rate while vigorous stirring would correspond to a high strain rate.

For example, if the resistance (shear stress) to stirring “appeared” to decrease with more vigorous

stirring (strain rate), the fluid would be classified a pseudoplastic. The phenomenon can be

characterized by an apparent viscosity, , which is defined as

=

du

dy

©Department of Aerospace, Physics and Space Sciences

(6)

Florida Institute of Technology

Fluid Mechanics Lab, Experiment #1

Figure 3. Definition of Apparent Viscosity.

The definition is applied as indicated in Figure 3.

Measurement of Viscosity of Liquids

GUNT Falling Ball Apparatus

This apparatus contains two transparent cylinders with 8L capacity each. The top of each cylinder

has a guide tube that enables safe insertion of the sphere. Two O-rings help mark the measuring

section and can be moved to set the distance. At the lower end of the cylinder contains a sluice

through which the spheres can removed without wasting significant amounts of fluid. The spheres

cannot exceed a diameter of 12mm. A stopwatch is provided to measure the sedimentation time.

By determining the sedimentation time, the settling velocity can be determined.

Figure 4 shows the apparatus used and Figure 5 shows the spheres provided with this apparatus.

Apparatus Specifications –

Dimensions : Height

– 1.330mm each

Inner Diameter – 92mm each

Capacity

– 8L each

©Department of Aerospace, Physics and Space Sciences

Florida Institute of Technology

Fluid Mechanics Lab, Experiment #1

Figure 1: GUNT Falling Ball Apparatus

Figure 2: Spheres used for GUNT apparatus

©Department of Aerospace, Physics and Space Sciences

Florida Institute of Technology

Fluid Mechanics Lab, Experiment #1

GUNT Falling Ball Viscometer comes with a set of 6 different balls, which pass through the

measuring tube. The properties of each ball are given in the table below. calipers are required to

ensure correct ball selection

Table 1: Standard data for spheres (GUNT)

Calculations

When a ball is dropped into a fluid, it gives rise to either a laminar or a turbulent flow. Both flows

have internal friction but turbulent gives rise to eddying, where the streamlines start intersecting

producing frictional force. The nature of flow can be determined by Reynolds number. At very

low Reynolds numbers (RD

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