viscosit of fluids.pdf

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MT-318-Topic B Wk 1 Lec 2 P1

Topic B Week 1 Second Lecture Hour

VISCOSITY OF FLUIDS

Numeric designations of figures, tables, equations, and text material are in reference toAPPLIED FLUID MECHANICS, 6

th Edition, by Robert L. Mott.

Text material : Chapter 2

B-1 VELOCITY GRADIENT IN A MOVING FLUID : VISCOSITY

When a thin layer of fluid is contained between a lower stationary (fixed) surface and

an upper moving surface, with a velocity (distance per unit time), the fluid in

direct contact with each boundary will have the same velocity as the boundary, hence

the fluid in contact with the lower surface will have zero velocity (will be stationary)

while the fluid in contact with the upper surface will have a velocity ; in-between

the two surfaces, different horizontal sub-layers of the fluid will have differentvelocities

y that increase with increasing distance y from the lower surface.

FIGURE 2.1

The change in with change in y , stated as y / , defines the velocity gradient,

which is essentially constant from the bottom surface to the top surface, as shown,

for a thin fluid layer.

The different horizontal sub-layers of fluid can be visualized as sliding, or shearing

over each other, requiring a shear stress (force per unit area) (tau), with this shear

stress increasing with increasing velocity gradient y / (as the velocity of the

moving surface is increased)


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The magnitude of the shear stress also depends on a property of the fluid called the

dynamic viscosity (or absolute viscosity) (eta) ; the dynamic viscosity divided

by the density of the fluid defines the kinematic viscosity (nu) , noting that

mass and weight are related through the equation mgw=

( Equation 1-2 ).

Shear stress (tau) )/( y= ( N/m = Pa , lb/ft , psi ) (2-1)

Dynamic (absolute) viscosity (eta) )/( = y ( N.s/m, lb.s/ft ) (2-2)

Kinematic viscosity (nu) /= ( m/s , ft/s ) (2-3)

The dynamic viscosity of a fluid is essentially its resistance to flow, such as would

occur when stirring a fluid, so that stirring oil requires more effort than stirring water

because oil has a higher dynamic viscosity than water ; on the other hand, faststirring requires more effort than slow stirring, for either fluid, because the velocity

gradient y / increases with increasing stirring speed.

B-2 NEWTONIAN FLUIDS AND NON-NEWTONIAN FLUIDS

A Newtonian fluid has constant dynamic viscosity so that the shear stress

increases linearly with increasing velocity gradient ; most of the common fluids can

be regarded as being Newtonian, including water, oil, gasoline, air, and natural gas.

A Non-Newtonian fluid has a dynamic viscosity that either increases or decreases

with increasing velocity gradient, hence the fluid behaves as if it is more viscous,or stiffer, either at high flow velocities or at low flow velocities ; molasses is an

example of the former, while non-drop paint is an example of the latter.

B-3 VISCOSITY VARIATION WITH TEMPERATURE

Since dynamic viscosity essentially refers to a fluids resistance to flow, a low

viscosity fluid is easier to pour and to pump than a high viscosity fluid ;

a relatively high viscosity however, is generally desirable for lubricating fluids.

In general, the dynamic viscosity of liquids decreases with increasing temperature,

while that of gases increases with increasing temperature, but the change is smaller

than that for liquids (with reference to Appendix D).

For liquids such as engine oils, the dynamic viscosity might be excessively high at low

temperatures making pumping difficult, and excessively low at high temperatures,

reducing the lubricating properties ; an oil that varies as little as possible with

temperature change is desirable.


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B-4 VISCOSITY MEASUREMENT

The most direct method of measuring dynamic viscosity is to apply the setup shown in

Sub-topic B-1 ( Figure 2.1 ) with Equation 2-1 ; this is done in the rotating drum

viscometer where the moving surface is that of a rotating drum and the fixed surfaceis that of a stationary outer cup, with a thin layer of the test fluid in-between.

FIGURE 2.4(a)

A specific rotational speed, together with a specific gap (layer thickness) determines

the velocity gradient, while the resisting torque measured by the meter, together with

the drum dimensions, determines the shear stress ; an allowance has to be made for

the fluid at the bottom, which has a variable velocity gradient that decreases inwards.

Indirect methods of viscosity measurement include measuring the time taken for aspecific volume of test fluid to pass through a capillary (small-diameter) tube, or to

pour out of a tank through a standard orifice (opening), as well as measuring the time

taken for a standard ball to fall a specific distance through the test fluid ;

all these indirect methods give comparative results, but actual viscosities may be

determined by calibration of the test equipment, using fluids of known viscosities

(with reference to Section 2.7 ).

B-5 PROPERTIES OF COMMON FLUIDS

Properties of fluids are obtained from producers, suppliers, technical organizations,

textbooks, and handbooks ; in fluid mechanics, caution should be exercised with theunits of the various quantities and these units should be included in all equations, with

appropriate conversions applied.

The density, specific weight, specific gravity, and viscosity of some

common fluids is listed in Appendices A , B , C , and E .

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