2. Viscosity
• Viscosity is a measure of the resistance to shape
deformation. It should not be confused with density.
Lubricating oil is more viscous than water but it is less
dense, and mercury is very dense but has a low viscosity.
• The viscosity of non-Newtonian fluids will vary depending
on the force applied over time or the amount of force
applied
3.
4. • You may have noticed that the dynamic viscosity of a fluid
is closely related to the shear modulus of a solid. The only
difference is that the shear strain is replaced by shear rate
• To calculate the viscous resistance of a fluid you can use
the formula:
5. • From there the power loss in an operation can be
calculated by using the formula:
• To find the torque required to over come viscous
resistance you need to use the formula: T=Fr
6. • The viscosity of a substance is sometimes defined in a
slightly different way for use in advanced fluid mechanics
calculations. It is known as kinematic viscosity which is
the ratio of dynamic viscosity and density. Kinematic
viscosity is denoted by the Greek letter v (nu)
7. Bingham plastic
• Here the stirrer or pump must first apply an initial yield
stress τ0, before shearing can begin. Afterwards the
graph is linear. Margerine, cooking fats, greases,
chocolate mixtures, toothpaste, some soap and detergent,
slurries, and some paper pulps exhibit this kind of
behaviour.
8.
9. • The rheogram curve follows the law form:
• where Kp is a constant for the fluid known as the
coefficient of rigidity. The apparent viscosity ηa at the
point A on the curve is the gradient of the line OA.
10. Pseudoplastic
• Here the fluid becomes progressively less viscous as the
shear rate increases due to intermolecular bonds being
broken. The graph will follow a curve. Rubber
solutions, adhesives, polymer solutions and mayonnaise
exhibit this kind of behaviour.
11.
12. • The curve follows a power law of the form:
• where K and n are constants for the fluid. The constant K
is known as the consistency coefficient of the fluid. The
index n is known as the behaviour flow index whose value
is always less than 1. The apparent viscosity at the point A
on the curve is the gradient of the line OA.
13. Casson plastic
• Here the stirrer or pump must apply to induce an initial
yield stress τ0, before shearing can begin. Afterwards the
graph follows a curve. Printing ink, non-drip paint, tomato
ketchup and blood behave in this way.
14.
15. • The rheogram curve follows a law of the form:
• where Kc and n are constants for the fluid. The constant
Kc is known as the Casson viscosity of the fluid. As with
pseudoplastic fluids, the behaviour flow index n has
values which are always less than 1. The apparent
viscosity at the point A on the curve is the gradient of the
line OA.
16. Dilatants
• Rheopectic or shear thickening fluids are very often fluids
which contain solid particles in suspension. They are also
referred to as dilatent fluids. Starch
solutions, quicksand, some cornflower and sugar
solutions, and iron powder dispersed in low-viscosity
liquids exhibit this kind of behaviour. The apparent
viscosity increases with shear rate
17.
18. • Like pseudoplastics it follows the law form:
• where K is again the consistency coefficient of the fluid
and the behaviour flow index n has values which are
always greater than 1. The apparent viscosity at the point
A on the curve is the gradient of the line OA.
20. Assignment pre-test
• A ball bearing of diameter 35mm is weighed whilst totally
•
•
•
•
immersed in oil of relative density 0.85 and its apparent weight
is 1.54 N. What is the density of the ball bearing material?
Water is observed to rise through a height of 50mm in a clean
glass capillary tube of internal diameter 0.3 mm. If the density
of water is 1000 kg/m3, determine its surface tension. To what
height would the same water rise in a capillary tube of internal
diameter 0.5mm?
Explain the difference between Newtonian and non-Newtonian
fluids.
What happens if you apply temperature to a Newtonian fluid?
What happens if you apply pressure to a Newtonian Fluid?
21. • Oil of dynamic viscosity 0.12Ns/m2 is used to lubricate
the slides of a machine worktable. The thickness of the oil
film is 0.25mm and the contact area is 0.15m2. Determine
the viscous resistance and the power dissipated when the
worktable is moving at a speed of 3m/s
22.
23. Viscous resistance in bearings
• A journal runs in a bearing 60 mm diameter and 60mm
long at 20 rev/s. The clearance gap is 1mm. The lubricant
in the clearance gap has a dynamic viscosity of 50cP. The
bearing must carry a side load of 800N.
Calculate the following:
-The friction force
-The friction torque
-The power loss
-The coefficient of friction
24. • A journal runs in a bearing 30mm diameter and 50mm
long at 30 rev/s. the clearance gap is 0.8mm. The
lubricant in the clearance gap has a dynamic viscosity of
120cP. The bearing must carry a side load of 600N
Calculate the following:
-The friction force
-The friction torque
-The power loss
-The coefficient of friction
25. Viscous resistance in thrust bearings (M1)
• Hint use the formula: T=ηπωD^4/32x
• A vertical rotor has a shaft 30mm in diameter that rests in
a recess and the weight is supported by a film of oil
0.5mm thick and has a dynamic viscosity of 110cP.
Calculate the friction torque and power loss at 1420
rev/min. (0.0026Nm, 0.387W)
• A vertical rotor has a shaft 100mm diameter that rests in a
recess and the weight is supported by a film of oil 0.75mm
thick and dynamic viscosity of 60cP. Calculate the friction
torque and power loss at 30 rev/s (0.148Nm, 27.9W)
