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- 1. VISCOSITY IN NEWTONIAN AND NON NEWTONIAN FLUIDS
- 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. • 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:
- 4. • 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
- 5. • 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)
- 6. 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.
- 7. • 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.
- 8. 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.
- 9. • 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.
- 10. 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.
- 11. • 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.
- 12. 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
- 13. • 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.
- 14. Examples
- 15. 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?
- 16. • 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
- 17. 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
- 18. • 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
- 19. 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)
- 20. Thrust on immersed surfaces

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