What is Fluid?????

1. What is Fluid????? • A fluid may be liquid, vapour or gas. It has no permanent shape but takes up the shape of a containing vessel or channel or is shaped by external forces (eg the atmosphere). • A fluid consists of atoms/molecules in random motion (translation) and in continual collision with the surroundings. • Fluids are readily deformable, and flow. • Solids have ‘frozen’ molecules that vibrate and do not translate. Solids resist change of shape.

2. What is Fluid????? FT Solid (Rectangular Block) Attached plates t B B t FT For a solid, application of a shear stress causes a deformation which, if modest, is not permanent and solid regains original position.

3. What is Fluid????? Sliding (shearing occur between fluid layer) FT Fluid at rest FT For a fluid, continuous deformation takes place with an infinite number of layers sliding over each other. Deformation continues until the force is removed.

4. What is Fluid????? FT FT to to 0<t<a to<t1<t2 t1 t2 FT FT a) Fluid a) Solid A fluid is a substance for which a shear stress tends to produce unlimited deformation.

5. Dimensions and Unit • Primary Dimensions

6. Dimensions and Unit

7. Dimensions and Unit

8. Viscosity A fluid offers resistance of motion due to its viscosity or internal friction. Viscosity arises from movement of molecules from one layer to another moving at a different velocity. Slower layer tend to retard faster layers hence resistance

9. Viscosity Shear stress Shear strain

10. Viscosity Rate of Shear strain

11. Viscosity For most fluids used in engineering it is found that the shear stress is directly proportional to rate of shear when straight and parallel flow is involved

12. Viscosity where is velocity change in y direction So, at any point is the true velocity gradient Newton's law of viscosity The constant of proportionality; m is called the dynamic viscosity or just viscosity

13. EXAMPLE 0 • Determine the unit of dynamic viscosity; m • Kinematic viscosity;u is defined as the ration of dynamic viscosity to fluid density; Determine the unit of Kinematic viscosity

14. u=5 m/s m=1.805kg/m-s y=0.02 mm Surface EXAMPLE 1 Circular plate slides over the larger flat surface on a thin film of liquid that has a thickness of 0.02 mm. The plate has an diameter of d=6.3cm and mass of 20 g. If the plate is given an initial velocity of 5m/s, calculate the force required to move the plate at a steady velocity.Assume dynamic viscosity of liquid m=1.805 kg/m-s

15. EXAMPLE 1.1 A board 1m by 1m that weight 25 N slides down an inclined ramp (slope = 20O) with a velocity of 2.0 cm/s. The board is separated from the ramp by a thin film of oil with a velocity of 0.05 N.s/m2. Neglect the edge effect, calculate the spacing between the board and the ramp

16. EXAMPLE 1 A board 1m by 1m that weight 25 N slides down an inclined ramp (slope = 20O) with a velocity of 2.0 cm/s. The board is separated from the ramp by a thin film of oil with a velocity of 0.05 N.s/m2. Neglect the edge effect, calculate the spacing between the board and the ramp

17. EXAMPLE 1.2 A piston moves inside a cylinder at a velocity of 5 m/s, as shown in figure. The 150 mm diameter piston is centrally located within the 150.2 mm inside diameter cylinder. The film of oil separating the piston from the cylinder has an an absolute viscosity of 0.40 N.s/m2. Assuming a linear velocity profile, find the a) Shear stress in the oil b) Force F required to maintain the given motion c) Force by which the required force would change if the velocity increased by a factor of 2

18. EXAMPLE 1.2

19. Viscosity Fluids which do not obey the Newton's law of viscosity are called as non-Newtonian fluids.Generally non-Newtonian fluids are complex mixtures: slurries, pastes, gels, polymer solutions etc.,

20. Viscosity Variation of Viscosity with Temperature For gases Power law Sutherland law

21. Viscosity Variation of Viscosity with Temperature For Liquid For water To = 273.16K, mo = 0.001792 kg/(m.s) and a = -1.94, b = -4.80 ,c = 6.74

22. CONTIMUUM macroscopic From a microscopic point of a view a fluid is not continuous and homogenous substance but consists of atom or molecules in random motion and with relatively large space between them. Under such circumstances it has no meaning refer to the velocity at a point in a fluid because that point may be empty space at particular instant. When we refer to the velocity of a fluid, we usually imply a quantity of fluid consisting of an enormous number of atoms of molecules-fluid velocity is a macroscopic concept. microscopic

23. DENSITY X Total Mass = m1 Total Volume = V1 Fluid Average Density =

24. DENSITY Density at point = dm/dV Average Density dV

25. Specific Weight The weight per unit volume of a fluid is called its specific volume and equal to rg, the product of its density and the acceleration of gravity rgair = (1.204 kg/m3) (9.807m/s2) = 11.8N/m3or = 0.0752lbf/ft3 rgwater = (998kg/m3) (9.807m/s2) = 9790N/m3or = 62.4lbf/ft3

26. Specific Gravity Specific gravity (SG) which is the ratio of density to the standard density of some reference fluid at 20oC and 1 atm

27. Compressibility and the Bulk modulus Bulk modulus (K) = (change in pressure) / (volumetric strain)

28. Compressibility and the Bulk modulus Bulk modulus (K) = (change in pressure) / (volumetric strain) Where the volumetric strain is the ratio of the change in volume to the initial volume or

29. Compressibility and the Bulk modulus From the mass conservation; or So that or

30. Compressibility and the Bulk modulus Typical values of Bulk Modulus: K = 2.05x109 N/m2for water K = 1.62 x 109 N/m2 for oil.