Fluid Mechanics : Properties of fluid: numerical : part 1

properties of fluid and numerical related to density, specific gravity, viscosity etc.

1. Course Name: FLUID MECHANICS Unit: Properties of fluid

2. Properties of Fluids Properties of fluids determine how fluids can be used in engineering and technology. They also determine the behaviour of fluids in fluid mechanics. They are: Density Viscosity Surface Tension Capillary Action Specific Weight Specific Gravity

3. DENSITY Mass Density is the mass per unit volume of a fluid. In other words, it is the ratio between mass (m) and volume (V) of a fluid. Density is denoted by the symbol ‘ ρ’. Its unit is kg/m 3 . Weight Density/ Specific Weight: of a fluid is the ratio of Weight of a fluid to its Volume. Denoted by ‘w’ w= w= ρ g N/m 3  

4. Specific Volume: =1/ ρ , m 3 /kg Specific gravity: Weight density of a liquid= S L X weight density of water =S L X density of water X g = S L X 1000 x 9.81 N/m 3 Density of a liquid ρ L = S L X ρ w = 1000 ρ w S Hg = 13.6 therefore the ρ Hg = ? Calculate : density , specific weight and weight of one liter of petrol of specific gravity = 0.7 density , specific weight and specific gravity of one liter of a liquid which weighs 7 N.  

5. Viscosity Viscosity is the fluid property that determines the amount of resistance of the fluid to shear stress. It is the property of the fluid due to which the fluid offers resistance to flow of one layer of the fluid over another adjacent layer.

6. Dynamic viscosity : μ τ α τ = μ μ = τ / , N.s/m 2 = Pa.s CGS: dyne.sec /cm 2 = Poise 1 poise = 1/10 N.s/m 2 1 centipoise = 1/100 poise  

7. KY NEMATIC VIS COSITY The kinematic viscosity (also called "momentum diffusivity") is the ratio of the dynamic viscosity μ to the density of the fluid ρ . ν = μ / ρ , m 2 /s In CGS: cm2/sec = stoke = 10 -4 m2/s 1centistoke = 1/100 stoke Newton’s law of viscosity : shear stress on a fluid element layer is directly proportional to rate of shear strain. τ α τ = μ  

8. Viscosity and temperature: For liquids : viscosity decreases with increase in temperature. For gases: increase with increase in temperature.

9. Fluids can be classified into five basic types. They are: Ideal Fluid : incompressible and no viscosity Real Fluid : possess viscosity Ideal -plastic Fluid : shear stress more than yirld value and newtonian Newtonian Fluid : real fluid , obey newton law of viscosity Non-Newtonian Fluid : real fluid , not obey newton law of viscosity.

10. Solve: Hint: given:

11. The velocity distribution for flow over a flat plate is given by u = y - y 2 in which u is velocity in meter per second at a distance y meter above the plate. Determine shear stress at y=0.25m and 0.3 m. take kinematic viscosity 6 stokes and the density of the liquid 1900kg/m 3 . solution: Shear stress: τ = μ (du/ dy ) to find dynamic viscosity : μ given , ν = 6 stokes = ……… m 2 /s ρ = 1900kg/m 3 ν = μ / ρ ; μ = …….. Ns/m 2 u = y - y 2 (du/ dy ) = (3/4 ) – 2y ( du/ dy ) y=0.25 = ………. ; τ y=0.25 = μ (du/ dy ) y=0.25 = ………… (du/ dy ) y=0.3 = ………. ; τ y=0.3 = μ (du/ dy ) y=0.3 = …………..  

12. Compressibility and Bulk Modulus K = Compressive stress/volumetric strain

13. SU RFACE TE NSION The property of fluids to resist tensile stresses on their surface is called as Surface Tension . Denoted by σ , N/m Surface tension on liquid droplet: p=4 σ /d Hollow bubble: 8 σ /d

14. CA PILLARY ACT ION Capillary action is the property of fluid to flow in a narrow spaces without assistance of and in opposition to external forces like gravity. The effect can be seen in the drawing up of liquids between the hairs of a paint-brush, in a thin tube, in porous materials such as paper and plaster, in some non-porous materials such as sand or in a cell. It occurs because of intermolecular forces between the liquid and surrounding solid surfaces.

15. Capillary rise: h= mm Capillary fall h= mm = 128 for Hg and glass tube = 0 for water and glass tube  

16. Vapour Pressure and Cavitation: Change from liquid state to vapour state: Vaporization. Pressure at which liquid is converted into liquid – vapour pressure. Pressure above the liquid surface is reduced then the boiling temperature will also reduce. Pressure equal or less than vapor pressure, boiling of the liquid will start, though the temperature of the liquid is 20 C.

17. Cavitation: worn out turbine blades. Phenomenon of formation of vapour bubbles of a flowing liquid in a region where the pressure of the liquid falls below the vapour pressure and sudden collapsing of these vapour bubbles in a region of higher pressure.

18. Determine the specific gravity of a fluid having viscosity 0.05 poise and kinematic viscosity 0.035 stokes. Determine the viscosity of a liquid having kinematic viscosity 6 stokes and specific gravity 1.9 .