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2. DEPARTMENT OF MECHANICAL ENGG IV-SEMESTER FLUID MECHANICS AND MACHINARY 2 CHAPTER NO. 1 PROPERTIES OF FLUID & FLUID PRESSURE

3. CHAPTER 1:- SYLLABUSDTEL. Definition of mass density, sp.wt.,sp.gravity, sp. Volume 1 Definition & type of viscosity with newton`s law of viscosity 2 Numerical on dynamic & kinematic viscosity 3 Definition on surface tension and it`s numerical 4 3 Definition of capillarity, compressibility,vapour press. 5 6Definition of ab. Press.,gauge press.,& it’s relationship

4. CHAPTER 1:- SYLLABUSDTEL. Definition of fluid press.,press. head, Intensity & numerical 7 Description of simple manometers 8 Description of differential manometer 9 Description on total press. & center of pressure 10 4 Total press. & center of pressure for vertically immersed Body. 11 12Total press. & center of pressure for Inclined immersed Body.

5. CHAPTER-1 SPECIFIC OBJECTIVE / COURSE OUTCOMEDTEL Define fluid properties. 1 Differentiate between fluid press. intensity,& press. head. 2 5 The student will be able to:

6. PROPERTIES OF FLUIDDTEL 2 6 Properties of fluid i) Density: Density is defined as ratio of the mass of a liquid to its volume. Density : mass of fluid /volume of fluid = m/v ii) Specific weight: weight of liquid per unit volume w = ƿ g iii)Specific volume: it is defined as volume of liquid per unit mass. Sp. Volume : volume of fluid/mass of fluid iv) Specific gravity: it is the ratio of specific weight of fluid to sp. wt. of pure water. S : sp. wt of liquid /sp. wt of pure water LECTURE 1:- PROPERTIES OF …

7. PROPERTIES OF FLUIDDTEL 2 7 Properties of fluid iii)Specific volume: it is defined as volume of liquid per unit mass. Sp. Volume : volume of fluid/mass of fluid iv) Specific gravity: it is the ratio of specific weight of fluid to sp. wt. of pure water. S : sp. wt of liquid /sp. wt of pure water LECTURE 1:- PROPERTIES OF …

8. DTEL VISCOSITY 8 LECTURE 2 :- PROPERTIES OF... Viscosity of fluid is a property of fluid that offers resistance to flow of one layer over the adjacent layer It the measure of internal fluid friction which causes resistance to flow. It is due to cohesion between liquid molecules. Newton’s law of viscosity : It states that shear stress in fluid layers is directly proportional to velocity gradient shear stress ( Ƭ ) α du/dy Ƭ = µ du/dy Where Ƭ = shear stress du/dy : velocity gradient µ : coeff. of dynamic viscosity

9. DTEL VISCOSITY 9 LECTURE 2 :- PROPERTIES OF... Dynamic viscosity : µ = Ƭ /du/dy It’s unit is N.s/m 2, poise 1 poise = 1/10 N.s/m 2 Kinematic viscosity: It is the ratio of dynamic viscosity to mass density of fluid. = µ / ƿ Unit of kinematic viscosity : m 2 / sec 1 Stoke = 10 -4 m2/sec

10. DTEL NUMERICAL 10 LECTURE 3 - PROPERTIES OF FLUID Prob : Find the kinematic viscosity of an oil having density 980 kg/m 3 when at a certain point in the oil, the shear stress is 0.25 N/m 2 and velocity gradient is 0.3/s Soln : Data mass density ƿ = 980 kg/m 3 Shear stress Ƭ = 0.25 Velocity gradient = du/dy = 0.3/s VISCOSITY

11. DTEL NUMERICAL 11 LECTURE 3 - PROPERTIES OF FLUID i)Shear stress T = µ. du/dy 0.25 = µ X 0.3 µ = 0.83 ii)Kinematic viscosity () = µ/ ƿ = 0.83/980 = 8.50 x 10 -4 m 2 /s.

12. DTEL 12 LECTURE 4 :- PROPERTIES OF.. The surface tension is the property which enables it to resist tensile stresses. It is due to cohesion between molecules at the surface of liquid. It is the force required to maintain unit film in equilibrium.It is denoted by σ Unit = N/m SURFACE TENSION

13. DTEL 13 LECTURE 4 :- PROPERTIES OF.. Prob: in a soap bubble, the internal pressure 30 N/m 2 in excess of outside pressure and surface tension of 0.15 N/m. calculate diameter of bubble. Soln: data P = 30 N/m 2 σ = 0. 15 N/m d = ? Surface tension of soap bubble σ = p. d/8 d = 8 σ /p = 8 x 0.15 / 30 = 0.04 m d = 4 mm SURFACE TENSION

14. DTEL Capillarity 14 LECTURE 5 :- PROPERTIES OF.. When the liquid molecules possess relatively greater affinity for solid molecules or, in other words, liquid has adhesion greater than cohesion then it will wet the solid surface in contact and will tend to rise at the point of contact. This results concave upwards and the angle of contact θ.which is less than 90◦. This is also known as ‘Capillary Rise’

15. DTEL Capillarity 15 LECTURE 5 :- PROPERTIES OF.. If the liquid has less attraction for solid molecules or, in other words, ‘Cohesion Predominates’, then liquid will not have tendency to wet the solid surface in contact and this will result in depression. The phenomenon of rise or fall of liquid in a tube is known as capillarity.

16. DTEL Capillarity 16 LECTURE 5 :- PROPERTIES OF.. Vapour pressure : A liquid kept in closed vessel evapourates even at room tempreture and occupies a space above the liquid surface. The pressure exerted by vapour formed on the surface liquid is called as vapour pressure. Compressibility : it is the measure of elasticity of fluid. fluid are compressed under pressure due change in their mass density. More mass can be accommodated in less volume. as the pressure is increased volume is decreased. dp α dv/v dp = k. dv/v where k= bulk modulus.

17. LECTURE 6:- PROPERTIES OF.. DTEL ATOM PRESS., GAUGE PRESS. 17 Complete Vacuum Atmospheric Pressure Pressure B Vacuum Pressure at B Absolute Pressure at B Gauge Pressure at A A Absolute Pressure at A

18. DTEL Atom.,Gauge press. 18 LECTURE 6: - PROPERTIES OF.. A blank of air surrounding the earth surface is called as Atmospheric Pressure. It is measured by mercury barometer. Atmospheric pressure is equal to101.325kN/m 3 10.3 m head of water 760 mm of mercury Gauge pressure If the pressure is measured above or below atmospheric pressure as a datum, it is called as gauge pressure. Atmospheric Pressure

19. DTEL Atom.,Gauge press. 19 LECTURE 6: - PROPERTIES OF.. Absolute pressure I f the pressure is measured above the absolute zero, then it is called as absolute pressure. Absolute pressure = atmospheric pressure + gauge pressure Absolute Vacuum it is the emptiness or space which contains no form of matter.

20. DTEL FLUID PRESS., PRESS HEAD 20 LECTURE 7 :- PROPERTIES OF FLUID Pressure : Is defined as force acting per unit area.. Consider a vessel containing the liquid of depth “h”.meter Let A= Area of base w = Specific weight of the liquid Kg/m 3. h = Height of water. Total pressure on bottom of vessel is weight of water contained in that vessel. Total force = w x A x h If ‘p’ is pressure intensity Then force = p x A p x A = w x A x h P = w x h h = p/w

21. DTEL FLUID PRESS., PRESS HEAD 21 LECTURE 7 :- PROPERTIES OF FLUID Pascals law : The intensity of pressure at any point in the fluid is same in all direction. Application of pascal’s law Hydraulic press (working based on pascal’s law)

22. DTEL MANOMETER 22 LECTURE 8 :- PROPERTIES OF FLUID U-TUBE MANOMETER

23. DTEL 23 MANOMETER MANOMETER U-TUBE MANOMETER It consist of thin glass tube of uniform bore diameter bent in U shape. It’s one end is connected to a point whose pressure is to be measured & other end is kept open to atmosphere. The U tube contains the manometric liquid whose sp. Gravity should be greater than the sp. Gravity of liquid to be measured LECTURE 8 :-PROPERTIES OF FLUID

24. DTEL 24 LECTURE 8 :-PROPERTIES OF FLUID For gauge pressure: h + s 1 h 1 = s 2 h 2 h = (s 2 h 2 - s 1 h 1 ) m of water For negative gauge pressure : Pressure in left limb = Pressure in right limb h + s 1 h 1 +s 2 h 2 = 0 h = -( s 1 h 1 + s 2 h 2 ) m of water MANOMETER

25. LECTURE 9:- PROPERTIES OF FLUIDDTEL DIFFERNTIAL MANOMETER 25 DIFFERENTIAL U- TUBE MANOMETER

26. LECTURE 9:- PROPERTIES OF FLUID DTEL MANOMETER 26 Differential manometer It is used for measuring the difference of pressure between any two points in a pipe or in two pipes. The two ends of U tube are connected at a point whose pressure difference is to be measured. Assume that the pressure at ‘a’ is greater than at point ‘b’ then the greater pressure will force heavy liquid in U tube to move downward, so that heavy liquid will rise in right limb.

27. LECTURE 9:- PROPERTIES OF FLUID DTEL MANOMETER 27 Differential manometer Let, h = Difference of liquid level S 1 = Sp. Gravity of liquid in pipe S 2 = Sp. Gravity of heavy liquid So, Difference of pressure in two points a & b is (h a – h b ) = h (S 2 – S 1 )

28. DTEL 28 Similarly, when points a & b are at different levels Let, h 1 & h 3 = Height of liquid in left & right limb h 1 & h 3 = Height of liquid in left & right limb h 2 = Difference of heavy liquid in left & right limb h 2 = Difference of heavy liquid in left & right limb h a & h b = Pressure in pipes a & b h a & h b = Pressure in pipes a & b S 1 & S 3 = Sp. Gravity of liquid in pipe a & b resp. S 1 & S 3 = Sp. Gravity of liquid in pipe a & b resp. S 2 = Sp. Gravity of heavy liquid S 2 = Sp. Gravity of heavy liquidThen, Pressure in L limb = Pressure in R limb Pressure in L limb = Pressure in R limb (h a + S 1 h 1 ) = S 2 h 2 + S 3 h 3 + h b (h a + S 1 h 1 ) = S 2 h 2 + S 3 h 3 + h b (h a – h b ) = S 2 h 2 + S 3 h 3 - S 1 h 1 (h a – h b ) = S 2 h 2 + S 3 h 3 - S 1 h 1 (h a – h b ) = S 2 h 2 + S 1 (h 3 - h 1 ) (h a – h b ) = S 2 h 2 + S 1 (h 3 - h 1 ) LECTURE 9:- PROPERTIES OF FLUID MANOMETER

29. LECTURE 10 :- PROPERTIES OF FLUIDDTEL TOTAL PRESSURE,COP. 29 Total Pressure : It is defined as the force exerted by a static fluid on surface either plane or curved area when the fluid comes in contact with the surface.This force always acts normal to the surface. Centre of pressure : Defined as the point of application of the total pressure on the surface. The surfaces may be 1.Vertical 2.Horizontal 3.Inclined 4.curved

30. LECTURE 10 :- PROPERTIES OF FLUIDDTEL TOTAL PRESSURE,COP. 30 TOTAL PRESSURE AND CENTRE OF PRESS. FOR HORIZONTAIIY SUBMERGED PLANE SURFACE Total pressure : F = w A h` Centre of pressure : h* = h` Where : w : sp. wt. of liquid A : area of submerged surface h` : center of gravity h* : center of pressure

31. LECTURE 11:-PROPERTIES OF FLUIDDTEL 31 TOTAL PRESSURE AND CENTRE OF PRESS. FOR VERTICALLY SUBMERGED PLANE SURFACE Total pressure : F = w A h` Centre of pressure : h* = IG /Ah` +liquid TOTAL PRESSURE,COP.

32. LECTURE 12:-PROPERTIES OF FLUIDDTEL 32 TOTAL PRESSURE AND CENTRE OF PRESS. FOR INCLINDED PLANE SURFACE Total pressure : F = w A h` Centre of pressure : h* = IG Sin 2 ø/Ah` +liquid Where : w : sp. wt. of surface A : area of submerged h` : center of gravity h* : center of pressure ø : angle of inclination TOTAL PRESSURE,COP.

33. DTEL 33 THANK YOU

34. DTEL References Books: 1 ) FLUID MECHANICS – BANSAL 2) FLUID MECHANICS AND M/CNARY BY- NIRALI PUBLICATION 34 References Web: