CEC 2103- MECHANICS OF FLUIDS III SEMESTER Dr.PRIYA VS Associate Professor

1. CEC2103 SCHOOL OF INFRASTRUCTURE DEPARTMENT OF CIVIL ENGINEERING CEC 2103- MECHANICS OF FLUIDS III SEMESTER Dr.PRIYA VS Associate Professor

2. CEC2103 COURSE OBJECTIVE • To impart understanding of key concepts and fundamental principles pertaining to fluid behavior, both in static and flowing conditions. • To provide sufficient knowledge to analyze and design engineering systems and devices involving fluids and flow. • To enhance student’s interest in fluid phenomena and its applications

3. CEC2103 COURSE OUTCOME At the end of the course, the student will be able to • Describe fluid properties, forces causing flow and will be able to solve problems involving fluid properties and fluid pressure measurements. • Compute the magnitude and location of hydrostatic forces on vertical, inclined and curved submerged surfaces and analyze the equilibrium of floating bodies. • Analyze the flow using principles of fluid kinematics

4. CEC2103 COURSE OUTCOME • Solve fluid problems using principle of fluid dynamics. • Describe the concepts of boundary layer theory, application off the concepts in determining the separation of boundary layer and to analyze the laminar and turbulent flows in circular pipes. • Apply the principles of dimensional analysis for fluid flow problems

5. CEC2103 MODULE 1Fluid properties and Pressure Measurement • Dimensions and units. • Properties of fluids. • Ideal and real fluid. • Definition of Pressure. • Pressure at a point. • Simple and differential manometer theory and Problems. • Pressure gauges.

6. Definitions Fluid mechanics It is the branch of science which deals with the behaviour of fluids at rest as well as in motion. Fluid static The study of fluid at rest. Fluid Kinematics The study of fluid in motion where pressure forces are not considered. Fluid Dynamics The study of fluids in motion where pressure forces are considered.

7. Properties of fluids Density Density or mass density of a fluid is defined as the ratio of mass of fluid to its volume. ρ = Mass of fluid (kg) Volume of fluid (m3) Specific Weight or Weight Density Specific weight of a fluid is the ratio between the weight of a fluid to its volume. w = Weight of the fluid Volume of the fluid w = (Mass of the fluid x Acceleration due to gravity) volume of the fluid w = ρ x g

8. Properties of fluids Specific volume Specific volume of the fluid is defined as the volume occupied by a unit mass of the fluid. Specific volume = Volume of the fluid (m3) Mass of the fluid (Kg) = 1/ ρ Specific Gravity Specific gravity is defined as the ratio of density of a fluid to the density of the standard fluid. S = Density of Liquid Density of water The standard fluid for liquid is water and for gas it is air.

9. Properties of fluids Viscosity Viscosity is defined as the property of a fluid which offers resistance to then movement of one layer of fluid over another adjacent layer of fluid.

10. Properties of fluids • Consider two layers of fluid at a distance “dy” apart with velocity of “U” and “U + dU”. • Viscosity together with relative viscosity causes shear stress acting between fluid layers. • Shear stress is proportional to the rate of change of velocity with respect to “y”. Ԏαdu dy Ԏ = μdu dy

11. Properties of fluids • μ = Coefficient of dynamic viscosity or viscosity. • μ = Ԏ / (du/dy) • Viscosity is also defined as the shear stress required to produce unit rate of shear strain. Units : SI system : Ns/ m2 CGS system : dyne-sec/ cm2 (Poise ) Newton’s Law of Viscosity It states that the shear stress (Ԏ) of a fluid element layer is directly proportional to the rate of shear strain.

12. Properties of fluids Kinematic Viscosity Kinematic viscosity is defined as the ratio between the dynamic viscosity and density of fluid. Units : SI system : m2 /s CGS system : cm2 /s (Stokes) ɣ = Viscosity Density ɣ = μ ρ

13. Properties of fluids • Types of Fluids • Ideal Fluid • Real Fluid • Newtonian Fluid • Non Newtonian Fluid

14. Properties of fluids • Effect of Temperature on Viscosity • Viscosity decreases with increase in temperature of liquid. • Viscous Forces • Cohesive Forces • Molecular momentum transfer • In liquid the cohesive forces dominates due to closely packed molecules and with the increase in temperature, the cohesive forces decreases hence decreasing the viscosity.

15. Properties of fluids Surface Tension Surface tension is defined as the tensile force acting on the surface of the liquid in contact with gas or on the surface between two immiscible liquid. Surface tension on liquid droplet P = 4 σ d Image source :http://www.eeeguide.com/surface-tension

16. Properties of fluids Surface tension on a hollow bubble P = 8 σ d Surface tension on a liquid jet P = σ * 2L L *d Where P = Pressure in N/ m2 σ = Surface tension in N/m d = diameter of the liquid droplet L = length of water jet Image source :http://www.eeeguide.com/surface-tension

17. Properties of fluids Capillarity Capillarity is defined as the phenomenon of rise or fall of a liquid surface in a small tube relative to adjacent general level of liquid when the tube is held vertically in the liquid. • Rise of liquid in the tube - Capillary rise • Fall of liquid in the tube - Capillary depression Factors affecting rise or fall 1.Denisty of liquid 2. Diameter of the tube 3.Surface tension of the liquid

18. Properties of fluids Expression for Capillary rise Under state of equilibrium weight of the liquid of height is balanced by the force at the surface of the liquid in the tube Weight of liquid = ρ x g x Area of tube x h = ρ x g x πd2 x h 4 Image source ::hittp://www.mechanicalbooster.com/2017/08/what-is-capillarity.html

19. Properties of fluids • Vertical component of the tensile force = σ x πd Cos θ • Equating two equations, • The capillary rise is given as h = 4 σ Cos θ • ρ x g x d • θ = 0 for clean water and glass tube • h = 4 σ • ρ x g x d • Where ρ= density; • σ= surface tension; • d = diameter of the tube

20. Properties of fluids Expression for Capillary depression If the glass tube is dipped in mercury the level of mercury in the tube is lower that the general level of the outside liquid. The capillary depression is h = - 4 σ Cos θ ρ x g x d θ = 128 ° for mercury and glass tube Where ρ= density; σ= surface tension ;d = diameter of the tube Image source :http://www.mechanicalbooster.com/2017/08/what-is-capillarity.html

21. Pressure The Pressure on a fluid is measured in two different systems Absolute Pressure: The Absolute pressure is defines as the pressure which is measured with reference to absolute vacuum pressure. Gauge Pressure: The Gauge pressure is defined as the pressure which is measured with the help of pressure measuring instrument, in which the atmospheric pressure is taken as datum.

22. Pressure A Gauge Pressure Absolute Pressure Vacuum Pressure B Pressure Absolute Pressure Absolute Zero Pressure Vacuum Pressure: It is defined as the pressure below the atmospheric pressure.

23. Pressure • PRESSURE MEASUREMENT • Manometer : Devices used to measure the pressure at a point in a fluid by balancing the column of fluid by the same or another column of the fluid. • Mechanical Gauges : Devices used for measuring pressure by balancing the fluid column by the spring or dead weight. Absolute Pressure = Atmospheric Pressure + Gauge Pressure Vacuum Pressure = Atmospheric Pressure – Absolute Pressure

24. Pressure • Manometer • Simple Manometer • Differential Manometer • Mechanical gauges • Bourdon tube pressure gauges • Dead-weight pressure gauges • Bellows pressure gauges

25. Pressure • Simple Manometer • It consists of a glass tube having one of its end connected to a point where pressure is to be measured and the other end remains open to atmosphere. The important types are • Piezometer. • U tube Manometer. • Single column manometer.

26. Pressure • Piezometer • Simplest method to measure pressure. • The rise of liquid gives the pressure head at that point. • If at a point A, the height of liquid is h. • Pressure at point A is P= ρ * g * h Image source :https://www.quora.com/What-is-a-piezometer

27. Pressure U Tube Manometer For Gauge Pressure h1 = Height of the light liquid above datum line. h2 = Height of the heavy liquid above datum line. S1 = Specific gravity of the light liquid.  S2 = Specific gravity of heavy liquid. ρ1 = Density of light liquid. ρ2 = Density of heavy liquid. Image source : https://www.slideshare.net/Fasildes/discussion-lect3

28. Pressure • Pressure above AA in the left column • = P + ρ1* g * h1 • Pressure above AA in the right column • = ρ2* g * h2 • Equating both, Pressure (P) at the point B is given as • P = (ρ2 * g * h2) – (ρ1 * g * h1) Image source : https://www.slideshare.net/Fasildes/discussion-lect3

29. Pressure U Tube Manometer For Vacuum Pressure h1 = Height of the light liquid above datum line. h2 = Height of the heavy liquid above datum line. S1 = Specific gravity of the light liquid.  S2 = Specific gravity of heavy liquid. ρ1 = Density of light liquid. ρ2 = Density of heavy liquid. Image source :https://www.slideshare.net/Fasildes/discussion-lect3

30. Pressure • Pressure above AA in the left column • = P + ρ1* g * h1 + ρ2* g * h2 • Pressure above AA in the right column = 0 • Equating both • P = - [ (ρ2 * g * h2) + (ρ1 * g * h1) ] Image source :https://www.slideshare.net/Fasildes/discussion-lect3

31. Pressure Single Column Manometer h1 = Height of the centre of pipe above XX. h2 = Rise of heavy liquid in the right limb. Δ h = Fall of mercury in a reservoir. S1 = Specific gravity of the liquid in pipe. S2 = Specific gravity of heavy liquid in reservoir and right limb. https://www.slideshare.net/Fasildes/discussion-lect3

32. Pressure • ρ1 = Density of liquid in pipe. • ρ2 = Density of heavy liquid in reservoir and right limb. • P= Pressure to measured at point A. • A= Cross sectional area of the reservoir. • a = Cross sectional area of the right limb. https://www.slideshare.net/Fasildes/discussion-lect3

33. Pressure • Fall of heavy liquid in reservoir will cause a rise of heavy liquid level in right limb • A x Δ h = a h2 • Δ h = a h2 • A • Considering the datum line YY • Pressure in the right limb above YY = ρ2* g * (Δ h + h2 ) • Pressure in the left limb above YY = P + ρ1* g *(Δ h + h1 ) • Equating both and substituting Δ h from the above equation and neglecting a/A ratio, the Pressure at the point A is given as • P = (ρ2 * g x * h2) - (ρ1 * g * h1)

34. Pressure Differential Manometer Case A: Both Pipes at different levels PA - PB= h * g *(ρg – ρ1 ) + (ρ2 * g * y) – (ρ1 * g * x) Case B: Both Pipes at same levels PA - PB= h * g *(ρg – ρ1) Image source https://www.slideshare.net/Fasildes/discussion-lect3

35. Pressure Inverted Manometer Pressure at Left limb = PA - (ρ1 * g * h1) Pressure at right limb = - PB - (ρ2 * g * h2) - (ρs * g * h) PA - PB= (ρ1 * g * h1) - (ρ2 * g * h2) - (ρs * g * h) Where ρs = density of the lighter liquid. h = fall of mercury. Image source : https://www.slideshare.net/Fasildes/discussion-lect3

36. References REFERENCES 1.Bansal, R.K., “Text book of Fluid Mechanics and Hydraulic Machines”, Laxmi Publications Ltd., New Delhi, 2005. 2. Modi, P.N. and Seth, S.M., ”Hydraulics and Fluid Mechanics including Hydraulics Machines”, Standard Book House, New Delhi, 2002. 3.https://www.slideshare.net/Fasildes/discussion-lect3. 4.https://www.quora.com/What-is-a-piezometer. 5.http://www.mechanicalbooster.com/2017/08/what-is-capillarity.html. 6.http://www.eeeguide.com/surface-tension.