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FLUID MECHANICS

FLUID MECHANICS. Aim of Course : to offers basic knowledge in fluid mechanics to obtain an understanding for the behaviour of fluids to solve some simple problems of the type encountered in Engineering practice.

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FLUID MECHANICS

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  1. FLUID MECHANICS Aim of Course: • to offers basic knowledge in fluid mechanics • to obtain an understanding for the behaviour of fluids • to solve some simple problems of the type encountered in Engineering practice

  2. Aim of fluid mechanics lectures: It is the aim of these lectures to help students in this process of gaining an understanding of, and an appreciation for, fluid motion—what can be done with it, what it might do to you, how to analyze and predict it.

  3. Objective of course At the end of the course, participants are expected to be able to: • Define and use basic fluid properties • Define and use basic concepts in fluid mechanics • Perform simple calculations in hydrostatics and kinematics • Make simple designs in hydraulics

  4. METHODS TO BE USED • Lectures • Workshops (tutorials) • Laboratory works Assessment methods • Class assignments, • Home assignments • Laboratory reports • Examination

  5. Lectures and class assignments Attendance to lectures is compulsory for all students. Class works (Tests) will be unannounced. Students who take all class test also get the full marks for attendance

  6. Tutorials and Laboratory Works Tutorials : 2hrs per week outside our usual schedule. Laboratory works: 1. Pressure gauges 2. Plane surfaces immersed in fluids 3. Floating bodies Reports on each laboratory work will be written by the group and defended at my office

  7. Literature • Fluid Mechanics (including Hydraulic Machines) – Dr. A. K. Jain, Khanna Publishers, Delhi, 2003 • Fluid Mechanics (6th edition) – frank M. White; McGraw-Hill 2008 • Introduction to Engineering Fluid Mechanics.- J. A. Fox 1985 • Fluid Mechanics:- J. F. Douglas; J. M. Gasiorek; J. A. Swaffield • Hydraulics,Fluid Mechanics and Fluid Machines – S. Ramamrutham

  8. Literature cont. 6. Essentials of Engineering Hydraulics – J. M. K. Dake, 1992 7. Hydrology and Hydraulic Systems – Ram S. Gupta Mechanics of Fluids – Bernard Massey, revised by john Ward- Smith

  9. WHAT IS A FLUID? Molecules of solids are so closely packed together that the attractive forces between the molecules are so large that a solid tends to retain it’s shape unless compelled by some external forces to change it. Fluids are composed of molecules with relatively larger distances between molecules and therefore the attractive forces between molecules are smaller than in solids.

  10. WHAT IS A FLUID? F F Shearτ Shearτ t1 t3 t0 t2 θ3 θ2 θ θ Fluid Solid

  11. Definition of fluid A fluid may be defined in two perspectives:-  a) The form in which it occurs naturally :- a substance that is capable of flowing and has no definite shape but rather assumes the shape of the container in which it is placed.

  12. DEFINITION OF FLUID b) By the deformation characteristics when acted upon by a shear stress: A fluid is a substance that deforms continuously under the action of a shearing stress no matter how small the stress. (Examples of fluid: gases (air, lpg), liquids (water, kerosene, etc)

  13. DISTINCTION BETWEEN SOLID AND FLUID There are plastic solids which flow under the proper circumstances and even metals may flow under high pressures. On the other hand there are viscous fluids which do not flow readily and one may easily confuse them with solid plastics. The distinction is that any fluid, no matter how viscous will yield in time to the slightest shear stress.

  14. SOLID AND FLUID But a solid, no matter how plastic, requires a certain limiting value of stress to be exerted before it will flow. Also when the shape of a solid is altered (without exceeding the plastic limit) by external forces, the tangential stresses between adjacent particles tend to restore the body to its original shape. With a fluid, these tangential stresses depend on the velocity of deformation and vanish as the velocity approaches zero

  15. LIQUID AND GAS A liquid is composed of relatively closed packed molecules with strong cohesive forces. Liquids are relatively incompressible. As a result, a given mass of fluid will occupy a definite volume of space if it is not subjected to extensive external pressures.

  16. GAS Gas molecules are widely spaced with relatively small cohesive forces. Therefore if a gas is placed into a container and all external pressure removed, it will expand until it fills the entire volume of the container. Gases are readily compressible. A gas is in equilibrium only when it is completely enclosed. The volume (or density) of a gas is greatly affected by changes in pressure or temperature or both. It is therefore necessary to take account of changes of pressure and temperature whenever dealing with gases.

  17. FLUID MECHANICS Fluid mechanics is the science of the mechanics of liquids and gases and is based on the same fundamental principles that are employed in solid mechanics. It studies the behaviour of fluids at rest and in motion. The study takes into account the various properties of the fluid and their effects on the resulting flow patterns in addition to the forces within the fluid and forces interacting between the fluid and its boundaries

  18. FLUID MECHANICS The study also includes the mathematical application of some fundamental laws :- conservation of mass - energy, Newton’s law of motion ( force - momentum equation ), laws of thermodynamics, together with other concepts and equations to explain observed facts and to predict as yet unobserved facts and to predict as yet unobserved fluid behaviour.

  19. FLUID MECHANICS The study of fluid mechanics subdivides into: • fluid statistics • fluid kinematics and • fluid dynamics

  20. Fluid Statics Fluid statics : is the study of the behaviour of fluids at rest. Since for a fluid at rest there can be no shearing forces all forces considered in fluid statics are normal forces to the planes on which they act.

  21. Fluid Kinematics Fluid kinematics: deals with the geometry (streamlines and velocities ) of motion without consideration of the forces causin g the motion. Kinematics is concerned with a description of how fluid bodies move.

  22. Fluid dynamics Fluid dynamics: is concerned with the relations between velocities and accelerations and the forces causing the motion.

  23. SYSTEM AND CONTROL VOLUME In the study of fluid mechanics, we make use of the basic laws in physics namely: • The conservation of matter (which is called the continuity equation) • Newton’s second law (momentum equation) • Conservation of energy (1st law of thermodynamics) • Second law of thermodynamics and • there are numerous subsidiary laws

  24. In employing the basic and subsidiary laws, either one of the following models of application is adopted: • The activities of each and every given mass must be such as to satisfy the basic laws and the pertinent subsidiary laws – SYSTEM • The activities of each and every volume in space must be such that the basic and the pertinent subsidiary laws are satisfied – CONTROL VOLUME

  25. SYSTEM & CONTROL VOLUME A system is a predetermined identifiable quantity of fluid. It could be a particle or a collection of particles. A system may change shape, position and thermal conditions but must always contain the same matter. A control volume refers to a definite volume designated in space usually with fixed shape. The boundary of this volume is known as the control surface. A control volume mode is useful in the analysis of situations where flow occurs into and out of a space

  26. SYSTEM & CONTROL VOLUME

  27. FORCES ACTING ON FLUIDS (BODY & SURFACE FORCES) Those forces on a body whose distributions act on matter without the requirement of direct contact are called body forces (e.g. gravity, magnetic, inertia, etc. Body forces are given on the basis of the force per unit mass of the material acted on. Those forces on a body that arise from direct contact of this body with other surrounding media are called surface forces eg. pressure force, frictional force, surface tension

  28. FLUID PROPERTIES Property :- is a characteristic of a substance which is invariant when the substance is in a particular state. In each state the condition of the substance is unique and is described by its properties. The properties of a fluid system uniquely determine the state of the system.

  29. EXTENSIVE & INTENSIVE PROPERTIES Extensive Properties: those properties of the substance whose measure depends on the amount of the substance present (weight, momentum, volume, energy) Intensive Properties: those properties whose measure is independent of the amount of substance present (temperature, pressure, viscosity, surface tension, mass density etc. volume per unit mass v and energy per unit mass e)

  30. PHYSICAL PROPERTIES OF FLUIDS Each fluid property is important in a particular field of application. Viscosity plays an important role in the problems of hydraulic friction. Mass density is important in uniform flow. Compressibility is a factor in water hammer. Vapour pressure is a factor in high velocity flow

  31. Mass density & unit (specific) weight Mass density and unit weight are the two important parameters that tend to indicate heaviness of a substance • Mass density is the mass per unit volume usually denoted by the Greek letter “rho” ρ=M/V kg/m3 At standard pressure (760 mmHg) and 4o C density of water = 1000 kg/mm3

  32. Specific Weight Specific volume : Is the reciprocal of the density ie. the volume occupied per unit mass of fluid. Vs = 1/ρ= V/M ( m3 / kg) Specific (unit ) weight:  (gamma) - Is the weight per unit volume of the substance (is and indication of how much a unit volume of a substance weighs.)  = W/V = Mg/V =ρg ( kgm/s2)

  33. FLUIDS PROPERTY- SPECIFIC GRAVITY Specific Gravity : Is the ratio of the weight of a substance to the weight of an equal volume of water at standard conditions.

  34. FLUIDS PROPERTY- VISCOSITY Viscosity : is the property of a fluid to offer resistance to shear stress. Fluids offer resistance to a shearing force. Viscosity is a property of a fluid that determines the amount of resistance. Viscosities of liquids vary inversely with temperature, while viscosities of gases vary directly with temperature

  35. FLUIDS PROPERTY- VISCOSITY F τ c c’ b b’ U θ y Y u a d

  36. FLUIDS PROPERTY- VISCOSITY At any point at a distance y from the lower plate, the velocity U(y) = Uo * (y/Y) Uodt/Y =θ (du/dy) = (Uo/Y) (θ/dt)=Uo/Y Experiments show that, other quantities being held constant F is directly proportional to the A (area) and the velocity U and inversely proportional to the distance between the plates Y

  37. FLUIDS PROPERTY- VISCOSITY

  38. Dynamic & kinematic viscosity The constant of proportionality, μ, in the above equation is called the dynamic viscosity with units Ns. /m2 Kinematic Viscosity : (nu) is the ratio of the dynamic viscosity to the density of the fluid.   =  / Ns / m2 kgm-3 = m2 / s

  39. NEWTONIAN &NON-NEWTONIAN FLUIDS Not all fluids show exactly the same relation between stress and the rate of deformation.  Newtonian fluids: are fluids for which shear stress is directly proportional to the rate angular deformation or a fluid for which the viscosity  is a constant for a fixed temperature and pressure. eg. Air, water, etc. Petroleum, kerosene, steam.

  40. NEWTONIAN &NON-NEWTONIAN FLUIDS Non-Newtonian fluids : are fluids which have a variable proportionality (viscosity  ) between stress and deformation rate. In such cases, the proportionality may depend on the length of time of exposure to stress as well as the magnitude of the stress eg. Plastics, paint, blood, ink, etc

  41. COMPRESSIBLE AND INCOMPRESSIBLE FLUIDS Compressible fluids are fluids whose specific volume v or (density, ρ) is a function of pressure. An incompressible fluid is a fluid whose density is not changed by external forces acting on the fluid. Hydrodynamics is the study of the behaviour of incompressible fluids whereas gas dynamics is the study of compressible fluid.

  42. Compressibility of fluid Compressibility of a fluid is a measure of the change in volume of the fluid when it is subjected to outside force. It is defined in terms of an average bulk modulus of elasticity K.

  43. SURFACE TENSION Explain from molecular theory These forces F tend to pull the surface molecules tightly to the lower layer and cause the surface to behave as though it were a membrane. The magnitude of this force per unit length is defined as surface tension  (sigma).

  44. Relative magnitude of molecular surface pressure

  45. Cohesive and adhesive forces

  46. Cohesive and adhesive forces • If the intermolecular cohesive forces between two molecules of the fluid is greater than the adhesive forces between the molecules of the container and the molecule of the fluid, - a convex meniscus is obtained. • On the other hand if the adhesive force of molecule of the container and fluid is greater than the cohesive force of the fluid molecules, case (b) - concave meniscus is obtained

  47. CAPILLARITY Is the rise or fall of a column of fluid (in a narrow tube called capillary tube) inserted in the fluid In the contact area between the fluid and container, we can have two cases ;

  48. CAPILLARITY RISE

  49. CAPILLARITY RISE OR FALL The rise or fall in the capillary tube is given by: Where h – capillary rise σ – surface tension force per unit length d – diameter; γ – weight density of fluid and

  50. HYDROSTATICS Hydrostatic deals with fluid at rest. Hydrostatics studies the laws governing the behaviour of fluid at equilibrium when it is subjected to external and internal forces and bodies at equilibrium when they are immersed in the fluid. Shear stress in a fluid at rest is always zero. Therefore in fluid at rest, the only stress we shall be dealing with is normal stresses.

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