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Fluidmechanics

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A complete course brief of fluid mechanics as per the AKTU syllabus.

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Fluidmechanics

  1. 1. Mohd Sharique Ahmad Assistant Professor Civil Department 6/21/2017 Mohd Sharique Ahmad 1
  2. 2. UNIT 1 Fluid and continuum 6/21/2017 Mohd Sharique Ahmad 2
  3. 3. Studies Mechanics: The oldest physical science that deals with both stationary and moving bodies under the influence of forces.  Statics: The branch of mechanics that deals with bodies at rest  Dynamics: The branch that deals with bodies in motion.  Fluid mechanics: The science that deals with the behavior of fluids at rest (fluid statics) or in motion (fluid dynamics), and the interaction of fluids with solids or other fluids at the boundaries.  Fluid dynamics: Fluid mechanics is also referred to as fluid dynamics by considering fluids at rest as a special case of motion with zero velocity. 6/21/2017 Mohd Sharique Ahmad 3
  4. 4.  Hydrodynamics: The study of the motion of fluids that can be approximated as incompressible (such as liquids, especially water, and gases at low speeds).  Hydraulics: A subcategory of hydrodynamics, which deals with liquid flows in pipes and open channels.  Gas dynamics: Deals with the flow of fluids that undergo significant density changes, such as the flow of gases through nozzles at high speeds.  Aerodynamics: Deals with the flow of gases (especially air) over bodies such as aircraft, rockets, and automobiles at high or low speeds.  Meteorology, oceanography, and hydrology: Deal with naturally occurring flows. 6/21/2017 Mohd Sharique Ahmad 4
  5. 5. Introduction  Fluid: A substance in the liquid or gas phase. A solid can resist an applied shear stress by deforming.  A fluid deforms continuously under the influence of a shear stress, no matter how small.  In solids, stress is proportional to strain, but in fluids, stress is proportional to strain rate.  When a constant shear force is applied, a solid eventually stops deforming at some fixed strain angle, whereas a fluid never stops deforming and approaches a constant rate of strain. 6/21/2017 Mohd Sharique Ahmad 5
  6. 6. Types of stresses acting in fluid 6/21/2017 Mohd Sharique Ahmad 6 Stress: Force per unit area. Normal stress: The normal component of a force acting on a surface per unit area. Shear stress: The tangential component of a force acting on a surface per unit area. Pressure: The normal stress in a fluid at rest. Zero shear stress: A fluid at rest is at a state of zero shear stress. When the walls are removed or a liquid container is tilted, a shear develops as the liquid moves to re-establish a horizontal free surface. The normal stress and shear stress at the surface of a fluid element. For fluids at rest, the shear stress is zero and pressure is the only normal stress
  7. 7. 6/21/2017 Mohd Sharique Ahmad 7 Intermolecular bonds are strongest in solids and weakest in gases. Solid: The molecules in a solid are arranged in a pattern that is repeated throughout. Liquid: In liquids molecules can rotate and translate freely. Gas: In the gas phase, the molecules are far apart from each other, and molecular ordering is nonexistent. The arrangement of atoms in different phases: (a) molecules are at relatively fixed positions in a solid, (b) groups of molecules move about each other in the liquid phase, and (c) individual molecules move about at random in the gas phase.
  8. 8. Gas and vapor are often used as synonymous words. Gas: The vapor phase of a substance is customarily called a gas when it is above the critical temperature. Vapor: Usually implies that the current phase is not far from a state of condensation. 6/21/2017 Mohd Sharique Ahmad 8 Macroscopic or classical approach: Does not require a knowledge of the behavior of individual molecules and provides a direct and easy way to analyze engineering problems. Microscopic or statistical approach: Based on the average behavior of large groups of individual molecules On a microscopic scale, pressure is determined by the interaction of individual gas molecules. However, we can measure the pressure on a macroscopic scale with a pressure gage.
  9. 9. Physical properties of fluids  Liquid can be easily distinguished from a solid or a gas.  A liquid takes the shape of vessel into which it is poured The properties of water are of much importance because the subject of hydraulics is mainly concerned with it. Some properties of water are : 1. Density 2. Specific Gravity 3.Viscosity 4.Vapour pressure 5.Cohesion 6.Adhesion 7.Surface Tension 8.Capillary 9.Compressibility 6/21/2017 Mohd Sharique Ahmad 9
  10. 10. Pressure-density-height relationship  When a fluid is contained in a vessel, it exerts force at all points on the sides and bottom and top of the container. The force per unit area is called pressure.  Hydrostatic law: it states that rate of pressure in a vertical direction is equal to weight density of the fluid at that point. P = ρ g H Where p is the pressure at any point in a liquid, g is acceleration due to gravity and H is the height of free surface above that point. 6/21/2017 Mohd Sharique Ahmad 10
  11. 11. Manometers A simple manometer is one which consists of a glass tube whose one end is connected to a point where pressure is to be measured and the other end remains open to atmosphere. Types of Manometer  Piezometer  U-Tube Manometer 6/21/2017 Mohd Sharique Ahmad 11 U-Tube Manometer
  12. 12. Pressure on plane and curved surfaces Total pressure : It is defined as the force exerted by static fluid on a surface (either plane or curved) when the fluid comes in contact with the surfaces. This force is always right angle or normal to the surrface P = w A ħ P= Weight of the liquid above the immersed surface A = total area of surface w = specific weight of liquid ħ = Distance of center of pressure from free surface of liquid. 6/21/2017 Mohd Sharique Ahmad 12
  13. 13. Centre of pressure  The point through which the resultant pressure acts is known as center of pressure and is always expressed in terms of depth from the liquid surface. 6/21/2017 Mohd Sharique Ahmad 13
  14. 14. Buoyancy  Buoyancy is the ability of an object to float. It is related to the object’s density  Archimedes Principle states that when a body is immersed in a fluid either wholly or partially, it is buoyed or lifted up by a force, which is equal to the weight of fluid dispatched by the body.  The point of application of the force of buoyancy on the body is known as the centre of buoyancy. It is always centre of gravity of the volume of fluid displaced. 6/21/2017 Mohd Sharique Ahmad 14
  15. 15. Types of equilibrium of floating bodies Types of Equilibrium of free bodies  Stable Equilibrium When a body is given a small angular displacement (i.e. Tilted slightly by some external force, then it returns back to its original position dur to internal forces  Unstable Equilibrium If the body does not return to its original position from the from the slightly displaced angular position and heels farther away, when given a small displacement  Neutral Equilibrium If a body, when given a small angular displacement occupies a new position and remains at rest in this new position. 6/21/2017 Mohd Sharique Ahmad 15
  16. 16. UNIT 2 Types of fluid flows 6/21/2017 Mohd Sharique Ahmad 16
  17. 17. CLASSIFICATION OF FLUID FLOWS Viscous flows: Flows in which the frictional effects are significant. Inviscid flow regions: In many flows of practical interest, there are regions (typically regions not close to solid surfaces) where viscous forces are negligibly small compared to inertial or pressure forces. 6/21/2017 Mohd Sharique Ahmad 17 Viscous versus Inviscid Regions of Flow The flow of an originally uniform fluid stream over a flat plate, and the regions of viscous flow (next to the plate on both sides) and inviscid flow (away from the plate)
  18. 18. Steady and unsteady • The term steady implies no change at a point with time. • The opposite of steady is unsteady. • The term uniform implies no change with location over a specified region. • The term periodic refers to the kind of unsteady flow in which the flow oscillates about a steady mean. • Many devices such as turbines, compressors, boilers, condensers, and heat exchangers operate for long periods of time under the same conditions, and they are classified as steady-flow devices. 6/21/2017 Mohd Sharique Ahmad 18 Oscillating wake of a blunt-based airfoil at Mach number 0.6. Photo (a) is an instantaneous image, while photo (b) is a long-exposure (time-averaged) image.
  19. 19. Laminar and turbulent flows  Laminar flow: The highly ordered fluid motion characterized by smooth layers of fluid. The flow of high-viscosity fluids such as oils at low velocities is typically laminar.  Turbulent flow: The highly disordered fluid motion that typically occurs at high velocities and is characterized by velocity fluctuations. The flow of low- viscosity fluids such as air at high velocities is typically turbulent.  Transitional flow: A flow that alternates between being laminar and turbulent 6/21/2017 Mohd Sharique Ahmad 19 Laminar, transitional, and turbulent flows over a flat plate.
  20. 20. Compressible and incompressible flows  Incompressible flow: If the density of flowing fluid remains nearly constant throughout (e.g., liquid flow).  Compressible flow: If the density of fluid changes during flow (e.g., high-speed gas flow) 6/21/2017 Mohd Sharique Ahmad 20 When analyzing rockets, spacecraft, and other systems that involve high-speed gas flows, the flow speed is often expressed by Mach number Ma = 1 Sonic flow Ma < 1 Subsonic flow Ma > 1 Supersonic flow Ma >> 1 Hypersonic flow
  21. 21. One, Two and Three dimensional flows • A flow field is best characterized by its velocity distribution. • A flow is said to be one-, two-, or three-dimensional if the flow velocity varies in one, two, or three dimensions, respectively. • However, the variation of velocity in certain directions can be small relative to the variation in other directions and can be ignored. 6/21/2017 Mohd Sharique Ahmad 21 Flow over a car antenna is approximately two-dimensional except near the top and bottom of the antenna The development of the velocity profile in a circular pipe. V = V(r, z) and thus the flow is two-dimensional in the entrance region, and becomes one-dimensional downstream when the velocity profile fully develops and remains unchanged in the flow direction, V = V(r).
  22. 22. Streamlines 6/21/2017 Mohd Sharique Ahmad 22 When the flow is steady, streamlines are often used to represent the trajectories of the fluid particles. A streamline is a line drawn in the fluid such that a tangent to the streamline at any point is parallel to the fluid velocity at that point. Steady flow is often called streamline flow.
  23. 23. Dimensional analysis  Dimensional Analysis is a mathematical technique which makes use of the study of the dimensions for solving several engineering problems. Fundamental dimensions The various physical quantities in fluids can be expressed in terms of these fundamental dimensions Mass M Time T Lenght L Temperature ϴ The other quantities which are expressed in these quantities are called as derieved quanities Force is expressed as MLT-2 6/21/2017 Mohd Sharique Ahmad 23
  24. 24. UNIT 3 Potential Flow 6/21/2017 Mohd Sharique Ahmad 24
  25. 25. Orifice meter  An orifice plate is a device used for measuring flow rate, for reducing pressure or for restricting flow (in the latter two cases it is often called a restriction plate). Either a volumetric or mass flow rate may be determined, depending on the calculation associated with the orifice plate. It uses the same principle as a Venturi nozzle, namely Bernoulli's principle which states that there is a relationship between the pressure of the fluid and the velocity of the fluid. When the velocity increases, the pressure decreases and vice versa 6/21/2017 Mohd Sharique Ahmad 25
  26. 26. Hot-wire anemometer An anemometer is a device used for measuring the speed of wind, and is also a common weather station instrument. The term is derived from the Greek word anemos, which means wind, and is used to describe any wind speed measurement instrument used in meteorology 6/21/2017 Mohd Sharique Ahmad 26 Hot wire anemometers use a very fine wire (on the order of several micrometres) electrically heated to some temperature above the ambient. Air flowing past the wire cools the wire. As the electrical resistance of most metals is dependent upon the temperature of the metal (tungsten is a popular choice for hot-wires), a relationship can be obtained between the resistance of the wire and the flow speed
  27. 27. Notches and Weirs  A notch may be defined as an opening provided in the side of a tank or vessel such that the liquid surface in the tank is below the top edge of the opening. A notch may be regarded as an orifice with the water surface below its upper edge. It is generally made of metallic plate.  A Weir may be defined as any regtangular obstruction in an open stream over which the flow takes place. It is made of masonary concrete. A weir may be used for measuring the rate of flow of water in rivers or streams. 6/21/2017 Mohd Sharique Ahmad 27
  28. 28. Similarity Laws  Models are designed on the basis of force which is dominating in the flow situation. The laws in which the models are designed for dynamic similarity are called model or similarity Laws. These are 1. Renolds model law 2. Froude model law 3. Euler model law 4. Weber model law 5. Mach model law 6/21/2017 Mohd Sharique Ahmad 28
  29. 29. Kinematics and dynamic similarity  Kinematics similarity It is the similarity of motion. If at the corresponding points in the model and in the prototype, the velocity or accelerations ratios are same and velocity or acceleration vector points in the same direction, the two flows are said to be kinematically similar.  Dynamic similarity It is the similarity of forces. The flows in the model and in the prototype are dynamically similar if at all the corresponding points, identical types of forces are parallel and bear the same ratio. 6/21/2017 Mohd Sharique Ahmad 29
  30. 30. UNIT 4 Laminar and turbulent flows 6/21/2017 Mohd Sharique Ahmad 30
  31. 31. Fluid flow mean velocity and pipe diameter for known flow rate Velocity of fluid in pipe is not uniform across section area. Therefore a mean velocity is used and it is calculated by the continuity equation for the steady flow as 6/21/2017 Mohd Sharique Ahmad 31 Pipe diameter can be calculated when volumetric flow rate and velocity is known as where is: D - internal pipe diameter; q - volumetric flow rate; v - velocity; A - pipe cross section area
  32. 32. Reynolds number, turbulent and laminar flow The nature of flow in pipe, by the work of Osborne Reynolds, is depending on the pipe diameter, the density and viscosity of the flowing fluid and the velocity of the flow. Dimensionless Reynolds number is used, and is combination of these four variables and may be considered to be ratio of dynamic forces of mass flow to the shear stress due to viscosity. Reynolds number is 6/21/2017 Mohd Sharique Ahmad 32 where : D - internal pipe diameter; v – velocity ρ - density; ν - kinematic viscosity μ - dynamic viscosity;
  33. 33. Flow in pipes is considered to be laminar if Reynolds number is less than 2320, and turbulent if the Reynolds number is greater than 4000. Between these two values is "critical" zone where the flow can be laminar or turbulent or in the process of change and is mainly unpredictable.  When calculating Reynolds number for non-circular cross section equivalent diameter (four time hydraulic radius d=4xRh) is used and hydraulic radius can be calculated as: Rh = cross section flow area / wetted perimeter 6/21/2017 Mohd Sharique Ahmad 33
  34. 34. Bernoulli equation - fluid flow head conservation  If friction losses are neglected and no energy is added to, or taken from a piping system, the total head, H, which is the sum of the elevation head, the pressure head and the velocity head will be constant for any point of fluid streamline.  This is the expression of law of head conservation to the flow of fluid in a conduit or streamline and is known as Bernoulli equation: 6/21/2017 Mohd Sharique Ahmad 34 where: Z1,2 - elevation above reference level; p1,2 - absolute pressure v1,2 – velocity ρ1,2 - density; g - acceleration of gravity
  35. 35. Pipe flow and friction pressure drop  As in real piping system, losses of energy are existing and energy is being added to or taken from the fluid (using pumps and turbines) these must be included in the Bernoulli equation.  For two points of one streamline in a fluid flow, equation may be written as follows: 6/21/2017 Mohd Sharique Ahmad 35 where : Z1,2 - elevation above reference level p1,2 - absolute pressure; hL - head loss due to friction in the pipe; Hp - pump head; HT - turbine head;
  36. 36. Head energy loss  Flow in pipe is always creating energy loss due to friction. Energy loss can be measured like static pressure drop in the direction of fluid flow with two gauges. General equation for pressure drop, known as Darcy's formula expressed in meters of fluid is: 6/21/2017 Mohd Sharique Ahmad 36 where is: hL - head loss due to friction in the pipe; f - friction coefficient; L - pipe length; D - internal pipe diameter To express this equation like pressure drop in newtons per square meter (Pascals) substitution of proper units leads to: where: Δ p - pressure drop due to friction in the pipe; f - friction coefficient; L - pipe length D - internal pipe diameter; Q - volumetric flow
  37. 37. Stokes’ law  George Gabriel Stokes derived an expression, now known as Stokes' law, for the frictional force – also called drag force – exerted on spherical objects with very small Reynolds numbers in a viscous fluid  The force of viscosity on a small sphere moving through a viscous fluid is given by Fd = 6π η R ν Fd is the frictional force – known as Stokes' drag – acting on the interface between the fluid and the particle η is the dynamic viscosity R is the radius of the spherical object v is the flow velocity relative to the object. 6/21/2017 Mohd Sharique Ahmad 37
  38. 38. Eddy viscosity  In the study of turbulence in fluids, a common practical strategy for calculation is to ignore the small-scale vortices (or eddies) in the motion and to calculate a large-scale motion with an eddy viscosity that characterizes the transport and dissipation of energy in the smaller-scale flow (see large eddy simulation). Values of eddy viscosity used in modeling ocean circulation may be from 5×104 to 1×106 Pa·s depending upon the resolution of the numerical grid. 6/21/2017 Mohd Sharique Ahmad 38
  39. 39. Siphon  The word siphon is used to refer to a wide variety of devices that involve the flow of liquids through tubes. In a narrower sense, the word refers particularly to a tube in an inverted 'U' shape, which causes a liquid to flow upward, above the surface of a reservoir, with no pump, but powered by the fall of the liquid as it flows down the tube under the pull of gravity, then discharging at a level lower than the surface of the reservoir from which it came. 6/21/2017 Mohd Sharique Ahmad 39
  40. 40. Water Hammer  Water hammer (or, more generally, fluid hammer) is a pressure surge or wave caused when a fluid (usually a liquid but sometimes also a gas) in motion is forced to stop or change direction suddenly (momentum change). A water hammer commonly occurs when a valve closes suddenly at an end of a pipeline system, and a pressure wave propagates in the pipe. It is also called hydraulic shock 6/21/2017 Mohd Sharique Ahmad 40
  41. 41. UNIT 5 Boundary layer 6/21/2017 Mohd Sharique Ahmad 41
  42. 42. Boundary layer over a flat plate  In fluid mechanics, a boundary layer is an important concept and refers to the layer of fluid in the immediate vicinity of a bounding surface where the effects of viscosity are significant. 6/21/2017 Mohd Sharique Ahmad 42 Boundary layer visualization, showing transition from laminar to turbulent condition
  43. 43.  Boundary laer Thickness It is defined as that distance from boundary in which the velocity reaches 99 percent of thee velocity of the free stream (u = 0.99U). It is denoted by the symbol δ. The commomnly adopted boundary layer thickness are  Displacement Thickness δ*  Momentum Thickness ϴ  Energy thickness δe 6/21/2017 Mohd Sharique Ahmad 43
  44. 44.  Displacement Thickness δ* It is the distance measured perpendicular to the boundary by which the main/free stream is displaced on account of formation of boundary layer. 6/21/2017 Mohd Sharique Ahmad 44
  45. 45.  Momentum Thickness ϴ It is defined as the distance measured perpendicular to the boundary of the solid body, by which the boundary should be displaced to compensate for reduction in the momentum of the flowing fluid on account of boundary layer formation  Energy Thickness δe It is defined as the distance, measured perpendicular to the boundary of the solid body, by which the boundary should compensate for the reduction in K.E. Of the flowing fluid on account of boundary layer formation. δe 6/21/2017 Mohd Sharique Ahmad 45
  46. 46. Laminar boundary layer  The laminar boundary is a very smooth flow, while the turbulent boundary layer contains swirls or "eddies." The laminar flow creates less skin friction drag than the turbulent flow, but is less stable. Boundary layer flow over a wing surface begins as a smooth laminar flow. As the flow continues back from the leading edge, the laminar boundary layer increases in thickness. 6/21/2017 Mohd Sharique Ahmad 46
  47. 47. Application of momentum equation Von Karman suggested a method based on the momentum equation by the use of which the growth of a boundary layer along a flat plate, the wall shear stress and the drag force could be determined τ₀/ρU2 = dϴ/dx The above equation is von Karman momentum equation for boundary layer flow, and is used to find out the frictional drag on smooth flat plate for both laminar and turbulent boundary layers 6/21/2017 Mohd Sharique Ahmad 47
  48. 48. Turbulent boundary layer  At some distance back from the leading edge, the smooth laminar flow breaks down and transitions to a turbulent flow. From a drag standpoint, it is advisable to have the transition from laminar to turbulent flow as far aft on the wing as possible, or have a large amount of the wing surface within the laminar portion of the boundary layer. The low energy laminar flow, however, tends to break down more suddenly than the turbulent layer 6/21/2017 Mohd Sharique Ahmad 48
  49. 49. Separation and its control, The forces acting on the fluid in the boundary layer are Inertia Force Viscous force Pressue force If these forces act over a over a long stretch, the boundary layer gets separated from the surface and moves into the main stream. This phenomenon is called separation. The point of the body of which the boundary layer is on the verge of separation from the surface is called point of separation. 6/21/2017 Mohd Sharique Ahmad 49
  50. 50. Drag and lift  Drag force: The component of force in the direction of flow (free stream) on a submerged body is called the drag force FD FD = CD A (ρU2/ 2)  Lift Force : The component of force at right angles to the direction of flow is called the lift force FL FL = CL A (ρU2/ 2) WhereCD = Co-efficient of drag (dimensionless) CL = Co- efficient of lift (dimensionless) ρ = Density of fluid U = Relative velocity of fluid w.r.t the body A = Area. 6/21/2017 Mohd Sharique Ahmad 50
  51. 51. An Aerofoil, Magnus effect Aerofoil An aerofoil is a streamlined body which may be either symmetrical or unsymmetrical Magnus Effect The generation of lift by spinning cylinder in a fluid stream is called Magnus Effect.  The effect has been successfully employed in the propulsion of ships  The magnus effect may also be used with advantage in games like table tennis, golf, cricket etc. 6/21/2017 Mohd Sharique Ahmad 51
  52. 52. Introduction to compressible flow  A compressible flow is that flow in which the density of the fluid changes during flow. Compressibility affects the drag co-efficients of bodies by formation of shock wave, discharge co-efficients of measuring devices such as orificemeters, venturimeters and pitot tubes, stagnation pressure and flows in converging- diverging sections. 6/21/2017 Mohd Sharique Ahmad 52
  53. 53. Thank You 6/21/2017 Mohd Sharique Ahmad 53

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