LECTURE NOTES

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FLUID MECHANICS,IV Semester CE, Course Code Category Hours Week Credits Maximum Marks. L T P C CIA SEE Total,ACE005 Core,3 1 4 30 70 100, Contact Classes 45 Tutorial Classes 15 Practical Classes Nil Total Classes 60. OBJECTIVES,The course should enable the students to. I Understand and study the effect of fluid properties on a flow system. II Apply the concept of fluid pressure its measurements and applications. III Explore the static kinematic and dynamic behavior of fluids. IV Assess the fluid flow and flow parameters using measuring devices. UNIT I PROPERTIES OF FLUIDS AND FLUID STATICS Classes 09. Introduction Dimensions and units Physical properties of fluids specific gravity viscosity surface. tension vapor pressure and their influences on fluid motion Pressure at a point Pascal s law Hydrostatic. law atmospheric gauge and vacuum pressures Measurement of pressure Pressure gauges Manometers. Simple and differential U tube Manometers, Hydrostatic Forces Hydrostatic forces on submerged plane horizontal vertical inclined and curved. surfaces Center of pressure buoyancy meta centre meta centric height Derivations and problems. UNIT II FLUID KINEMATICS Classes 09, Description of fluid flow Stream line path line and streak lines and stream tube Classification.
of flows Steady and unsteady uniform and non uniform laminar and turbulent rotational and. irrotational flows Equation of continuity for 1 D 2 D and 3 D flows stream and velocity. potential functions flow net analysis,UNIT III FLUID DYNAMICS Classes 09. Euler s and Bernoulli s equations for flow along a streamline for 3 D flow Navier Stoke s equations. Explanationary Momentum equation and its applications. Forces on pipe bend Pitot tube Venturimeter and Orifice meter classification of orifices flow over. rectangular triangular trapezoidal and stepped notches Broad crested weirs. UNIT IV BOUNDARY LAYER THEORY Classes 09, Approximate Solutions of Navier Stoke s Equations Boundary layer BL concepts Prandtl. contribution Characteristics of boundary layer along a thin flat plate Vonkarmen momentum integral. equation laminar and turbulent boundary layers no deviation BL in transition separation of BL. control of BL flow around submerged objects Drag and Lift forces Magnus effect. UNIT V CLOSED CONDUIT FLOW Classes 09, Reynold s experiment Characteristics of Laminar Turbulent flows Flow between parallel plates flow. through long pipes flow through inclined pipes Laws of Fluid friction Darcy s equation minor losses. pipes in series and pipes in parallel Total energy line and hydraulic gradient line Pipe network problems. variation of friction factor with Reynold s number Moody s chart Water hammer effect. Text Books, 1 Modi and Seth Fluid Mechanics Standard book house 2011. 2 S K Som G Biswas Introduction to Fluid Machines Tata Mc Graw Hill publishers Pvt Ltd. 3 Potter Mechanics of Fluids Cengage Learning Pvt Ltd 2001. 4 V L Streeter and E B Wylie Fluid Mechanics McGraw Hill Book Co 1979. 5 R K Rajput A Text of Fluid Mechanics and Hydraulic Machines S Chand company Pvt Ltd. 6th Edition 2015,Reference Books, 1 Shiv Kumar Fluid Mechanics Basic Concepts Principles Ane Books Pvt Ltd 2010.
2 Frank M White Fluid Mechanics Tata McGraw Hill Pvt Ltd 8th Edition 2015. 3 R K Bansal A text of Fluid Mechanics and Hydraulic Machines Laxmi Publications P ltd. New Delhi 2011, 4 D Ramdurgaia Fluid Mechanics and Machinery New Age Publications 2007. 5 Robert W Fox Philip J Pritchard Alan T McDonald Introduction to Fluid Mechanics Student. Edition Seventh Wiley India Edition 2011,Web References. 1 http nptel ac in courses 112105171 1,2 http nptel ac in courses 105101082. 3 http nptel ac in courses 112104118 ui TOC htm,E Text Books. 1 http engineeringstudymaterial net tag fluid mechanics books. 2 http www allexamresults net 2015 10 Download Pdf Fluid Mechanics and Hydraulic Machines by. rk Bansal html, 3 http varunkamboj typepad com files engineering fluid mechanics 1 pdf.
PROPERTIES OF FLUIDS AND FLUID STATICS,Introduction to Fluid Mechanics. Definition of a fluid, A fluid is defined as a substance that deforms continuously under the action of a shear stress. however small magnitude present It means that a fluid deforms under very small shear stress. but a solid may not deform under that magnitude of the shear stress. By contrast a solid deforms when a constant shear stress is applied but its deformation does not. continue with increasing time In Fig L1 1 deformation pattern of a solid and a fluid under the. action of constant shear force is illustrated We explain in detail here deformation behaviour of a. solid and a fluid under the action of a shear force. In Fig L1 1 a shear force F is applied to the upper plate to which the solid has been bonded a. shear stress resulted by the force equals to where A is the contact area of the upper plate. We know that in the case of the solid block the deformation is proportional to the shear. stress t provided the elastic limit of the solid material is not exceeded. When a fluid is placed between the plates the deformation of the fluid element is illustrated in. Fig L1 3 We can observe the fact that the deformation of the fluid element continues to increase. as long as the force is applied The fluid particles in direct contact with the plates move with the. same speed of the plates This can be interpreted that there is no slip at the boundary This fluid. behavior has been verified in numerous experiments with various kinds of fluid and boundary. In short a fluid continues in motion under the application of a shear stress and can not. sustain any shear stress when at rest,Fluid as a continuum. In the definition of the fluid the molecular structure of the fluid was not mentioned As we know. the fluids are composed of molecules in constant motions For a liquid molecules are closely. spaced compared with that of a gas In most engineering applications the average or macroscopic. effects of a large number of molecules is considered We thus do not concern about the behavior. of individual molecules The fluid is treated as an infinitely divisible substance a continuum at. which the properties of the fluid are considered as a continuous smooth function of the space. variables and time, To illustrate the concept of fluid as a continuum consider fluid density as a fluid property at a. small region Density is defined as mass of the fluid molecules per unit volume Thus the mean. density within the small region C could be equal to mass of fluid molecules per unit volume. When the small region C occupies space which is larger than the cube of molecular spacing the. number of the molecules will remain constant This is the limiting volume above which the. effect of molecular variations on fluid properties is negligible. The density of the fluid is defined as, Note that the limiting volume is about for all liquids and for gases at atmospheric.
temperature Within the given limiting value air at the standard condition has. approximately molecules It justifies in defining a nearly constant density in a region. which is larger than the limiting volume, In conclusion since most of the engineering problems deal with fluids at a dimension which is. larger than the limiting volume the assumption of fluid as a continuum is valid For example the. fluid density is defined as a function of space for Cartesian coordinate system x y and z and. time t by This simplification helps to use the differential calculus for solving. fluid problems,Properties of fluid, Some of the basic properties of fluids are discussed below. Density As we stated earlier the density of a substance is its mass per unit volume In fluid. mechanic it is expressed in three different ways, Mass density r is the mass of the fluid per unit volume given by Eq L1 1. Typical values water 1000 kg,Air at standard pressure and temperature STP. Specific weight w As we express a mass M has a weight W Mg The specific weight of the. fluid can be defined similarly as its weight per unit volume. Typical values water,Relative density Specific gravity S.
Specific gravity is the ratio of fluid density specific weight to the fluid density specific weight. of a standard reference fluid For liquids water at is considered as standard fluid. Similarly for gases air at specific temperature and pressure is considered as a standard reference. Units pure number having no units,Typical vales Mercury 13 6. Specific volume Specific volume of a fluid is mean volume per unit mass i e the reciprocal. of mass density,Typical values Water, In section L1 definition of a fluid says that under the action of a shear stress a fluid continuously. deforms and the shear strain results with time due to the deformation Viscosity is a fluid. property which determines the relationship between the fluid strain rate and the applied shear. stress It can be noted that in fluid flows shear strain rate is considered not shear strain as. commonly used in solid mechanics Viscosity can be inferred as a quantative measure of a fluid s. resistance to the flow For example moving an object through air requires very less force. compared to water This means that air has low viscosity than water. Let us consider a fluid element placed between two infinite plates as shown in fig Fig 2 1 The. upper plate moves at a constant velocity under the action of constant shear force The. shear stress t is expressed as, where is the area of contact of the fluid element with the top plate Under the action of. shear force the fluid element is deformed from position ABCD at time t to position AB C D at. time fig L2 1 The shear strain rate is given by,Shear strain rate L2 6. Where is the angular deformation,From the geometry of the figure we can define.
The limit of both side of the equality gives L 2 5. The above expression relates shear strain rate to velocity gradient along the y axis. Newton s Viscosity Law, Sir Isaac Newton conducted many experimental studies on various fluids to determine. relationship between shear stress and the shear strain rate The experimental finding showed that. a linear relation between them is applicable for common fluids such as water oil and air The. relation is,Substituting the relation gives in equation L 2 5. Introducing the constant of proportionality, where is called absolute or dynamic viscosity Dimensions and units for are. and respectively In the absolute metric system basic unit of co efficient of viscosity. is called poise 1 poise, Typical relationships for common fluids are illustrated in Fig L2 3. The fluids that follow the linear relationship given in equation L 2 7 are called Newtonian. Kinematic viscosity v, Kinematic viscosity is defined as the ratio of dynamic viscosity to mass density.
Typical values water,Non Newtonian fluids, Fluids in which shear stress is not linearly related to the rate of shear strain are non Newtonian. fluids Examples are paints blot polymeric solution etc Instead of the dynamic viscosity. apparent viscosity which is the slope of shear stress versus shear strain rate curve is used. for these types of fluid, Based on the behavior of non Newtonian fluids are broadly classified into the following. a Pseudo plastics shear thinning fluids decreases with increasing shear strain rate. For example polymer solutions colloidal suspensions latex paints pseudo plastic. b Dilatants shear thickening fluids increases with increasing shear strain rate. Examples Suspension of starch and quick sand mixture of water and sand. c Plastics Fluids that can sustain finite shear stress without any deformation but once. shear stress exceeds the finite stress they flow like a fluid The relation between the. shear stress and the resulting shear strain is given by. Fluids with n 1 are called Bingham plastic some examples are clay suspensions tooth paste. and fly ash, d Thixotropic fluid Fig L 2 4 decreases with time under a constant applied shear. Example Ink crude oils,e Rheopectic fluid increases with increasing time. Example some typical liquid solid suspensions, As shown in the figure a cubical block of 20 cm side and of 20 kg weight is allowed to slide.
down along a plane inclined at 300 to the horizontal on which there is a film of oil having. viscosity 2 16x10 3 N s m2 What will be the terminal velocity of the block if the film thickness. is 0 025mm,Given data Weight 20 kg,Block dimension 20x20x20 cm3. Driving force along the plane,Shear force,Contact area. Answer 28 38m s, If the equation of a velocity profile over a plate is v 5y 2 y where v is the velocity in m s. determine the shear stress at y 0 and at y 7 5cm Given the viscosity of the liquid is 8 35. Given Data Velocity profile, Substituting y 0 and y 0 075 on the above equation we get shear stress at. respective depths,Answer 0 835,Surface tension and Capillarity.
Surface tension, In this section we will discuss about a fluid property which occurs at the interfaces of a liquid. and gas or at the interface of two immiscible liquids As shown in Fig L 3 1 the liquid. molecules A is under the action of molecular attraction between like molecules cohesion. However the molecule B close to the interface is subject to molecular attractions between both. like and unlike molecules adhesion As a result the cohesive forces cancel for liquid molecule. In the definition of the fluid the molecular structure of the fluid was not mentioned As we know the fluids are composed of molecules in constant motions For a liquid molecules are closely spaced compared with that of a gas In most engineering applications the average or macroscopic effects of a large number of molecules is considered We

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