MECHANICS OF FLUIDS. (For B.E. Mechanical Engineering Students) As per New Revised Syllabus of APJ Abdul Kalam Technological University

Size: px
Start display at page:

Download "MECHANICS OF FLUIDS. (For B.E. Mechanical Engineering Students) As per New Revised Syllabus of APJ Abdul Kalam Technological University"

Transcription

1 MECHANICS OF FLUIDS (For B.E. Mechanical Engineering Students) As per New Revised Syllabus of APJ Abdul Kalam Technological University Dr. S.Ramachandran, M.E., Ph.D., Mr. K.Pandian, M.E., Mr. YVS. Karthick, M.E., Sathyabama University Jeppiaar Nagar, Chennai AIR WALK PUBLICATIONS (Near All India Radio) 80, Karneeshwarar Koil Street Mylapore, Chennai Ph.: ,

2 First Edition: July 2016 Price : Rs. 300/- ISBN: ISBN : and

3 ME203 MECHANICS OF FLUIDS Syllabus Chapter 1 : Introduction Introduction: Fluids and continuum, Physical properties of fluids, density, specific weight, vapour pressure, Newton s law of viscosity. Ideal and real fluids, Newtonian and non-newtonian fluids. Fluid Statics - Pressure-density-height relationship, manometers, pressure on plane and curved surfaces, center of pressure, buoyancy, stability of immersed and floating bodies, fluid masses subjected to uniform accelerations, measurement of pressure. Chapter 2: Kinematics of Fluid Flow Kinematics of fluid flow: Eulerian and Lagrangian approaches, classification of fluid flow, 1-D, 2-D and 3-D flow, steady, unsteady, uniform, non-uniform, laminar, turbulent, rotational, irrotational flows, stream lines, path lines, streak lines, stream tubes, velocity and acceleration in fluid, circulation and vorticity, stream function and potential function, Laplace equation, equipotential lines flow nets, uses and limitations FIRST INTERNAL EXAM Chapter 3: Dynamics of Fluid Flow Dynamics of Fluid flow: Fluid Dynamics: Energies in flowing fluid, head, pressure, dynamic, static and total head, Control volume analysis of mass, momentum and energy, Equations of fluid dynamics: Differential equations of mass, energy and momentum (Euler s equation), Navier-Stokes equations (without proof) in rectangular and cylindrical co-ordinates, Bernoulli s equation and its applications: Venturi and Orifice meters, Notches and Weirs (description only for notches and weirs). Hydraulic coefficients, Velocity measurements: Pitot tube and Pitot-static tube.

4 Chapter 4 : Pipe Flow Pipe Flow: Viscous flow: Reynolds experiment to classify laminar and turbulent flows, significance of Reynolds number, critical Reynolds number, shear stress and velocity distribution in a pipe, law of fluid friction, head loss due to friction, Hagen Poiseuille equation. Turbulent flow: Darcy- Weisbach equation, Chezy s equation Moody s chart, Major and minor energy losses, hydraulic gradient and total energy line, flow through long pipes, pipes in series, pipes in parallel, equivalent pipe, siphon, transmission of power through pipes, efficiency of transmission, Water hammer, Cavitation. SECOND INTERNAL EXAM Chapter 5 : Concept of Boundary Layer Concept of Boundary Layer: Growth of boundary layer over a flat plate and definition of boundary layer thickness, displacement thickness, momentum thickness and energy thickness, laminar and turbulent boundary layers, laminar sub layer, velocity profile, Von- Karman momentum integral equations for the boundary layers, calculation of drag, separation of boundary and methods of control. Chapter 6: Dimensional Analysis Dimensional Analysis and Hydraulic similitude: Dimensional analysis, Buckingham s theorem, important dimensional numbers and their significance, geometric, Kinematic and dynamic similarity, model studies. Froude, Reynold, Weber, Cauchy and Mach laws- Applications and limitations of model testing, simple problems only END SEMESTER EXAM

5 Contents C.3 Contents 1. Introduction 1.1 Introduction Fluids and Continuum Distinction between solid and fluid Properties of Fluids Gas and Liquid Density (or) mass Density Specific weight (or) Weight density Specific Volume v Specific gravity (or) Relative density s Temperature Viscosity Kinematic Viscosity () Compressibility 1 K Relationship between Bulk Modulus K and pressure p of a Gas for Isothermal and Isentropic Process Vapour Pressure Cavitation Gas and Gas laws Surface Tension Surface Tension on Droplet Surface Tension on a Hollow Bubble Surface Tension on a Liquid Jet Capillarity Expression for Capillary Rise Expression for Capillary Fall Thermodynamic Properties

6 C.4 Mechanics of Fluids 1.4 Newton s Law of Viscosity Types of Fluid Fluid Statics Concept of Fluid Static Pressure Pressure of Fluids P Atmospheric Pressure Absolute zero Pressure (or) Absolute pressure Gauge Pressure Vacuum Pressure Pressure - Density - Height Relationship Manometry Pressure on Plane and Curved Surfaces Total pressure Centre of pressure Pressure on submerged horizontal plane surface Pressure on submerged vertical plane surface The Hydrostatic paradox Pressure on immersed inclined plane surface Pressure on immersed curved surface Buoyancy Centre of Buoyancy Stability of Immersed Body Stability of Floating body Metacentre M Oscillation (or) Rolling of a Floating body Fluid Masses Subjected to Uniform Accelerations Fluid masses subjected to uniform horizontal acceleration Fluid mass subjected to uniform vertical acceleration

7 Contents C Measurement of Pressure Manometers Mechanical Gauges Pressure Measurement Methods Bourdon gauge (C-Type) Diaphragm-type pressure gauge Bellows Dead Weight Pressure Gauge Capacitive Pressure Transducer Strain Gauge Pressure Transducer Simple Manometers Differential Manometer Problems in Simple Manometer Problems In Differential Manometer Kinematics of Fluid Flow 2.1 Introduction Concept of System Control Volume Fluid Characteristics Types of Fluid Flow Steady Flow and Unsteady Flow Uniform and Non-Uniform Flows Laminar Flow and Turbulent Flow Incompressible and Compressible Flow Rotational Flow and Irrotational Flow One Dimensional Flow Two-dimensional Flow Three-dimensional Flow Flow Visualization - Lines of Flow Stream Line

8 C.6 Mechanics of Fluids Stream Tube Path Line Streak Line Velocity Field Velocity field and acceleration Mean Velocity of Flow Principles of Fluid Flow Principle of Conservation of mass Continuity Equation in one Dimension Continuity Equation In Cartesian Co-ordinates In Three Dimensions Equation of continuity in polar coordinates (Rotation and Circulation) Types of Motion or Deformation of Fluid Element Circulation and Vorticity Velocity Potential Function Properties of Potential Function Stream Function Properties of Stream Function Relation between Stream Function and Velocity Potential Function Equipotential Line Line of constant stream function Flow Net Condition of flow net to be a set of square Methods of drawing Flow Nets Uses of Flow nets Limitations of Flow Nets Dynamics of Fluid Flow 3.1 Introduction

9 Contents C Equations of Motion Principle of Conservation of Energy Euler s equation along a Stream Line Bernoulli s Equation Important points in Bernoulli s Equation Assumptions for derivation of Bernoulli s Equation Bernoulli s Equation for Real Fluid Navier-stokes Equations Bernoulli s Equation: Applications Venturi Meter Orifice Meter Problems in Venturimeter Problems in Orificemeter Principle of Conservation of Momentum Moment of Momentum Equation Problems in Momentum Equations Pitot-tube Problems in Pitot Tube Notches And Weirs Discharge over a rectangular notch Ventilation of Weirs Discharge over a Triangular Notch (or Weir) Discharge over a Trapezoidal Notch (or Weir) Discharge over a Stepped Notch Effect on discharge due to error in Measurement of Head Time required to empty a Reservoir or Tank Velocity of approach End contractions Discharge over a Cippoletti weir (or Notch) 3.101

10 C.8 Mechanics of Fluids Discharge over a Submerged or Drowned weir Discharge over a narrow crested weir Discharge over a Broad Crested Weir Discharge over a sharp-crested weir Discharge over an Ogee weir Pipe Flow 4.1 Introduction Reynolds Number Significance of Reynolds Number Critical Reynolds Number Reynolds Experiment Shear Stress Distribution and Velocity Distribution for Laminar Flow Through Circular Tubes Ratio of maximum velocity (U max to average velocity u Loss of head for a given length of pipe (Hagen poiseuille formula) Law of Fluid Friction Head loss due to friction (for laminar flow) Hagen Poiseuille Equation (in terms of Discharge) Turbulent Flow Frictional Loss in Pipe Flow Darcy- Weisbach s Equation - Expression For Loss Of Head Due To Friction In Pipes Chezy s Formula for Loss of head due to friction in pipes Shear Stress in Turbulent Flow

11 Contents C Velocity Distribution for Turbulent Flow in Pipes Hydrodynamical Smooth and Rough Boundary Pipe Roughness Velocity Distribution for Turbulent flow in Smooth pipes Velocity Distribution for Turbulent flow in Rough pipes Friction Factor - Resistance of Smooth and Rough Pipe in Darcy-weisbach Equation Moody s Chart Energy Losses in Pipes Major energy (Head) losses Minor energy losses Loss of head due to sudden enlargement h e Loss of head due to sudden contraction: h c Loss of head due to obstruction: h obs Loss of head due to entrance of pipe: h i Loss of head due to exit of pipe: h Loss of head due to bend in pipe h b Loss of head due to various pipe fittings h fitting Hydraulic Gradient Line (H.G.L) and Total Energy Line (T.E.L) Total Energy Line (T.E.L) (or) Energy Gradient Line (E.G.L) Hydraulic Gradient Line (H.G.L) Salient points to draw the T.E.L and H.G.L Flow Through Long Pipes Under Constant Head H Flow Through Pipes in Series (or) Flow Through Compound Pipes Equivalent Pipe

12 C.10 Mechanics of Fluids Total head loss in compound pipe neglecting minor losses Total head loss in equivalent pipe Flow Through Parallel Pipes Flow Through Branched Pipes Siphon (Flow Through Pipeline with Negative Pressure) Power Transmission Through Pipes Efficiency of power transmission Condition for maximum power transmission Maximum efficiency of Transmission of power max Important Note about Power Water Hammer Cavitation Nature of cavitation Effects of cavitation Precautions Concept of Boundary Layer 5.1 Concept of Boundary Layer Boundary layer theory Growth of Boundary Layer Over a Flat Plate Laminar boundary layer Turbulent Boundary layer Laminar Sub - layer Boundary layer thickness Displacement Thickness Momentum Thickness Energy thickness

13 Contents C Von Karman Momentum Integral Equation for Boundary Layer Drag Force F D on Plate of Length L Local Coefficient of Drag C D Average Coefficient of Drag C D Velocity Profiles Turbulent Boundary Layer on a Flat Plate Drag and Lift Coefficient Drag Force F D Lift force F L Total Drag on a Flat Plate Boundary Layer Separation Location of point of Separation Methods of controlling boundary layer separation Dimensional Analysis 6.1 Definition Introduction Dimensional Homogeneity Methods of Dimensional Analysis Rayleigh s Method Buckingham s - - Theorem Important Dimensional Numbers (a) Reynold s Number R e (b) Froude Number: F r (c) Euler Number E u (d) Weber Number W e (e) Mach Number (M) (f) Cauchy Number C a

14 C.12 Mechanics of Fluids 6.6 Advantages of Dimensional Analysis Similarity Laws and Models Similitude Geometric Similarity Kinematic Similarity Dynamic Similarity Reynolds model law (Viscous forces are predominant in fluid flow) Froude model law: (Gravity force is predominant) Euler s model law: (Pressure forces are predominant) Weber model law: (Surface tension is a dominant force) Mach model law (Velocity of flow is comparable to the velocity of sound; compressible flow) Model Testing of Partially Submerged Bodies Classification of Hydraulic Models Undistorted models Distorted models Scale Ratios for Distorted models Other scale ratios Applications for Model Testing Limitations of Model Testing Supplementary - Chapter 3 Static, Dynamic and Total Head... S.1 Control Volume Analysis... S.2 Hydraulic Coefficients... S.3 Pitot-static tube... S.11

15 Chapter 1 Introduction Introduction: Fluids and continuum, Physical properties of fluids, density, specific weight, vapour pressure, Newtons law of viscosity. Ideal and real fluids, Newtonian and non-newtonian fluids. Fluid Statics-Pressure-density-height relationship, manometers, pressure on plane and curved surfaces, center of pressure, buoyancy, stability of immersed and floating bodies, fluid masses subjected to uniform accelerations, measurement of pressure. 1.1 INTRODUCTION Fluid mechanics is the science which deals with the mechanics of liquids and gases. Fluid is a substance capable of flowing. Fluid mechanics may be divided into three branches. 1. Fluid Statics 2. Fluid Kinematics 3. Fluid Dynamics rest. Fluid statics is the study of mechanics of fluids at Fluid kinematics is the study of mechanics of fluids in motion. Fluid Kinematics deals with velocity, acceleration and stream lines without considering the forces causing the motion. Fluid dynamics is concerned with the relations between velocities, accelerations and the forces exerted by (or) upon fluids in motion.

16 1.2 Mechanics of Fluids FLUIDS AND CONTINUUM A fluid is a substance that deforms continuously when subjected to even an infinitesimal shear stress. This continuous deformation under the application of shear stress constitutes a flow. Solids can resist tangential stress at static conditions undergoing a definite deformation while a fluid can do it only at dynamic conditions undergoing a continuous deformation as long as the shear stress is applied Distinction between solid and fluid Table 1.1 Solid Fluid 1. Solid is a substance which 1. A fluid is a substance undergoes a finite deformation which undergoes continuous depending upon elastic limit deformation under application on application of a force. of a shear force, no matter how small the force might be. 2. Atoms (molecules) are 2. Atoms are comparatively usually closer together in loosely packed in fluid. solid. 3. Intermolecular attractive 3. Inter molecular forces are forces between the molecules not so large enough to hold of a solid are large the various elements of the fluid together and hence fluid will flow under the action of slightest stress. 4. A solid has a definite shape. 4. A fluid has no definite shape of its own but it conforms to the shape of the container vessel.

17 Introduction 1.3 The concept of continuum assumes a continuous distribution of mass within the matter or system with no empty space. In the continuum approach, properties of a system such as density, viscosity, temperature, etc can be expressed as continuous functions of space and time. The continuum concept is basically an approximation, in the same way planets are approximated by point particles when dealing with celestial mechanics, and therefore results in approximate solutions. Consequently, assumption of the continuum concept can lead to results which are not of desired accuracy. However, under the right circumstances, the continuum concept produces extremely accurate results. A dimensionless parameter known as knudsen number K n /L, where is the mean free path and L is the characteristic length, aptly describes the degree of departure from continuum. The continuum concept usually holds good when k n Fluid mechanics is a sub discipline of continuum mechanics as illustrated below. Continuum Mechanics (The study of the physics of continuous materials) Solid Mechanics (The study of the physics of continuous materials with a defined rest shape) Fluid Mechanics (The study of the physics of continuous materials which deform when subjected to a force)

18 1.4 Mechanics of Fluids PROPERTIES OF FLUIDS Gas and Liquid A fluid may be either a gas or a liquid. The molecules of a gas are much farther apart than those of a liquid. Hence a gas is highly compressible and a liquid is relatively incompressible. A vapour is a gas whose temperature and pressure are very closely nearer to the liquid phase. So steam is considered as vapour. A gas may be defined as a highly super heated vapour, i.e its state is far away from the liquid phase. So air is considered as a gas. Fluids are having the following properties: Table 1.2 Quantity Symbol Unit 1. Density (or) mass density kg/m 3 2. Specific weight (or) weight density w N/m 3 3. Specific volume v m 3 /kg 4. Specific gravity s No unit 5. Compressibility 1 K 6. Vapour pressure p N/m 2 7. Cohesion and Adhesion 8. Surface tension N/m 9. Capillary rise (or) fall h m 10. Viscosity-Dynamic viscosity (or) Ns/m 2 viscosity 11. Kinematic viscosity m 2 /s The above properties are discussed in detail.

19 Introduction Density (or) mass Density The density of a fluid is its mass per unit volume. Density mass volume kg m 3 So the unit of density is kg/m 3 and dimension is ML 3 The density of liquids is normally constant while that of gases changes with the variation of pressure and temperature. Density of water at 4C is 1000 kg/m Specific weight (or) Weight density Specific weight is the weight per unit volume. Its symbol is w. Specific weight represents the force exerted by gravity on a unit volume of fluid. Specific weight w Weight of fluid Volume of fluid N m 3 Specific weight and density are related w Weight of fluid Mass of fluid g Volume of fluid Volume of fluid g... mass Volume So w g...(1.1) Where g acceleration due to gravity.

20 1.6 Mechanics of Fluids - The specific weight of water at 4 C is 9810 N/m 3. Density is absolute since it depends on mass and independent of location. Specific weight, on the other hand, is not absolute, since it depends on value of g which varies from place to place. Density and specific weight of fluids vary with temperature Specific Volume v Specific volume is the volume occupied by a unit mass of fluid. Its symbol is v. Its unit is m 3 /kg v Volume of fluid Mass of fluid V Mass m3 kg Specific volume is the reciprocal of density v 1...(1.2) Note: v Specific volume; V Volume; u, v and V Velocity of flow Specific gravity (or) Relative density s Specific gravity of a liquid is the ratio of its density to that of pure water at a standard temp. 4C. Its symbol is s. It has no unit. s Density of liquid Density of water w...(1.3) where w 1000 kg/m 3 Density of liquid s w

21 Introduction 1.7 Specific gravity can also be defined in terms of specific weight. s Specific weight of liquid specific weight of water w w w Specific weight of liquid w s w w...(1.4) where w w 9810 N/m 3 The specific gravity of gas is the ratio of its density to that of air Temperature It is intensive thermodynamic property which determines the hotness or the level of heat intensity of a body. A body is said to be hot if it is having high temperature indicating high level of heat intensity. Similarly a body is said to be cold if it is at low temperature indicating low level of heat intensity. The temperature of a body is measured by an instrument called thermometer. Temperatures are measured in well known two scales: (i) Centigrade scale C (ii) Fahrenheit scale F Both the scales are inter convertible as follows F 1.8C 32 C F Viscosity Viscosity is the resistance offered to the movement of one layer of fluid by another adjacent layer of the fluid.

22 1.8 Mechanics of Fluids - u Velocity profile Y dy y u+du u du Fig Velocity Variation. Refer Fig Fluid is divided into different layers one over the other. Consider two layers of fluid. One is moving with velocity u. Another layer is moving with u du The distance between the layer is dy. The top layer causes a shear stress on the adjacent lower layer while the lower layer causes a shear stress on the adjacent top layer. This shear stress (denoted by ) is proportional to rate of change of velocity with respect to y. i.e du dy... (1.5) du dy... (1.6) The proportionality constant is and is known as coefficient of viscosity (or) absolute viscosity (or) dynamic viscosity (or) simply viscosity. du Velocity gradient (or) rate of shear strain (or) dy rate of shear deformation.

23 Introduction 1.9 The equation (1.6) can be rearranged as To find unit of : du/dy Shear stress Change in velocity Change of distance Force/Area Length Time 1 Length Force Time Length 2 N/m 2 m/s/m Ns m 2 In MKS Unit System, Force is measured in kgf So unit of kgfsec m 2 In CGS System, Force is Measured in dyne dyne sec So unit of cm 2 or poise [... dyne sec 1 cm 2 1 poise] In SI System Force is represented in Newton N So unit of N s m 2 Pa s [... N/m 2 Pascal Pa] Numerical Conversion From MKS unit to CGS unit.

24 1.10 Mechanics of Fluids - We know that 1 kgf 9.81 N So, 1 kgf Sec m N S m 2 kgf Sec 1 m kg 1 m/sec sec m 2 [... Force N m a] g 10 2 cm/sec 2 sec 10 4 cm g cm/sec 2 sec 10 4 cm 2 kgf Sec 1 m dyne sec cm 2 [... 1 g cm sec 2 1 dyne] kgf Sec poise m 2 In S.I Units [... dyne sec 1 cm 2 1 poise] kgf sec 1 m poise kgf sec Also 1 m N sec m 2 1 N Sec m poise 10 poise poise [... 1 kgf 9.81 N]

25 Introduction 1.11 So, 1 N sec m 2 10 poise [ in S.I unit sec is represented as S] So 1 Ns m 2 10 poise Sometimes unit of viscosity is given at centipoise 1 Centipoise CP poise A widely known metric unit for viscosity is the poise (p) 1 poise 0.1 Ns/m 2 in S.I units 1 centipoise 0.01 poise Ns/m Kinematic Viscosity () Kinematic viscosity is the ratio of dynamic viscosity to the density of the fluid. The symbol for kinematic viscosity is...(1.7) Unit for kinematic viscosity N s/m2 kg/m 3 kg m s 2 s 1 m 2 m3 kg... N kg m s 2 m2 s In metric system, is in stoke 1 stoke 1 cm 2 /s 10 4 m 2 /s in S.I units 1 centistoke 10 6 m 2 /s

26 1.12 Mechanics of Fluids - Variation of Viscosity with temperature The viscosity of liquids decreases with the increase of temperature while the viscosity of gases increases with the increase of temperature. This is due to the reason that in liquids the cohesive forces predominates the molecular momentum transfer, due to closely packed molecules and with the increase in temperature, the cohesive forces decreases with the result of decreasing viscosity. But in case of gases the cohesive force are small and molecular momentum transfer predominates. With the increase in temperature, molecular momentum transfer increases and hence viscosity increases. The relationship between viscosity and temperature for (a) Liquids: t t 2...(1.8) (b) Gases: Where 0 t t 2...(1.9) Viscosity of liquid/gas at tc, in poise 0 Viscosity of liquid/gas at 0C, in poise, are constants for liquid/gas Compressibility 1 K Compressibility of a liquid is inverse of its bulk modulus of elasticity.

27 Introduction 1.13 Bulk modulus K Compressive Stress Volumetric strain Consider a cylinder piston mechanism Let P 1 initial pressure inside the cylinder P 2 Final pressure inside the cylinder V 1 Initial volume V 2 Final volume K Increase in Pressure Volumetric strain C ylinder Piston dp dv V dp dv V...(1.10) Since rise in pressure reduces the volume by d V, the strain is indicated as dv V dv V Fig. 1.2 Compressibility 1 K Relationship between Bulk Modulus K and pressure p of a Gas for Isothermal and Isentropic Process For Isothermal Process We know that for Isothermal process PV constant Partial diffirenting the above equation we get PdV VdP 0

28 1.14 Mechanics of Fluids - P VdP dv dp dv/v...(1.11) From equation 1.10 we know that K P K For Isothermal process. For Adiabatic (or) isentropic process dp dv/v We know that for Adiabatic process PV constant Ratio of Specific heat Partial differentiating the above equation we get P V 1 dv V dp 0 dividing above equation by V 1, we get P dv VdP 0 P VdP dv K We get P K, for adiabatic or Isentropic Process Vapour Pressure When the liquid is kept in a closed vessel, it evaporates into vapour and this vapour occupies the space between the free surface of the liquid and top of the vessel. This vapour exerts a partial pressure on the free surface of the liquid. This pressure is known as vapour pressure of liquid Cavitation Now consider a flow of liquid in a system. If the pressure at any point in this flowing liquid becomes equal to the vapour pressure, the vaporization of the liquid begins and bubbles are formed. When these bubbles are carried

29 Introduction 1.15 by flowing liquid into region of high pressure, these bubbles collapse creating very high pressure. The metallic surface above which this liquid is flowing is subjected to these high pressures causing pitting action on surface. This process is called cavitation Gas and Gas laws The gas is the term applied to the state of any substance of which the evaporation from the liquid state is complete. Substances like Oxygen, air, Nitrogen and hydrogen etc may be regarded as gases within the temperature limits. A vapour may be defined as a partially evaporated liquid and consists of pure gasesous state together with the particles of liquid in suspension. Examples of vapour are not steam, ammonia, SO 2, CO 2 etc. A perfect gas or an ideal gas is one which obeys all gas laws under all conditions of temperature and pressures. No gas known is perfect i.e., no gas strictly obeys the gas laws but within the temperature limits of applied thermodynamics many gases like H 2, O 2, N 2 and even air may be regarded as perfect gases. Gas laws: Three variables control the physical properties of a gas. The pressure exerted by gas P, the volume V occupied by it and its temperature T. If any of these two variable are known then the third can be calculated by gas laws. Gas laws does not apply to vapours.

30 1.16 Mechanics of Fluids - Boyle s law: Boyle s law states that The volume of a given mass of a gas varies inversely as its absolute pressure, provided the temperature remains constant. V 1 or PV constant P Charles laws: Charle s law states The volume of a given mass of a gas varies directly as its absolute temperature, provided the pressure is kept constant. The variation is same for all gases. V T or V T Constant law). Perfect gas law (combination of boyle s and charle s Let us assume we have a perfect gas at absolute pressure, volume and absolute temperature of P 1, V 1 and T 1 respectively. Suppose the gas expands or contracts at a constant temperature to its volume V 1 such that the corresponding volume of its new absolute pressure is P 2. According to boyle s law P 1 V 1 P 2 V (1) Now let gas be expanded (or contracted) further such that the pressure remains constant and its volume and absolute temperature change from V 1 1 to V 2 and T 1 to T 2 respectively. According to charles law

31 Introduction 1.17 V 1 T 1 V 2 T 1 or V 1 V 2 T 1 T 2...(2) Substituting (2) in (1) we get i.e P 1 V 1 P 2 V 2 T 1 T 2 P V T constant. or P 1 V 1 T 1 P 2 V 2 T 2 If v is the Volume of unit mass of gas, then this constant is R (characteristic gas constant) i.e Pv R or Pv RT which is called the equation of T perfect gas or characteristic gas equation. If m is mass of gas under consideration, then the equation becomes PV mrt Surface Tension When a liquid is put inside a narrow tube, the free surface of the liquid displays either a rise (or) depression near the walls of the tube. This phenomena is attributed to a property of fluids known as surface tension. Soap bubbles, small droplets of water and dew on a dry solid surface also are attributed to surface tension. Surface Tension is also defined as the tensile force acting on the surface of a liquid in contact with a gas or on the surface between two immiscible liquids such that the contact surface behaves like a membrane under tension. The magnitude of this force per unit length of the free

32 1.18 Mechanics of Fluids - surface will have the same value as the surface energy per unit area. Surface tension in a liquid is caused by (i) Cohesive forces i.e forces of attraction between molecules of the same material or fluid and (ii) Adhesive forces i.e forces of attraction between molecules of different materials, say, the attraction between molecules of liquid and the molecules of container (or) air. Example for Cohesive Force When mercury is poured on the floor, it does not wet the surface of floor and forms sphere. When two spheres of mercury are brought close together, they combine together to form a bigger sphere. This means that the mercury molecules have cohesive tendency and have no tendency to adhere (adhesion) to the floor (solid surface). Example for Adhesive Force When water is poured on the floor, the water molecules wet the surface. This means that water molecules have adhesive tendency to adhere to the floor (solid surface). At the interface between a liquid and a gas ie at the liquid surface, and at the interface between two immiscible (not mixable) liquids, the out of balance attraction force between molecules forms an imaginary film capable of resisting tension. This liquid property is known as surface tension. Because the tension acts on a surface, we compare such forces by measuring the tension per unit length of surface. The surface tension is denoted by the symbol. The unit of surface tension is N/m.

33 Introduction 1.19 A B Consider a liquid in a vessel as shown in Fig. 1.3 Consider two molecules A and B of a liquid in a mass of liquid. The molecule A is attracted in all directions equally by the surrounding molecules of the liquid. Thus the resultant force acting on the molecule A is zero. But the molecule B is situated near the free surface. This molecule B is acted upon by upward and downward forces which are unbalanced. Thus net resultant force on molecule B is acting in a downward direction. Like molecule B, all the molecules near the free surface experience a downward force. So the free surface of the liquid acts like a very thin film under tension of the surface of the liquid Surface Tension on Droplet Let us consider a spherical droplet of liquid of radius r. The surface tension on the surface of droplet in N m P Pressue intensity inside the droplet r Radius of droplet Fig.1.3. Surface tension in excess of the outside pressure intensity

34 1.20 Mechanics of Fluids - P Water Droplet SurfaceTension Pressure Forces Fig.1.4 Forces on droplet Let us assume that the droplet is cut into two halves as shown in Fig The forces acting on one half (say left half) will be (i) Tensile force acting around the circumference of the cut portion (This tensile force is due to surface tension) and is given as circumference 2r (ii) Pressure force on the area P r 2 Under equibibrium conditions, these two forces will be equal and opposite in direction. Equate both forces, we get, Water droplet Fig.1.5.Pressure inside a water droplet d P r 2 2r P 2 r or 4 d...(1.12) where d dia of droplet

35 Introduction 1.21 The equation shows that with the decrease of radius of the droplet, pressure intensity inside the droplet increases Surface Tension on a Hollow Bubble Soap bubble d A hollow bubble (soap bubble) has two surfaces in contact with air, one inside and other outside. The above two surfaces are subjected to surface tension. In such case, Surface tension on both circumferences Fig.1.6. Pressure inside a soap bubble 2 2r we can equate two forces acting on bubble P r r P 4 r or P 8 d...(1.13) Surface Tension on a Liquid Jet Consider a liquid jet of diameter d and length L as shown in Fig P Pressure intensity inside the liquid jet above the outside pressure Surface tension of the liquid

36 1.22 Mechanics of Fluids - Consider the equilibrium of forces acting on the half of the liquid jet Force acting on jet P area of half of jet d (rectangle). P L d. Force due to surface tension 2L L P L d 2L P 2L L d 2 d r P r Fig.1.7 Force on liquid jet Capillarity Capillarity is the property of exerting forces on fluids by fine tubes. It is due to cohesion and adhesion. Capillarity may be defined as a phenomenon of rise or fall of a liquid surface in a small tube relative to the adjacent general level of liquid when the tube is held vertically in the liquid. When a fine glass tube is partially immersed in water, the water will rise in the tube to a height of h m above the water level. This happens when cohesion is of less effect than adhesion. On the otherhand, if the same tube is partially immersed in mercury, the mercury level in tube will be lower than the adjacent mercury level. This happens because cohesion predominates than adhesion.

37 Introduction 1.23 The rise of the liquid surface is called capillary rise and the depression of the liquid surface is called capillary depression (or) capillary fall. Mercury h=capillary fall water (a) capillary Rise (b) Capillary Depression Fig.1.8. Capillary Rise (or) Fall Expression for Capillary Rise Refer capillary rise in Fig 1.8 (a) Lifting force created by surface tension Vertical component of the surface tension force circumference cos d cos Weight of the liquid of height h in the tube mass g Volume g Area h g 4 d2 h g

38 1.24 Mechanics of Fluids - get, Under equilibrium condition, equate both forces, we d cos 4 d2 h g Capillary rise h 4 cos g d...(1.14) Where h: Height of liquid in the tube (or) capillary rise : Surface tension of liquid. : Angle of contact between liquid and glass tube. : Density of liquid Generally value is approximately equal to zero and hence cos 1 then Capillary rise h 4 gd...(1.15) Expression for Capillary Fall Refer Capillary Fall in Fig. 1.8 (b) Hydrostatic force acting upward P 4 d2 g h 4 d2 Downward force making depression due to surface tension d cos Under equilibrium condition, g h 4 d2 d cos

39 Introduction 1.25 Capillary fall h 4 cos g d Thermodynamic Properties The characteristic equation (or) equation of state for perfect gases is given as PV m RT... (i) Where V Volume of gas in m 3 m mass of gas in kg R Characteristic gas constant or simply gas constant R for air kj/kg K T absolute temperature in K Kelvin T tc 273 The equation can be written Pv RT P R T... (ii)... (iii) Where v specific volume in m 3 /kg density in kg/m 3 Also, we can write the equation as P 1 V 1 P 2 V 2 P 3 V 3 constant T 1 T 2 T 3 For Isothermal process, temperature remains constant Pv constant or PV constant. For Isentropic process

40 1.26 Mechanics of Fluids - Pv constant or PV constant. For Polytropic process, Pv n constant [n index of compression (or) expansion] [n ranges from 0 to ] ratio of specific heats C p C v C p and C v specific heats of a gas at constant pressure and constant volume respectively According to Avagadro s hypothesis, all the pure gases at the same temperature and pressure have the same number of molecules per unit volume. For any gas, PVm MRT... (iv) Where Vm molar Volume. (molar volume is the volume occupied by the molecular mass of any gas at standard temperature and pressure). T Absolute temp in K; M Molecular weight So the equation (iv) can be written as PV m R T R MR Universal gas constant From Avagadro s law, When P N/m 2 and T K Molar volume Vm 22.4 m3 /kg mol PV m R T R PV m T

41 Introduction J/kg mol K kj/kg mol K R kj/kg mole K for any gas [Universal gas constant] R R for gas A M for gas A R R air M for air kj/kg K [... M for air kg/kg mol] 1.4 NEWTON S LAW OF VISCOSITY A fluid is a substance that deforms continuously when subjected to a shear stress, no matter how small that shear stress may be. A shear force is the force component tangent to a surface, and this force divided by the area of the surface is the average shear stress over the area. Shear stress at a point is the limiting value of shear force to area as the area is reduced to the point. In the Fig 1.9, a substance is placed between two closely spaced parallel plates so large that conditions at their edges may be neglected. The lower plate is fixed and a force F is applied to the upper plate, which exerts a shear stress. If A is the area of plate, then shear stress is Y b b c c V u F t a d y x Fig.1.9. Deformation Due to Constant Shear Force

42 1.28 Mechanics of Fluids - F/A on any substance between plates. When the force F causes the upper plate to move with a steady (Non zero) velocity, no matter how small the magnitude of F, one may conclude that the substance between the two plates is a fluid. The fluid in the area abcd flows to the new position abcd, each fluid particle moving parallel to the plate and the velocity u varying uniformly from zero at the stationary plate to V at upper plate. Experimental results shows that F AV t...(1.16) where is the proportionality factor called coefficient of viscosity. If F/A then...(1.17) Substituting 1.17 in 1.16 we get Shear Stress V t V t is the angular velocity or rate of angular deformation. The angular velocity may also be written as du/dy as both V/t and du/dy express the velocity change divided by the distance over which the change occurs. Now in the differential form, du. This equation is called dy Newton s law of viscosity. Newton s law of viscosity states that the shear stress on a fluid layer is directly proportional to the rate of statics strain. The constant of proportionality is called the coefficient of viscosity Shear Stress du/dy

43 Introduction Types of Fluid du dy...(1.18) All the fluids can be classified into the following types 1. Ideal fluid 2. Real fluid 3. Newtonian fluid 4. Non-newtonian fluid 5. Ideal plastic fluid 1. Ideal Fluid: A fluid with no viscosity is called ideal fluid. Practically, no fluid is ideal since all fluids have some viscosity. This fluid is represented by the horizontal axis in the following graph. 2. Real Fluid: A fluid having viscosity is called Real fluid 3. Newtonian Fluid: A fluid which obeys the Newton s law of viscosity is called Newtonian fluid. In Newtonian fluids there is a linear relation between and rate of deformation du/dy as shown in Fig.1.10 This means that regardless of the forces acting on a fluid, it continues to flow. For example, water is a Newtonian fluid as it continues to display fluid properties no matter how much it is stirred or mixed. 4. Non-Newtonian Fluid: The fluid which does not obey the newton s law of viscosity is called Non-newtonian fluid. Here there is a non-linear relationship between and du/dy. So, stirring a non-newtonian fluid can leave a gap behind which will gradually fill up over time, as such in materials such as pudding. Alternatively, stirring a

44 1.30 Mechanics of Fluids - non-newtonian fluid can cause the viscosity to decrease, so the fluid appears thinner as seen in non-drip paints. Elastic solid =shear stress ideal plastic Non - Newtonian fluid New tonian fluid ideal fluid (Velocity gradient) du/dy Fig Types of fluids. 5. Ideal Plastic Fluid: A fluid in which shear stress is more than the yield value and shear stress is proportional to the rate of shear strain (or velocity gradient), is called ideal plastic fluid. It is shown in Fig 1.10 by straightline intersecting the vertical axis at the yield stress. SOLVED PROBLEMS Problem 1.1 A mass of liquid weight 500 N, is exposed to standard earth s gravity g m/s 2. (i) What is its mass? (ii) What will be its weight in a planet with acceleration due to gravity is 3.5 m/s 2?

45 Introduction 1.31 Solution Given: Weight W 500 N, g m/s 2, g m/s 2 Case (i) To find: Mass M and weight W 1 Weight W 500 N; g m/s 2 W mg Case (ii) Mass m W g Mass m kg kg Mass of liquid m kg (Mass remains constant) W 1 mg 1 where g 1 Acceleration due to gravity in a planet. W N W N Problem 1.2 Determine the specific gravity of a fluid having viscosity of 0.07 poise and kinematic viscosity of stokes. Given: 0.07 poise, stokes. To Find: Specific Gravity s.

46 1.32 Mechanics of Fluids - Solution: s specific gravity w 0.07 poise Ns m stokes m 2 s.. Ns. 1 poise 0.1 m 2 We know kinematic viscosity Dynamic viscosity Density of fluid... 1 stoke 10 4 m 2 Ns ; kg/m 3 But s w So s 1000 [... w density of water 1000 kg/m 3 ] s Specific gravity of fluid s

47 Introduction 1.33 Problem 1.3 Determine the viscosity of oil having kinematic viscosity of 6 stokes and specific gravity of 2. Given: 6 ; stokes; s 2 To Find: Solution: viscosity of oil? We know that s 2 ; 6 stokes m 2 /s (FAQ) [... 1 stoke 10 4 m 2 /s] s w s w kg/m 3 So Ns/m 2... w 1000 kg/m 3 Problem 1.4: The space between two parallel plates kept 3 mm apart is filled with an oil of dynamic viscosity of 0.2 Pa-s. What is the shear stress on the lower fixed plate, if the upper one is moved with a velocity of 1.5 m/s. Given: Solution: dy 3 mm, 0.2 Pa s 0.2 Ns m 2 du 1.5 m/s To Find: 0.2 Pa.s 0.2 Ns m 2 According to Newtons law of viscosity

48 1.34 Mechanics of Fluids - Shear Stress du dy where shear stress on the lower fixed plate. du Change of velocity u m/s distance between two plates dy 3 mm Upper moving plate m 1.5m/s du dy N/m 2 Oil of = 0.2 Poise Lower fixed plate dy = 3 mm Shear stress on lower plate 100 N/m 2 Problem 1.5: A 2.5 cm wide gap between two large plane surfaces are filled with glycerine. What surface force is required to drag a very thin plate of 0.75 m 2 in area between the surfaces at a speed of 0.5 m/s, if it is at a distance of 1 cm from one of the surfaces? Take Ns/m 2 Given: dy 2.5 cm dy 1 1 cm m dy m A 0.75 m 2 u 0.5 m/s Ns/m 2

49 Introduction 1.35 Solution Note: Since it is very thin plate, the weight of the plate and buoyant force are neglected. 1cm dy 1 dy 2 Area of thin plate 0.75 m 2 du u m/s dy 1 1 cm m dy cm m Ns/m 2 2.5cm To Find Drag Force to Lift the Plate: Drag force on both sides A Shear stress on both sides du dy 1 du dy 2 du dy 1 du dy [ ] N/m 2 Drag force on both sides A N

50 1.36 Mechanics of Fluids - Problem 1.6: If the velocity distribution over a plate is given by u y y 2 in which u is the velocity in m/s at a distance of y meters above the plate, determine the shear stress at y 0.10 m when coefficient of viscosity is 0.86 Ns/m 2 Solution Given: u y y 2 ; 0.86 Ns/m 2 To Find: 0.1? y 0.1 m 0.86 Ns/m 2 u y y 2 Velocity gradient du dy 1 2y when y 0.1 m, du dy s To Find Shear stress at y 0.1 m 0.1 du dy N/m N/m Problem 1.7: A fluid of specific gravity 0.9 flows along a surface with a velocity profile given by v 4y 8y 3 m/s, where y is in m. What is the velocity gradient at the boundary? If the kinematic viscosity is 0.36 S, What is the shear stress at the boundary? (FAQ)

51 Introduction 1.37 Given Solution: Specific gravity of fluid 0.9 Kinematic viscosity, 0.36 stokes Velocity V 4y 8y 3 m/s m 2 /s (a) velocity gradient at the boundary =? (b) shear stress at boundary? V 4y 8y 3 dv dy 4 8 3y y 2 (a) Velocity gradient at the boundary, ie y 0, dv dy Ans y 0 (b) Shear stress, dv dy Specific gravity S 0.9 Density of fluid Density of water Density of fluid 0.9 density of water kg/m 3 w.k.t NS/m 2

52 1.38 Mechanics of Fluids - Shear stress at boundary, i.e dv dy y N/m 2 Ans Problem 1.8: A cubical block having 200 mm edge and mass of 25 kg slides down an inclined plane surface which makes an angle of 20 with the horizontal. On the plane, there is a thin film of oil of thickness mm and viscosity Ns/m 2. What terminal velocity will be attained by the block? Solution Given: l 200 mm 0.2 m Mass m 25 kg 20 t mm Ns/m Ns/m 2 Area m 2 W Wt. of block N 20 o m =25kg dy=thickness=0.026m m w wsin20 o =20 o To Find Shear Stress: Component of W along their inclined plane i.e shear force F W sin

53 Introduction sin N Shear stress on the F bottom surface of cube A To Find Terminal Velocity u We know, du dy N/m du du m/s du u 0 So, Terminal Velocity u m/s Problem 1.9: A plate having an area of 0.8 m 2 is sliding down the inclined plane at 25 to the horizontal with a velocity of 0.36 m/s. There is a cushion of fluid, 1.8 mm thick between the plane and the plate. Find the viscosity of the fluid if the weight of the plate is 442 N. Given: A 0.8 m 2 25 u 0.36 m/s t dy 1.8 mm W 442 N Solution Area of plate 0.8 m 2 Weight of plate 442 N

54 1.40 Mechanics of Fluids - Velocity of plate u 0.36 m/s du u m/s plate dy=1.8m m u=0.36m /s Thickness of film 25 o t dy 1.8 mm 25 o m To Find Viscosity of Fluid w sin w = 442N Component of W along the plate Shear stress F A We know, du dy shear force F W sin 442 sin N N/m2 Viscosity Ns/m poise Problem 1.10: A metal plate of size 0.6 m 0.6 m and 1 mm thick and weighing 25 N is to be lifted up edgewise with uniform velocity of 0.2 m/s in the gap between two flat surfaces. The plate is in the middle of the gap of width 20 mm and the gap contains oil of relative density 0.85 and viscosity 16 poise. Calculate the vertical force required for this job.

55 Introduction 1.41 Solution: Given : Dimensions of the plate dy =dy 1 2 t=dy 1 1 t=dy m Area of plate m 2 Since the plate is in the middle of the gap, t 1 t 2 dy 1 dy mm m 20mm 1mm Relative density specific gravity s 0.85 Dynamic viscosity 16 poise 1.6 Ns/m 2 Velocity of the plate u 0.2 m/s; So du u m/s Weight of the plate 25 N To Find Force Required to Lift the Plate Drag force (or viscous resistance) against the motion of the plate, F 1 A 2 A where 1 and 2 are the shear stresses on both sides of the plate. 1 du dy 1 and 2 du dy 2 F A [ 1 2 ] A du 1 1 dy 1 dy 2

56 1.42 Mechanics of Fluids Force F N Upward thrust (or) buoyant force on the plate Specific weight Volume of oil displaced N [Note: When a body is immersed in a fluid, upward force (or) buoyant force acts on body to move the body upward. This buoyant force is equal to weight of fluid displaced by the body. So Weight of fluid displaced Sp. weight Volume of fluid displaced Now Weight of the body 25 N acts downward. Buoyant force is acting upward. Effective weight of the plate N Total force required to lift the plate at a velocity of 0.2 m/s F effective weight of plate N. Problem 1.11: A vertical gap of 30 mm width and infinitely long, contain oil of specific gravity 0.9 and viscosity 3.5 Ns/m 2. A metal plate 1.0 m 1.0 m 10 mm having a mass of 20 Kg is to be lifted through the gap at a constant speed of 0.15 m/s. Determine the force required. The plate is situated 5 mm from the left end.

Fluid Mechanics and Machinery

Fluid Mechanics and Machinery Fluid Mechanics and Machinery For III Semester B.E., Mechanical Engineering Students As per Latest Syllabus of Anna University - TN With Short Questions & Answers and University Solved Papers New Regulations

More information

UNIT I FLUID PROPERTIES AND STATICS

UNIT I FLUID PROPERTIES AND STATICS SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code : Fluid Mechanics (16CE106) Year & Sem: II-B.Tech & I-Sem Course & Branch:

More information

R09. d water surface. Prove that the depth of pressure is equal to p +.

R09. d water surface. Prove that the depth of pressure is equal to p +. Code No:A109210105 R09 SET-1 B.Tech II Year - I Semester Examinations, December 2011 FLUID MECHANICS (CIVIL ENGINEERING) Time: 3 hours Max. Marks: 75 Answer any five questions All questions carry equal

More information

CE 6303 MECHANICS OF FLUIDS L T P C QUESTION BANK 3 0 0 3 UNIT I FLUID PROPERTIES AND FLUID STATICS PART - A 1. Define fluid and fluid mechanics. 2. Define real and ideal fluids. 3. Define mass density

More information

INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad AERONAUTICAL ENGINEERING QUESTION BANK : AERONAUTICAL ENGINEERING.

INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad AERONAUTICAL ENGINEERING QUESTION BANK : AERONAUTICAL ENGINEERING. Course Name Course Code Class Branch INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad - 00 0 AERONAUTICAL ENGINEERING : Mechanics of Fluids : A00 : II-I- B. Tech Year : 0 0 Course Coordinator

More information

s and FE X. A. Flow measurement B. properties C. statics D. impulse, and momentum equations E. Pipe and other internal flow 7% of FE Morning Session I

s and FE X. A. Flow measurement B. properties C. statics D. impulse, and momentum equations E. Pipe and other internal flow 7% of FE Morning Session I Fundamentals of Engineering (FE) Exam General Section Steven Burian Civil & Environmental Engineering October 26, 2010 s and FE X. A. Flow measurement B. properties C. statics D. impulse, and momentum

More information

Fluid Mechanics. du dy

Fluid Mechanics. du dy FLUID MECHANICS Technical English - I 1 th week Fluid Mechanics FLUID STATICS FLUID DYNAMICS Fluid Statics or Hydrostatics is the study of fluids at rest. The main equation required for this is Newton's

More information

1 FLUIDS AND THEIR PROPERTIES

1 FLUIDS AND THEIR PROPERTIES FLUID MECHANICS CONTENTS CHAPTER DESCRIPTION PAGE NO 1 FLUIDS AND THEIR PROPERTIES PART A NOTES 1.1 Introduction 1.2 Fluids 1.3 Newton s Law of Viscosity 1.4 The Continuum Concept of a Fluid 1.5 Types

More information

ENGINEERING FLUID MECHANICS. CHAPTER 1 Properties of Fluids

ENGINEERING FLUID MECHANICS. CHAPTER 1 Properties of Fluids CHAPTER 1 Properties of Fluids ENGINEERING FLUID MECHANICS 1.1 Introduction 1.2 Development of Fluid Mechanics 1.3 Units of Measurement (SI units) 1.4 Mass, Density, Specific Weight, Specific Volume, Specific

More information

S.E. (Mech.) (First Sem.) EXAMINATION, (Common to Mech/Sandwich) FLUID MECHANICS (2008 PATTERN) Time : Three Hours Maximum Marks : 100

S.E. (Mech.) (First Sem.) EXAMINATION, (Common to Mech/Sandwich) FLUID MECHANICS (2008 PATTERN) Time : Three Hours Maximum Marks : 100 Total No. of Questions 12] [Total No. of Printed Pages 8 Seat No. [4262]-113 S.E. (Mech.) (First Sem.) EXAMINATION, 2012 (Common to Mech/Sandwich) FLUID MECHANICS (2008 PATTERN) Time : Three Hours Maximum

More information

HYDRAULICS STAFF SELECTION COMMISSION CIVIL ENGINEERING STUDY MATERIAL HYDRAULICS

HYDRAULICS STAFF SELECTION COMMISSION CIVIL ENGINEERING STUDY MATERIAL HYDRAULICS 1 STAFF SELECTION COMMISSION CIVIL ENGINEERING STUDY MATERIAL Syllabus Hydraulics ( Fluid Mechanics ) Fluid properties, hydrostatics, measurements of flow, Bernoulli's theorem and its application, flow

More information

Steven Burian Civil & Environmental Engineering September 25, 2013

Steven Burian Civil & Environmental Engineering September 25, 2013 Fundamentals of Engineering (FE) Exam Mechanics Steven Burian Civil & Environmental Engineering September 25, 2013 s and FE Morning ( Mechanics) A. Flow measurement 7% of FE Morning B. properties Session

More information

B.E/B.Tech/M.E/M.Tech : Chemical Engineering Regulation: 2016 PG Specialisation : NA Sub. Code / Sub. Name : CH16304 FLUID MECHANICS Unit : I

B.E/B.Tech/M.E/M.Tech : Chemical Engineering Regulation: 2016 PG Specialisation : NA Sub. Code / Sub. Name : CH16304 FLUID MECHANICS Unit : I Department of Chemical Engineering B.E/B.Tech/M.E/M.Tech : Chemical Engineering Regulation: 2016 PG Specialisation : NA Sub. Code / Sub. Name : CH16304 FLUID MECHANICS Unit : I LP: CH 16304 Rev. No: 00

More information

VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur

VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur 603 203 DEPARTMENT OF CIVIL ENGINEERING QUESTION BANK III SEMESTER CE 8302 FLUID MECHANICS Regulation 2017 Academic Year 2018 19 Prepared by Mrs.

More information

FE Fluids Review March 23, 2012 Steve Burian (Civil & Environmental Engineering)

FE Fluids Review March 23, 2012 Steve Burian (Civil & Environmental Engineering) Topic: Fluid Properties 1. If 6 m 3 of oil weighs 47 kn, calculate its specific weight, density, and specific gravity. 2. 10.0 L of an incompressible liquid exert a force of 20 N at the earth s surface.

More information

Experiment- To determine the coefficient of impact for vanes. Experiment To determine the coefficient of discharge of an orifice meter.

Experiment- To determine the coefficient of impact for vanes. Experiment To determine the coefficient of discharge of an orifice meter. SUBJECT: FLUID MECHANICS VIVA QUESTIONS (M.E 4 th SEM) Experiment- To determine the coefficient of impact for vanes. Q1. Explain impulse momentum principal. Ans1. Momentum equation is based on Newton s

More information

Petroleum Engineering Dept. Fluid Mechanics Second Stage Dr. Ahmed K. Alshara

Petroleum Engineering Dept. Fluid Mechanics Second Stage Dr. Ahmed K. Alshara Continents Chapter 1. Fluid Mechanics -Properties of fluids -Density, specific gravity, specific volume and Viscosity -Newtonian and non Newtonian fluids -Surface tension Compressibility -Pressure -Cavitations

More information

MECHANICAL PROPERTIES OF FLUIDS:

MECHANICAL PROPERTIES OF FLUIDS: Important Definitions: MECHANICAL PROPERTIES OF FLUIDS: Fluid: A substance that can flow is called Fluid Both liquids and gases are fluids Pressure: The normal force acting per unit area of a surface is

More information

NPTEL Quiz Hydraulics

NPTEL Quiz Hydraulics Introduction NPTEL Quiz Hydraulics 1. An ideal fluid is a. One which obeys Newton s law of viscosity b. Frictionless and incompressible c. Very viscous d. Frictionless and compressible 2. The unit of kinematic

More information

ACE Engineering College

ACE Engineering College ACE Engineering College Ankushapur (V), Ghatkesar (M), R.R.Dist 501 301. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * MECHANICS OF FLUIDS & HYDRAULIC

More information

Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015

Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015 Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015 I. Introduction (Chapters 1 and 2) A. What is Fluid Mechanics? 1. What is a fluid? 2. What is mechanics? B. Classification of Fluid Flows 1. Viscous

More information

Approximate physical properties of selected fluids All properties are given at pressure kn/m 2 and temperature 15 C.

Approximate physical properties of selected fluids All properties are given at pressure kn/m 2 and temperature 15 C. Appendix FLUID MECHANICS Approximate physical properties of selected fluids All properties are given at pressure 101. kn/m and temperature 15 C. Liquids Density (kg/m ) Dynamic viscosity (N s/m ) Surface

More information

Fundamentals of Fluid Mechanics

Fundamentals of Fluid Mechanics Sixth Edition Fundamentals of Fluid Mechanics International Student Version BRUCE R. MUNSON DONALD F. YOUNG Department of Aerospace Engineering and Engineering Mechanics THEODORE H. OKIISHI Department

More information

Liquids and solids are essentially incompressible substances and the variation of their density with pressure is usually negligible.

Liquids and solids are essentially incompressible substances and the variation of their density with pressure is usually negligible. Properties of Fluids Intensive properties are those that are independent of the mass of a system i.e. temperature, pressure and density. Extensive properties are those whose values depend on the size of

More information

CHAPTER 1 Fluids and their Properties

CHAPTER 1 Fluids and their Properties FLUID MECHANICS Gaza CHAPTER 1 Fluids and their Properties Dr. Khalil Mahmoud ALASTAL Objectives of this Chapter: Define the nature of a fluid. Show where fluid mechanics concepts are common with those

More information

10 - FLUID MECHANICS Page 1

10 - FLUID MECHANICS Page 1 0 - FLUID MECHANICS Page Introduction Fluid is a matter in a state which can flow. Liquids, gases, molten metal and tar are examples of fluids. Fluid mechanics is studied in two parts: ( i ) Fluid statics

More information

Petroleum Engineering Department Fluid Mechanics Second Stage Assist Prof. Dr. Ahmed K. Alshara

Petroleum Engineering Department Fluid Mechanics Second Stage Assist Prof. Dr. Ahmed K. Alshara Continents Petroleum Engineering Department Fluid Mechanics Second Stage Assist Prof. Dr. Ahmed K. Alshara Chapter 1. Fluid Mechanics -Properties of fluids -Density, specific gravity, specific volume and

More information

Chapter -5(Section-1) Friction in Solids and Liquids

Chapter -5(Section-1) Friction in Solids and Liquids Chapter -5(Section-1) Friction in Solids and Liquids Que 1: Define friction. What are its causes? Ans : Friction:- When two bodies are in contact with each other and if one body is made to move then the

More information

Chapter 1 INTRODUCTION

Chapter 1 INTRODUCTION Chapter 1 INTRODUCTION 1-1 The Fluid. 1-2 Dimensions. 1-3 Units. 1-4 Fluid Properties. 1 1-1 The Fluid: It is the substance that deforms continuously when subjected to a shear stress. Matter Solid Fluid

More information

PROPERTIES OF FLUIDS

PROPERTIES OF FLUIDS Unit - I Chapter - PROPERTIES OF FLUIDS Solutions of Examples for Practice Example.9 : Given data : u = y y, = 8 Poise = 0.8 Pa-s To find : Shear stress. Step - : Calculate the shear stress at various

More information

V/ t = 0 p/ t = 0 ρ/ t = 0. V/ s = 0 p/ s = 0 ρ/ s = 0

V/ t = 0 p/ t = 0 ρ/ t = 0. V/ s = 0 p/ s = 0 ρ/ s = 0 UNIT III FLOW THROUGH PIPES 1. List the types of fluid flow. Steady and unsteady flow Uniform and non-uniform flow Laminar and Turbulent flow Compressible and incompressible flow Rotational and ir-rotational

More information

MECHANICAL PROPERTIES OF FLUIDS

MECHANICAL PROPERTIES OF FLUIDS CHAPTER-10 MECHANICAL PROPERTIES OF FLUIDS QUESTIONS 1 marks questions 1. What are fluids? 2. How are fluids different from solids? 3. Define thrust of a liquid. 4. Define liquid pressure. 5. Is pressure

More information

CE MECHANICS OF FLUIDS UNIT I

CE MECHANICS OF FLUIDS UNIT I CE 6303- MECHANICS OF FLUIDS UNIT I 1. Define specific volume of a fluid and write its unit [N/D-14][M/J-11] Volume per unit mass of a fluid is called specific volume. Unit: m3 / kg. 2. Name the devices

More information

Fluid Mechanics Introduction

Fluid Mechanics Introduction Fluid Mechanics Introduction Fluid mechanics study the fluid under all conditions of rest and motion. Its approach is analytical, mathematical, and empirical (experimental and observation). Fluid can be

More information

MULTIPLE-CHOICE PROBLEMS:(Two marks per answer) (Circle the Letter Beside the Most Correct Answer in the Questions Below.)

MULTIPLE-CHOICE PROBLEMS:(Two marks per answer) (Circle the Letter Beside the Most Correct Answer in the Questions Below.) MULTIPLE-CHOICE PROLEMS:(Two marks per answer) (Circle the Letter eside the Most Correct Answer in the Questions elow.) 1. The absolute viscosity µ of a fluid is primarily a function of: a. Density. b.

More information

Introduction to Marine Hydrodynamics

Introduction to Marine Hydrodynamics 1896 1920 1987 2006 Introduction to Marine Hydrodynamics (NA235) Department of Naval Architecture and Ocean Engineering School of Naval Architecture, Ocean & Civil Engineering First Assignment The first

More information

GATE PSU. Chemical Engineering. Fluid Mechanics. For. The Gate Coach 28, Jia Sarai, Near IIT Hauzkhas, New Delhi 16 (+91) ,

GATE PSU. Chemical Engineering. Fluid Mechanics. For. The Gate Coach 28, Jia Sarai, Near IIT Hauzkhas, New Delhi 16 (+91) , For GATE PSU Chemical Engineering Fluid Mechanics GATE Syllabus Fluid statics, Newtonian and non-newtonian fluids, Bernoulli equation, Macroscopic friction factors, energy balance, dimensional analysis,

More information

Chapter 1 Fluid and their Properties

Chapter 1 Fluid and their Properties June -15 Jan - 16 GTU Paper Analysis (New Syllabus) Chapter 1 Fluid and their Properties Sr. No. Questions Theory 2. Explain the following terms: Relative density 2. Kinematic viscosity 3. Cavitation 4.

More information

ME3560 Tentative Schedule Spring 2019

ME3560 Tentative Schedule Spring 2019 ME3560 Tentative Schedule Spring 2019 Week Number Date Lecture Topics Covered Prior to Lecture Read Section Assignment Prep Problems for Prep Probs. Must be Solved by 1 Monday 1/7/2019 1 Introduction to

More information

BFC FLUID MECHANICS BFC NOOR ALIZA AHMAD

BFC FLUID MECHANICS BFC NOOR ALIZA AHMAD BFC 10403 FLUID MECHANICS CHAPTER 1.0: Principles of Fluid 1.1 Introduction to Fluid Mechanics 1.2 Thermodynamic Properties of a Fluid: Density, specific weight, specific gravity, viscocity (kelikatan)berat

More information

A drop forms when liquid is forced out of a small tube. The shape of the drop is determined by a balance of pressure, gravity, and surface tension

A drop forms when liquid is forced out of a small tube. The shape of the drop is determined by a balance of pressure, gravity, and surface tension A drop forms when liquid is forced out of a small tube. The shape of the drop is determined by a balance of pressure, gravity, and surface tension forces. 2 Objectives 3 i i 2 1 INTRODUCTION Property:

More information

ME3560 Tentative Schedule Fall 2018

ME3560 Tentative Schedule Fall 2018 ME3560 Tentative Schedule Fall 2018 Week Number 1 Wednesday 8/29/2018 1 Date Lecture Topics Covered Introduction to course, syllabus and class policies. Math Review. Differentiation. Prior to Lecture Read

More information

William В. Brower, Jr. A PRIMER IN FLUID MECHANICS. Dynamics of Flows in One Space Dimension. CRC Press Boca Raton London New York Washington, D.C.

William В. Brower, Jr. A PRIMER IN FLUID MECHANICS. Dynamics of Flows in One Space Dimension. CRC Press Boca Raton London New York Washington, D.C. William В. Brower, Jr. A PRIMER IN FLUID MECHANICS Dynamics of Flows in One Space Dimension CRC Press Boca Raton London New York Washington, D.C. Table of Contents Chapter 1 Fluid Properties Kinetic Theory

More information

1. The Properties of Fluids

1. The Properties of Fluids 1. The Properties of Fluids [This material relates predominantly to modules ELP034, ELP035] 1.1 Fluids 1.1 Fluids 1.2 Newton s Law of Viscosity 1.3 Fluids Vs Solids 1.4 Liquids Vs Gases 1.5 Causes of viscosity

More information

CH.1 Overview of Fluid Mechanics/22 MARKS. 1.1 Fluid Fundamentals.

CH.1 Overview of Fluid Mechanics/22 MARKS. 1.1 Fluid Fundamentals. Content : 1.1 Fluid Fundamentals. 08 Marks Classification of Fluid, Properties of fluids like Specific Weight, Specific gravity, Surface tension, Capillarity, Viscosity. Specification of hydraulic oil

More information

CLASS SCHEDULE 2013 FALL

CLASS SCHEDULE 2013 FALL CLASS SCHEDULE 2013 FALL Class # or Lab # 1 Date Aug 26 2 28 Important Concepts (Section # in Text Reading, Lecture note) Examples/Lab Activities Definition fluid; continuum hypothesis; fluid properties

More information

TOPICS. Density. Pressure. Variation of Pressure with Depth. Pressure Measurements. Buoyant Forces-Archimedes Principle

TOPICS. Density. Pressure. Variation of Pressure with Depth. Pressure Measurements. Buoyant Forces-Archimedes Principle Lecture 6 Fluids TOPICS Density Pressure Variation of Pressure with Depth Pressure Measurements Buoyant Forces-Archimedes Principle Surface Tension ( External source ) Viscosity ( External source ) Equation

More information

150A Review Session 2/13/2014 Fluid Statics. Pressure acts in all directions, normal to the surrounding surfaces

150A Review Session 2/13/2014 Fluid Statics. Pressure acts in all directions, normal to the surrounding surfaces Fluid Statics Pressure acts in all directions, normal to the surrounding surfaces or Whenever a pressure difference is the driving force, use gauge pressure o Bernoulli equation o Momentum balance with

More information

AMME2261: Fluid Mechanics 1 Course Notes

AMME2261: Fluid Mechanics 1 Course Notes Module 1 Introduction and Fluid Properties Introduction Matter can be one of two states: solid or fluid. A fluid is a substance that deforms continuously under the application of a shear stress, no matter

More information

Chapter 1 Fluid Characteristics

Chapter 1 Fluid Characteristics Chapter 1 Fluid Characteristics 1.1 Introduction 1.1.1 Phases Solid increasing increasing spacing and intermolecular liquid latitude of cohesive Fluid gas (vapor) molecular force plasma motion 1.1.2 Fluidity

More information

MULTIPLE-CHOICE PROBLEMS :(Two marks per answer) (Circle the Letter Beside the Most Correct Answer in the Questions Below.)

MULTIPLE-CHOICE PROBLEMS :(Two marks per answer) (Circle the Letter Beside the Most Correct Answer in the Questions Below.) Test Midterm 1 F2013 MULTIPLE-CHOICE PROBLEMS :(Two marks per answer) (Circle the Letter Beside the Most Correct nswer in the Questions Below.) 1. The absolute viscosity µ of a fluid is primarily a function

More information

COURSE NUMBER: ME 321 Fluid Mechanics I. Fluid: Concept and Properties

COURSE NUMBER: ME 321 Fluid Mechanics I. Fluid: Concept and Properties COURSE NUMBER: ME 321 Fluid Mechanics I Fluid: Concept and Properties Course teacher Dr. M. Mahbubur Razzaque Professor Department of Mechanical Engineering BUET 1 What is Fluid Mechanics? Fluid mechanics

More information

Chapter 9. Solids and Fluids. States of Matter. Solid. Liquid. Gas

Chapter 9. Solids and Fluids. States of Matter. Solid. Liquid. Gas Chapter 9 States of Matter Solids and Fluids Solid Liquid Gas Plasma Solids Have definite volume Have definite shape Molecules are held in specific locations By electrical forces Vibrate about equilibrium

More information

Chapter 9: Solids and Fluids

Chapter 9: Solids and Fluids Chapter 9: Solids and Fluids State of matters: Solid, Liquid, Gas and Plasma. Solids Has definite volume and shape Can be crystalline or amorphous Molecules are held in specific locations by electrical

More information

CE MECHANICS OF FLUIDS

CE MECHANICS OF FLUIDS CE60 - MECHANICS OF FLUIDS (FOR III SEMESTER) UNIT II FLUID STATICS & KINEMATICS PREPARED BY R.SURYA, M.E Assistant Professor DEPARTMENT OF CIVIL ENGINEERING DEPARTMENT OF CIVIL ENGINEERING SRI VIDYA COLLEGE

More information

University of Engineering and Technology, Taxila. Department of Civil Engineering

University of Engineering and Technology, Taxila. Department of Civil Engineering University of Engineering and Technology, Taxila Department of Civil Engineering Course Title: CE-201 Fluid Mechanics - I Pre-requisite(s): None Credit Hours: 2 + 1 Contact Hours: 2 + 3 Text Book(s): Reference

More information

Chapter 9. Solids and Fluids

Chapter 9. Solids and Fluids Chapter 9 Solids and Fluids States of Matter Solid Liquid Gas Plasma Solids Have definite volume Have definite shape Molecules are held in specific locations By electrical forces Vibrate about equilibrium

More information

Fluid Mechanics-61341

Fluid Mechanics-61341 An-Najah National University College of Engineering Fluid Mechanics-61341 Chapter [1] Fundamentals 1 The Book (Elementary Fluid Mechanics by Street, Watters and Vennard) Each chapter includes: Concepts

More information

University of Hail Faculty of Engineering DEPARTMENT OF MECHANICAL ENGINEERING. ME Fluid Mechanics Lecture notes. Chapter 1

University of Hail Faculty of Engineering DEPARTMENT OF MECHANICAL ENGINEERING. ME Fluid Mechanics Lecture notes. Chapter 1 University of Hail Faculty of Engineering DEPARTMENT OF MECHANICAL ENGINEERING ME 311 - Fluid Mechanics Lecture notes Chapter 1 Introduction and fluid properties Prepared by : Dr. N. Ait Messaoudene Based

More information

EXPERIMENT No.1 FLOW MEASUREMENT BY ORIFICEMETER

EXPERIMENT No.1 FLOW MEASUREMENT BY ORIFICEMETER EXPERIMENT No.1 FLOW MEASUREMENT BY ORIFICEMETER 1.1 AIM: To determine the co-efficient of discharge of the orifice meter 1.2 EQUIPMENTS REQUIRED: Orifice meter test rig, Stopwatch 1.3 PREPARATION 1.3.1

More information

Chapter 4 DYNAMICS OF FLUID FLOW

Chapter 4 DYNAMICS OF FLUID FLOW Faculty Of Engineering at Shobra nd Year Civil - 016 Chapter 4 DYNAMICS OF FLUID FLOW 4-1 Types of Energy 4- Euler s Equation 4-3 Bernoulli s Equation 4-4 Total Energy Line (TEL) and Hydraulic Grade Line

More information

Chapter 10. Solids and Fluids

Chapter 10. Solids and Fluids Chapter 10 Solids and Fluids Surface Tension Net force on molecule A is zero Pulled equally in all directions Net force on B is not zero No molecules above to act on it Pulled toward the center of the

More information

CHARACTERISTIC OF FLUIDS. A fluid is defined as a substance that deforms continuously when acted on by a shearing stress at any magnitude.

CHARACTERISTIC OF FLUIDS. A fluid is defined as a substance that deforms continuously when acted on by a shearing stress at any magnitude. CHARACTERISTIC OF FLUIDS A fluid is defined as a substance that deforms continuously when acted on by a shearing stress at any magnitude. In a fluid at rest, normal stress is called pressure. 1 Dimensions,

More information

REE 307 Fluid Mechanics II. Lecture 1. Sep 27, Dr./ Ahmed Mohamed Nagib Elmekawy. Zewail City for Science and Technology

REE 307 Fluid Mechanics II. Lecture 1. Sep 27, Dr./ Ahmed Mohamed Nagib Elmekawy. Zewail City for Science and Technology REE 307 Fluid Mechanics II Lecture 1 Sep 27, 2017 Dr./ Ahmed Mohamed Nagib Elmekawy Zewail City for Science and Technology Course Materials drahmednagib.com 2 COURSE OUTLINE Fundamental of Flow in pipes

More information

Nicholas J. Giordano. Chapter 10 Fluids

Nicholas J. Giordano.  Chapter 10 Fluids Nicholas J. Giordano www.cengage.com/physics/giordano Chapter 10 Fluids Fluids A fluid may be either a liquid or a gas Some characteristics of a fluid Flows from one place to another Shape varies according

More information

Fluid Mechanics Testbank By David Admiraal

Fluid Mechanics Testbank By David Admiraal Fluid Mechanics Testbank By David Admiraal This testbank was created for an introductory fluid mechanics class. The primary intentions of the testbank are to help students improve their performance on

More information

Tutorial 10. Boundary layer theory

Tutorial 10. Boundary layer theory Tutorial 10 Boundary layer theory 1. If the velocity distribution law in a laminar boundary layer over a flat plate is assumes to be of the form, determine the velocity distribution law. At y = 0, u= 0

More information

Lesson 6 Review of fundamentals: Fluid flow

Lesson 6 Review of fundamentals: Fluid flow Lesson 6 Review of fundamentals: Fluid flow The specific objective of this lesson is to conduct a brief review of the fundamentals of fluid flow and present: A general equation for conservation of mass

More information

INTRODUCTION DEFINITION OF FLUID. U p F FLUID IS A SUBSTANCE THAT CAN NOT SUPPORT SHEAR FORCES OF ANY MAGNITUDE WITHOUT CONTINUOUS DEFORMATION

INTRODUCTION DEFINITION OF FLUID. U p F FLUID IS A SUBSTANCE THAT CAN NOT SUPPORT SHEAR FORCES OF ANY MAGNITUDE WITHOUT CONTINUOUS DEFORMATION INTRODUCTION DEFINITION OF FLUID plate solid F at t = 0 t > 0 = F/A plate U p F fluid t 0 t 1 t 2 t 3 FLUID IS A SUBSTANCE THAT CAN NOT SUPPORT SHEAR FORCES OF ANY MAGNITUDE WITHOUT CONTINUOUS DEFORMATION

More information

Hydraulics. B.E. (Civil), Year/Part: II/II. Tutorial solutions: Pipe flow. Tutorial 1

Hydraulics. B.E. (Civil), Year/Part: II/II. Tutorial solutions: Pipe flow. Tutorial 1 Hydraulics B.E. (Civil), Year/Part: II/II Tutorial solutions: Pipe flow Tutorial 1 -by Dr. K.N. Dulal Laminar flow 1. A pipe 200mm in diameter and 20km long conveys oil of density 900 kg/m 3 and viscosity

More information

Figure 3: Problem 7. (a) 0.9 m (b) 1.8 m (c) 2.7 m (d) 3.6 m

Figure 3: Problem 7. (a) 0.9 m (b) 1.8 m (c) 2.7 m (d) 3.6 m 1. For the manometer shown in figure 1, if the absolute pressure at point A is 1.013 10 5 Pa, the absolute pressure at point B is (ρ water =10 3 kg/m 3, ρ Hg =13.56 10 3 kg/m 3, ρ oil = 800kg/m 3 ): (a)

More information

Fluid Mechanics c) Orificemeter a) Viscous force, Turbulence force, Compressible force a) Turbulence force c) Integration d) The flow is rotational

Fluid Mechanics c) Orificemeter a) Viscous force, Turbulence force, Compressible force a) Turbulence force c) Integration d) The flow is rotational Fluid Mechanics 1. Which is the cheapest device for measuring flow / discharge rate. a) Venturimeter b) Pitot tube c) Orificemeter d) None of the mentioned 2. Which forces are neglected to obtain Euler

More information

Chapter 10 - Mechanical Properties of Fluids. The blood pressure in humans is greater at the feet than at the brain

Chapter 10 - Mechanical Properties of Fluids. The blood pressure in humans is greater at the feet than at the brain Question 10.1: Explain why The blood pressure in humans is greater at the feet than at the brain Atmospheric pressure at a height of about 6 km decreases to nearly half of its value at the sea level, though

More information

UNIT II Real fluids. FMM / KRG / MECH / NPRCET Page 78. Laminar and turbulent flow

UNIT II Real fluids. FMM / KRG / MECH / NPRCET Page 78. Laminar and turbulent flow UNIT II Real fluids The flow of real fluids exhibits viscous effect that is they tend to "stick" to solid surfaces and have stresses within their body. You might remember from earlier in the course Newtons

More information

Benha University College of Engineering at Benha Questions For Corrective Final Examination Subject: Fluid Mechanics M 201 May 24/ 2016

Benha University College of Engineering at Benha Questions For Corrective Final Examination Subject: Fluid Mechanics M 201 May 24/ 2016 Benha University College of Engineering at Benha Questions For Corrective Final Examination Subject: Fluid Mechanics M 01 May 4/ 016 Second year Mech. Time :180 min. Examiner:Dr.Mohamed Elsharnoby Attempt

More information

Chapter 14. Lecture 1 Fluid Mechanics. Dr. Armen Kocharian

Chapter 14. Lecture 1 Fluid Mechanics. Dr. Armen Kocharian Chapter 14 Lecture 1 Fluid Mechanics Dr. Armen Kocharian States of Matter Solid Has a definite volume and shape Liquid Has a definite volume but not a definite shape Gas unconfined Has neither a definite

More information

LECTURE NOTES FLUID MECHANICS (ACE005)

LECTURE NOTES FLUID MECHANICS (ACE005) LECTURE NOTES ON FLUID MECHANICS (ACE005) B.Tech IV semester (Autonomous) (2017-18) Dr. G. Venkata Ramana Professor. DEPARTMENT OF CIVIL ENGINEERING INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) DUNDIGAL,

More information

Chemical and Biomolecular Engineering 150A Transport Processes Spring Semester 2017

Chemical and Biomolecular Engineering 150A Transport Processes Spring Semester 2017 Chemical and Biomolecular Engineering 150A Transport Processes Spring Semester 2017 Objective: Text: To introduce the basic concepts of fluid mechanics and heat transfer necessary for solution of engineering

More information

COURSE CODE : 3072 COURSE CATEGORY : B PERIODS/ WEEK : 5 PERIODS/ SEMESTER : 75 CREDIT : 5 TIME SCHEDULE

COURSE CODE : 3072 COURSE CATEGORY : B PERIODS/ WEEK : 5 PERIODS/ SEMESTER : 75 CREDIT : 5 TIME SCHEDULE COURSE TITLE : FLUID MECHANICS COURSE CODE : 307 COURSE CATEGORY : B PERIODS/ WEEK : 5 PERIODS/ SEMESTER : 75 CREDIT : 5 TIME SCHEDULE MODULE TOPIC PERIOD 1 Properties of Fluids 0 Fluid Friction and Flow

More information

Higher Education. Mc Grauu FUNDAMENTALS AND APPLICATIONS SECOND EDITION

Higher Education. Mc Grauu FUNDAMENTALS AND APPLICATIONS SECOND EDITION FLUID MECHANICS FUNDAMENTALS AND APPLICATIONS SECOND EDITION Mc Grauu Higher Education Boston Burr Ridge, IL Dubuque, IA Madison, Wl New York San Francisco St. Louis Bangkok Bogota Caracas Kuala Lumpur

More information

Chapter 14. Fluid Mechanics

Chapter 14. Fluid Mechanics Chapter 14 Fluid Mechanics States of Matter Solid Has a definite volume and shape Liquid Has a definite volume but not a definite shape Gas unconfined Has neither a definite volume nor shape All of these

More information

Fluids and their Properties

Fluids and their Properties Chapter (1) Fluids and their Properties Dr. KHALIL MAHMOUD ALASTAL Eng.Mohammed AbuRahma Eng.Reem Sbaih 2017 Newton s Law of Viscosity: - / Non-Newtonian Fluids: - Mass Density: - / Specific weight: -

More information

Contents. I Introduction 1. Preface. xiii

Contents. I Introduction 1. Preface. xiii Contents Preface xiii I Introduction 1 1 Continuous matter 3 1.1 Molecules................................ 4 1.2 The continuum approximation.................... 6 1.3 Newtonian mechanics.........................

More information

Fluid Mechanics Abdusselam Altunkaynak

Fluid Mechanics Abdusselam Altunkaynak Fluid Mechanics Abdusselam Altunkaynak 1. Unit systems 1.1 Introduction Natural events are independent on units. The unit to be used in a certain variable is related to the advantage that we get from it.

More information

PROPERTIES OF BULK MATTER

PROPERTIES OF BULK MATTER PROPERTIES OF BULK MATTER CONCEPTUAL PROBLEMS Q-01 What flows faster than honey. Why? Ans According to poiseuille s formula, the volume V of a liquid flowing per second through a horizontal narrow tube

More information

11.1 Mass Density. Fluids are materials that can flow, and they include both gases and liquids. The mass density of a liquid or gas is an

11.1 Mass Density. Fluids are materials that can flow, and they include both gases and liquids. The mass density of a liquid or gas is an Chapter 11 Fluids 11.1 Mass Density Fluids are materials that can flow, and they include both gases and liquids. The mass density of a liquid or gas is an important factor that determines its behavior

More information

Fluid Properties and Units

Fluid Properties and Units Fluid Properties and Units CVEN 311 Continuum Continuum All materials, solid or fluid, are composed of molecules discretely spread and in continuous motion. However, in dealing with fluid-flow flow relations

More information

CE FLUID MECHANICS AND MECHINERY UNIT I

CE FLUID MECHANICS AND MECHINERY UNIT I CE 6451- FLUID MECHANICS AND MECHINERY UNIT I 1. Define specific volume of a fluid and write its unit. [N/D-14] Volume per unit mass of a fluid is called specific volume. Unit: m3 / kg. 2. Name the devices

More information

Chapter -6(Section-1) Surface Tension

Chapter -6(Section-1) Surface Tension Chapter -6(Section-1) Surface Tension Free surface of the liquid tends to minimize the surface area. e.g.(1)if the small quantity of mercury is allowed to fall on the floor, it converted in to small spherical

More information

What s important: viscosity Poiseuille's law Stokes' law Demo: dissipation in flow through a tube

What s important: viscosity Poiseuille's law Stokes' law Demo: dissipation in flow through a tube PHYS 101 Lecture 29x - Viscosity 29x - 1 Lecture 29x Viscosity (extended version) What s important: viscosity Poiseuille's law Stokes' law Demo: dissipation in flow through a tube Viscosity We introduced

More information

5 ENERGY EQUATION OF FLUID MOTION

5 ENERGY EQUATION OF FLUID MOTION 5 ENERGY EQUATION OF FLUID MOTION 5.1 Introduction In order to develop the equations that describe a flow, it is assumed that fluids are subject to certain fundamental laws of physics. The pertinent laws

More information

Hydraulics for Urban Storm Drainage

Hydraulics for Urban Storm Drainage Urban Hydraulics Hydraulics for Urban Storm Drainage Learning objectives: understanding of basic concepts of fluid flow and how to analyze conduit flows, free surface flows. to analyze, hydrostatic pressure

More information

Table of Contents. Preface... xiii

Table of Contents. Preface... xiii Preface... xiii PART I. ELEMENTS IN FLUID MECHANICS... 1 Chapter 1. Local Equations of Fluid Mechanics... 3 1.1. Forces, stress tensor, and pressure... 4 1.2. Navier Stokes equations in Cartesian coordinates...

More information

Lecturer, Department t of Mechanical Engineering, SVMIT, Bharuch

Lecturer, Department t of Mechanical Engineering, SVMIT, Bharuch Fluid Mechanics By Ashish J. Modi Lecturer, Department t of Mechanical Engineering, i SVMIT, Bharuch Review of fundamentals Properties of Fluids Introduction Any characteristic of a system is called a

More information

Subject-wise Tests. Tests will be activated at 6:00 pm on scheduled day

Subject-wise Tests. Tests will be activated at 6:00 pm on scheduled day Subject-wise Tests Tests will be activated at 6:00 pm on scheduled day Test No Test-01 Test-02 SM-1 Economic development in India since independence with emphasis on Andhra Pradesh + Science & Technology

More information

Fluid Engineering Mechanics

Fluid Engineering Mechanics Fluid Engineering Mechanics Chapter Fluid Properties: Density, specific volume, specific weight, specific gravity, compressibility, viscosity, measurement of viscosity, Newton's equation of viscosity,

More information

Reference : McCabe, W.L. Smith J.C. & Harriett P., Unit Operations of Chemical

Reference : McCabe, W.L. Smith J.C. & Harriett P., Unit Operations of Chemical 1 Course materials (References) Textbook: Welty J. R., Wicks, C. E., Wilson, R. E., & Rorrer, G., Fundamentals of Momentum Heat, and Mass Transfer, 4th Edition, John Wiley & Sons.2000 Reference : McCabe,

More information

Dr. S. Ramachandran Prof. R. Devaraj. Mr. YVS. Karthick AIR WALK PUBLICATIONS

Dr. S. Ramachandran Prof. R. Devaraj. Mr. YVS. Karthick AIR WALK PUBLICATIONS Fluid Machinery As per Revised Syllabus of Leading Universities including APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY Dr. S. Ramachandran Prof. R. Devaraj Professors School of Mechanical Engineering Sathyabama

More information

BACHELOR OF TECHNOLOGY IN MECHANICAL ENGINEERING (COMPUTER INTEGRATED MANUFACTURING)

BACHELOR OF TECHNOLOGY IN MECHANICAL ENGINEERING (COMPUTER INTEGRATED MANUFACTURING) No. of Printed Pages : 6 BME-028 BACHELOR OF TECHNOLOGY IN MECHANICAL ENGINEERING (COMPUTER INTEGRATED MANUFACTURING) Term-End Examination December, 2011 00792 BME-028 : FLUID MECHANICS Time : 3 hours

More information

General Physics I (aka PHYS 2013)

General Physics I (aka PHYS 2013) General Physics I (aka PHYS 2013) PROF. VANCHURIN (AKA VITALY) University of Minnesota, Duluth (aka UMD) OUTLINE CHAPTER 12 CHAPTER 19 REVIEW CHAPTER 12: FLUID MECHANICS Section 12.1: Density Section 12.2:

More information