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  • MECHANICAL FLUID MECHANICS

    1 | P a g e THE GATE COACH All Rights Reserved 28, Jia Sarai N.Delhi-16, 26528213,-9998

  • MECHANICAL FLUID MECHANICS

    2 | P a g e THE GATE COACH All Rights Reserved 28, Jia Sarai N.Delhi-16, 26528213,-9998

    FLUID MECHANICS

    &

    HYDRAULIC MACHINES

    CONTENTS

    1 INTRODUCTION TO FLUIDS

    Solid, Liquid and Gases 6

    Concept of continuum 9

    Mass density, specific weight, and specific

    gravity

    9

    Compressibility and bulk modulus 12

    Viscosity 14

    Surface tension and capillarity 19

    Capillary or meniscus effect 24

    Vapour pressure 26

    Newtonian and Non-Newtonian fluids 28

    2 PRESSURE AND ITS MEASUREMENT

    Pressure and its relationship with height 40

    Pascals law 40

    Pressure density height relationship: hydrostatic

    law

    42

    Manometers 46

    Simple manometers 47

    Differential manometers 53

    3 HYDROSTATIC FORCES ON

    Force on a horizontal submerged plane surface 55

    Force on a vertical plane submerged surface 56

    Force on an inclines submerged plane surface 58

    Force on curved submerged surfaces 60

    Pressure Diagram 62

  • MECHANICAL FLUID MECHANICS

    3 | P a g e THE GATE COACH All Rights Reserved 28, Jia Sarai N.Delhi-16, 26528213,-9998

    SUBMERGED BODIES

    4 BUOYANCY AND FLOATATION

    Archimedes principle 74

    Principle of floatation 75

    Equilibrium of a floating body 76

    Metacentric height 80

    Oscillation of a floating body 81

    5 LIQUIDS IN RELATIVE EQUILIBRIUM

    Liquid in a container subjected to uniform acceleration in the horizontal direction

    88

    Liquid in a container subjected to uniform acceleration in the vertical direction

    89

    Liquid in a container subjected to uniform acceleration along inclined plane

    91

    Liquid in a container subjected to constant rotation 92

    6 FLUID KINEMATICS

    Fluid flow 97

    Classification of fluid flow 98

    Streamlines, Path lines, Streak lines 107

    Flow rate and Continuity Equation 109

    Differential equation of continuity 110

    Rotational Flow 111

    Stream function 114

    Potential function 117

    Circulation 121

    7 FLUID DYNAMICS

    Eulers equation along a straight line 126

    Eulers equation in Cartesian coordinate 129

    Bernoullis theorem 130

    Kinetic energy correction factor 134

    Venturi meter 135

    Orifice meter 137

  • MECHANICAL FLUID MECHANICS

    4 | P a g e THE GATE COACH All Rights Reserved 28, Jia Sarai N.Delhi-16, 26528213,-9998

    Pitot tube 137

    8 LAMINAR AND VISCOUS FLOW

    Navier Stokes equation 142

    Relationship between pressure gradient and shear stress 143

    Laminar flow between parallel stationary plates 144

    Laminar flow between parallel plates having relative motion

    147

    Laminar flow in circular pipes 150

    9 LAMINAR AND VISCOUS FLOW

    Introduction 159

    Flow losses in pipe 160

    Darcy Equation 161

    Minor Head Loss 164

    Pipes in series and parallel 169

    Concept of equivalent pipe 170

    Hydraulic gradient lines and total energy lines 171

    10 DIMENSIONAL ANALYSIS

    Reyleigh Method 178

    Buckingham pi-theorem 178

    Model Analysis 180

    Dimensionless No. 182

    11 Boundary Layer theory 186

    Boundary layer theory over a smooth plate 186

    Drag force on a flat plate 189

  • MECHANICAL FLUID MECHANICS

    5 | P a g e THE GATE COACH All Rights Reserved 28, Jia Sarai N.Delhi-16, 26528213,-9998

    BOUNDARY LAYER FLOW

    Thermal boundary layer 191

    Separation Boundary layer 192

    12 NOTCHES AND WEIRS

    Introduction 193

    Geometry of flow motion 194

    Discharge over a rectangular weir 197

    Discharge over a submerged rectangular weir 199

    Discharge over a broad weir 200

    Discharge over a triangular weir or V-notch 201

    Discharge over a trapezoidal weir 202

    13 FLOW THROUGH ORIFICE AND MOUTHPIECES

    Introduction 204

    Hydraulic coefficient 205

    Discharge through a sharp edged large orifice 207

    Discharge through a submerged orifice 208

    Discharge through a partially submerged orifice 209

    Flow through external cylindrical mouthpiece 210

    Flow through re-entrant 211

    14 OPEN CHANNEL FLOW

    Related terms 216

    Classification 218

    The Chezy Equation 218

    Economic section for maximum discharge 220

    Most economical rectangular section 220

    Most economical trapezoidal section 221

    Most economical circular section 224

    15 IMPACT OF FREE JETS

    Impulse momentum theorem 229

    Jet striking a stationary flat plate 230

    Jet striking a stationary flat plate inclined at an angle 231

    Jet striking a moving straight plate 232

    Jet striking a moving straight plate inclined at an angle 234

    Jet striking at centre of stationary vane 235

    Jet striking at centre of moving vane 236

    Jet striking stationary vane tangentially at one tip 238

    Jet striking moving vane tangentially at one tip 239

  • MECHANICAL FLUID MECHANICS

    6 | P a g e THE GATE COACH All Rights Reserved 28, Jia Sarai N.Delhi-16, 26528213,-9998

    16 HYDRAULIC TURBINE

    Impulse and reaction turbine 243

    Pelton turbine 244

    Head , power and efficiency 248

    Design aspects of Pelton Wheel 250

    Radial flow impulse turbine 252

    Francis turbine 255

    Propeller and Kaplan turbine 259

    Model Relationships 265

    17 HYDRAULIC PUMP

    Classification 273

    Centrifugal pump 273

    Velocity diagram 276

    Pump losses and efficiency 280

    Pressure rise in impeller 282

    Priming 285

    Axial flow pump 286

    Reciprocating pumps 287

    18 HYDRAULIC SYSTEMS

    Hydraulic accumulator 296

    Torque convertor 297

    Hydraulic Ram 297

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    7 | P a g e THE GATE COACH All Rights Reserved 28, Jia Sarai N.Delhi-16, 26528213,-9998

    1. BUOYANCY AND FLOATATION

    ARCHIMEDES PRINCIPLE

    Fluid exerts pressure on the surfaces of a body which is either partially or completely

    submerged into it.

    We consider a potato shaped irregular body ABCD (fig.) completely submerged in

    a fluid at rest. The body may be of any size, shape and weight distribution.

    The body consider is acted upon by two system of forces:

    I. A downward gravitational force due to weight of the body; this body force acts through the centre of mass or centre of gravity of the body.

    II. An external pressure force acting all around the surface of the body.

    Horizontal force

  • MECHANICAL FLUID MECHANICS

    8 | P a g e THE GATE COACH All Rights Reserved 28, Jia Sarai N.Delhi-16, 26528213,-9998

    A horizontal component of force equal to the force on a horizontal projection into a

    vertical plane. We consider any vertical plane drawn through the body.

    The projected areas of the two sections ABD and BCD of the body onto a vertical plane

    are equal.

    Consequently the horizontal forces on these two surfaces are equal and opposite, and so the net horizontal force is zero.

    Vertical force

    A vertical component of force equal to the weight of the fluid vertically above the curved

    surface.

    For the submerged body under consideration, a vertically downward force F1 acting on

    the upper surface equals the weight of volume of fluid ABCEF.

    Likewise, a vertically upward force F2 acting on the lower surface equals the weight of volume of fluid ADCEF.

    Buoyant force

    A body submerged in a fluid experience an upward thrust due to fluid pressure. This force is called buoyant force;

    Buoyancy

    The tendency of the body to be lifted upward in a fluid due to buoyant force is called buoyancy.

    Centre of Buoyancy

    The line of action of the buoyant force is vertical and passes through the centre of gravity

    of the displaced fluid, i.e. the centroid of the displaced volume. This centroid of the displaced fluid volume is called the centre of buoyancy.

  • MECHANICAL FLUID MECHANICS

    9 | P a g e THE GATE COACH All Rights Reserved 28, Jia Sarai N.Delhi-16, 26528213,-9998

    Depending on the ratio of the weight W of a body and the buoyant force Fb, three cases

    are possible:

    W>Fb; the body tends to move downwards and eventually sinks W=Fb; the body floats and is only partially submerged W

  • MECHANICAL FLUID MECHANICS

    10 | P a g e THE GATE COACH All Rights Reserved 28, Jia Sarai N.Delhi-16, 26528213,-9998

    NEUTRAL EQUILIBRIUM

    The body remains at rest in any position to which it may be displaced. No net force tends

    to return the body to its original state or to drive it further away from the original

    condition.

    SUBMERGED BODY

    Stability of a submerged body is determined by the location of centre of gravity G with respect to centroid of the displaced volume, i.e., the centre of buoyancy B.

    Stable: G is located below B

    Neutral: G is located at B

    Unstable: G is located above B

    Stable configuration of an aerostatic balloon

    The aerostatic balloon considered above will be in unstable when placed in the title

    position. When displaced from the position, it will return to original position.

    Likewise a system comprising a ship with a small hull and a tall mast which is very heavily weighed at the top