A Textbook of Fluid Mechanics and Hydraulic Machines

A Textbook of Fluid Mechanics and Hydraulic Machines
in SI UNITS
Er. R.K. RAJPUT
M.E. (Hons.), Gold Medallist; Grad. (Mech.Engg. & Elect. Engg.); M.I.E. (India);
M.S.E.S.I.; M.I.S.T.E.; C.E. (India)
Recipient of:
‘‘Best Teacher (Academic) Award’’
‘‘Distinguished Author Award’’
“Jawahar Lal Nehru Memorial Gold Medal’’
for an outstanding research paper
(Institution of Engineers–India)
Principal (Formerly):
 Thapar Polytechnic College;
 Punjab College of Information Technology
NOMENCLATURE
a Acceleration
A Area
A
s Area of suction pipe, surge tank
A
d Area of delivery pipe
B Width of wheel (turbine)
b Width, bed width of rectangular or trapezoidal channel
c
p
Specific heat at constant pressure
CP Centipoise
C
v Specific heat at constant volume
C Chezy’s discharge coefficient
C Celerity of a pressure wave
C
c
Coefficient of contraction
C
d Discharge coefficient of weirs, orifice plates
C
D Drag coefficient
C
D Local drag coefficient
C
v Coefficient of velocity
d Diameter of orifice plate, pipe, particle
D Diameter of pipe, wheel
d
d Diameter of delivery pipe
d
s Diameter of suction pipe
e Linear strain
E Young’s modulus of elasticity of material
f Darcy Weisbach friction coefficient, frequency
F Force
F
B Force exerted by boundary on the fluid
F
D Drag force on the body
F
L Lift force
F
r
Froude number
g Gravitational acceleration
h Piezometric head, specific enthalpy
h
d Delivery head
h
f Frictional loss of head
h
s
Suction head
H
g
Gross head
H Total energy head, net head
h
ad Acceleration head for delivery pipe
h
as Acceleration head for suction pipe
I Moment of inertia (of area), moment of inertia (of mass)
l
d Length of delivery pipe
l
s Length of suction pipe
l
d´ Length of delivery pipe between cylinder to air vessel
l
s
´ Length of suction pipe between cylinder and air vessel
k Roughness height
K Conveyance
K Head loss coefficient, bulk modulus of elasticity, blade friction coefficient
Kt
Vane thickness factor
Ku
Speed ratio
K
f Flow ratio
m Mass
M Momentum, Mach number
n ratio B/D
N Manning’s roughness coefficient, revolutions per minute
N
s Specific speed
p, ps Pressure, stagnation pressure
P Power, shaft power (turbine), Poise, force
q Discharge per unit width, discharge per jet
Q Discharge, heat
r Distance from the centre
R Radius of pipe, hydraulic radius, radius of pipe bend
R
o Universal gas constant
Re Reynolds number
S Specific gravity, bed slope of channel
t Thickness, time
T Absolute temperature in Kelvins
T Torque, water surface width
u Instantaneous velocity at a point in X-direction
u
f Shear friction velocity
U Free stream velocity
V
d Velocity of flow in delivery pipe
V Velocity of flow in the cylinder
V
s Velocity of flow in suction pipe
v Instantaneous velocity at a point in Y-direction
v Specific volume
v
c Critical velocity
Va
Velocity of approach
v Time averaged velocity at a point in Y-direction
Vr
Relative velocity
V
f Velocity of flow (in turbines and pumps)
V
w Velocity of swirl (in turbines and pumps)
V Volume
w Weight density, Instantaneous velocity at a point in Z-direction
W Weight of fluid, workdone
x Distance in X-direction
y Distance in Y-direction, depth of flow
yc Critical depth
x– Depth of centroid of area below water surface
Z Number of buckets/vanes
z elevation
Greek Notations
α Energy correction factor, Mach angle, angle
β Momentum correction factor, angle
γ Ratio of specific heats
δ Boundary layer thickness
δ´ Laminar sub-layer thickness
δ Displacement thickness of boundary layer
*∆s Change in entropy
η Efficiency, dimensionless distance (y/δ)
θ Angle, momentum thickness of boundary layer
µ Coefficient of dynamic viscosity
ν Kinematic viscosity
ρ Mass density of fluid
σ Coefficient of surface tension, cavitation number (Thoma number)
τ Shear stress
τ
0 Bottom shear stress
φ Angle, velocity potential
ψ Stream function
ω Angular velocity
Γ Circulation
Ω Vorticity
Subscript 0 refer to any quantity at reference section
Subscripts 1, 2 refer to any quantity at section 1 or 2
Subscripts x, y, z refer to any quantity in x, y, z direction
Subscripts m, p refer to any quantity in model and prototype
Subscript r refer to the ratio of any quantity in model to that in prototype
CONTENTS
PART – I
FLUID MECHANICS

1. PROPERTIES OF FLUIDS 1–42
   1.1. Introduction 1
   1.2. Fluid 2
   1.3. Liquids and their Properties 3
   1.4. Density 3
   1.4.1. Mass density 3
   1.4.2. Weight density 3
   1.4.3. Specific volume 3
   1.5. Specific Gravity 3
   1.6. Viscosity 4
   1.6.1. Newton’s law of viscosity 5
   1.6.2. Types of fluids 5
   1.6.3. Effect of temperature on viscosity 8
   1.6.4. Effect of pressure on viscosity 8
   1.7. Thermodynamic Properties 23
   1.8. Surface Tension and Capillarity 25
   1.8.1. Surface tension 25
   1.8.1.1. Pressure inside a water droplet, soap bubble
   and a liquid jet 26
   1.8.2. Capillarity 28
   1.9. Compressibility and Bulk Modulus 34
   1.10. Vapour Pressure 37
   Highlights 39
   Objective Type Questions 40
   Theoretical Questions 41
   Unsolved Examples 41
2. PRESSURE MEASUREMENT 43—96
   2.1. Pressure of a Liquid 43
   2.2. Pressure Head of a Liquid 43
   2.3. Pascal’s Law 45
   2.4. Absolute and Gauge Pressures 48
   2.5. Measurement of Pressure 53
   2.5.1. Manometers 54
   2.5.1.1. Simple manometers 54
   2.5.1.2. Differential manometers 63
   2.5.1.3. Advantages and limitations of manometers 81
   2.5.2. Mechanical gauges 812.6. Pressure at a Point in Compressible Fluid 83
   Highlights 91
   Objective Type Questions 92
   Theoretical Questions 93
   Unsolved Examples 93
3. HYDROSTATIC FORCES ON SURFACES 97—159
   3.1. Introduction 97
   3.2. Total Pressure and Centre of Pressure 97
   3.3. Horizontally Immersed Surface 97
   3.4. Vertically Immersed Surface 98
   3.5. Inclined Immersed Surface 116
   3.6. Curved Immersed Surface 129
   3.7. Dams 140
   3.8. Possibilities of Dam Failure 142
   3.9. Lock Gates 151
   Highlights 155
   Objective Type Questions 156
   Theoretical Questions 157
   Unsolved Examples 157
4. BUOYANCY AND FLOATATION 160—191
   4.1. Buoyancy 160
   4.2. Centre of Buoyancy 160
   4.2. Types of Equilibrium of Floating Bodies 165
   4.3.1. Stable equilibrium 165
   4.3.2. Unstable equilibrium 165
   4.3.3. Neutral equilibrium 165
   4.4. Metacentre and Metacentric Height 165
   4.5. Determination of Metacentric Height 166
   4.5.1. Analytical method 166
   4.5.2. Experimental method 167
   4.6. Oscillation (Rolling of a Floating Body) 187
   Highlights 189
   Objective Type Questions 189
   Theoretical Questions 190
   Unsolved Examples 190
5. FLUID KINEMATICS 192—258
   5.1. Introduction 192
   5.2. Description of Fluid Motion 192
   5.2.1. Langrangian method 192
   5.2.2. Eulerian method 193
   5.3. Types of Fluid Flow 195 5.3.1. Steady and unsteady flows 195
   5.3.2. Uniform and non-uniform flows 196
   5.3.3. One, two and three dimensional flows 196
   5.3.4. Rotational and irrotational flows 197
   5.3.5. Laminar and turbulent flows 197
   5.3.6. Compressible and incompressible flows 197
   5.4. Types of Flow Lines 198
   5.4.1. Path line 198
   5.4.2. Stream line 198
   5.4.3. Stream tube 198
   5.4.4. Streak line 199
   5.5. Rate of Flow or Discharge 207
   5.6. Continuity Equation 207
   5.7. Continuity Equation in Cartesian Co-ordinates 209
   5.8. Equation of Continuity in Polar Coordinates 211
   5.9. Circulation and Vorticity 218
   5.10. Velocity Potential and Stream Function 227
   5.10.1. Velocity potential 227
   5.10.2. Stream function 228
   5.10.3. Relation between stream function and velocity potential 231
   5.11. Flow Nets 231
   5.11.1. Methods of drawing flow nets 231
   5.11.2. Uses and limitations of flow nets 232
   Highlights 253
   Objective Type Questions 255
   Theoretical Questions 257
   Unsolved Examples 257
6. FLUID DYNAMICS 259—385
   6.1. Introduction 259
   6.2. Different Types of Heads (or Energies) of a Liquid in Motion 259
   6.3. Bernoulli’s Equation 260
   6.4. Euler’s Equation for Motion 262
   6.5. Bernoulli’s Equation for Real Fluid 276
   6.6. Practical Applications of Bernoulli’s Equation 291
   6.6.1. Venturimeter 291
   6.6.1.1. Horizontal venturimeters 292
   6.6.1.2. Vertical and inclined venturimeters 298
   6.6.2. Orificemeter 303
   6.6.3. Rotameter and elbow meter 308
   6.6.3.1. Rotameter 308
   6.6.3.2. Elbow meter 309
   6.6.4. Pitot Tube 3106.7. Free Liquid Jet 313
   6.8. Impulse-Momentum Equation 320
   6.9. Kinetic Energy and Momentum Correction Factors (Coriolis Co-efficients) 336
   6.10. Moment of Momentum Equation 343
   6.11. Vortex Motion 345
   6.11.1. Forced vortex flow 345
   6.11.2. Free vortex flow 346
   6.11.3. Equation of motion for vortex flow 346
   6.11.4. Equation of forced vortex flow 347
   6.11.5. Rotation of liquid in a closed cylindrical vessel 354
   6.11.6. Equation of free vortex flow 361
   6.12. Liquids in Relative Equilibrium 364
   6.12.1. Liquid in a container subjected to uniform acceleration in the
   horizontal direction 364
   6.12.2. Liquid in a container subjected to uniform acceleration in the
   vertical direction 373
   6.12.3. Liquid in container subjected to uniform acceleation along
   inclined plane 375
   Highlights 376
   Objective Type Questions 379
   Theoretical Questions 381
   Unsolved Examples 382
7. DIMENSIONAL AND MODEL ANALYSIS 386—456
   DIMENSIONAL ANALYSIS
   7.1. Dimensional Analysis—Introduction 386
   7.2. Dimensions 387
   7.3. Dimensional Homogeneity 389
   7.4. Methods of Dimensional Analysis 390
   7.4.1. Rayleigh’s method 390
   7.4.2. Buckingham’s π-method/theorem 394
   7.4.3. Limitations of dimensional analysis 415
   MODEL ANALYSIS
   7.5. Model Analysis—Introduction 415
   7.6. Similitude 416
   7.7. Forces Influencing Hydraulic Phenomena 417
   7.8. Dimensionless Numbers and their Significance 418
   7.8.1. Reynolds number (Re) 418
   7.8.2. Froude’s number (Fr ) 419
   7.8.3. Euler’s number (Eu) 419
   7.8.4. Weber number (We) 419
   7.8.5. Mach number (M ) 420
   7.9. Model (or Similarity) Laws 420
   7.10. Reynolds Model Law 4207.11. Froude Model Law 434
   7.12. Euler Model Law 445
   7.13. Weber Model Law 446
   7.14. Mach Model Law 447
   7.15. Types of Models 449
   7.15.1. Undistorted models 449
   7.15.2. Distorted models 449
   7.16. Scale Effect in Models 450
   7.17. Limitations of Hydraulic Similitude 451
   Highlights 451
   Objective Type Questions 453
   Theoretical Questions 454
   Unsolved Examples 454
8. FLOW THROUGH ORIFICES AND MOUTHPIECES 457—507
   8.1. Introduction 457
   8.2. Classification of Orifices 457
   8.3. Flow Through an Orifice 458
   8.4. Hydraulic Co-efficients 458
   8.4.1. Co-efficient of contraction (Cc) 458
   8.4.2. Co-efficient of velocity (Cv) 459
   8.4.3. Co-efficient of discharge 459
   8.4.4. Co-efficient of resistance (Cr) 459
   8.4. Experimental Determination of Hydraulic Co-efficients 460
   8.5.1. Determination of co-efficient of velocity (Cv). 460
   8.5.2. Determination of co-efficient of discharge (Cd) 461
   8.5.3. Determination of co-efficient of contraction (Cc) 462
   8.5.4. Loss of head in orifice flow 462
   8.6. Discharge Through a Large Rectangular Orifice 470
   8.7. Discharge Through Fully Submerged Orifice 472
   8.8. Discharge Through Partially Submerged Orifice 473
   8.9. Time Required for Emptying a Tank Through an Orifice at its Bottom 474
   8.10. Time Required for Emptying a Hemispherical Tank 483
   8.11. Time Required for Emptying a Circular Horizontal Tank 487
   8.12. Classification of Mouthpieces 490
   8.13. Discharge Through an External Mouthpiece 490
   8.14. Discharge Through a Convergent-divergent Mouthpiece 493
   8.15. Discharge Through an Internal Mouthpiece (or Re-entrant or Borda’s
   Mouthpiece) 496
   8.15.1. Mouthpiece running free 496
   8.15.2. Mouthpiece running full 497
   Highlights 503
   Objective Type Questions 505Theoretical Questions 506
   Unsolved Examples 506
9. FLOW OVER NOTCHES AND WEIRS 508—533
   9.1. Definitions 508
   9.2. Types/Classification of Notches and Weirs 508
   9·2·1. Types of notches 508
   9·2·2. Types of weirs 509
   9.3. Discharge Over a Rectangular Notch or Weir 509
   9.4. Discharge Over a Triangular Notch or Weir 511
   9.5. Discharge Over a Trapezoidal Notch or Weir 513
   9.6. Discharge Over a Stepped Notch 514
   9.7. Effect on Discharge Over a Notch or Weir due to Error in the
   Measurement of Head 516
   9.8. Velocity of Approach 518
   9.9. Empirical Formulae for Discharge Over Rectangular Weir 518
   9.10. Cippoletti Weir or Notch 521
   9.11. Discharge Over a Broad Crested Weir 522
   9.12. Discharge Over a Narrow-crested Weir 523
   9.13. Discharge Over an Ogee Weir 523
   9.14. Discharge Over Submerged or Drowned Weir 523
   9.15. Time Required to empty a Reservoir or a Tank with Rectangular and Triangular
   Weirs or Notches 526
   Highlights 528
   Objective Type Questions 530
   Theoretical Questions 532
   Unsolved Examples 533
10. LAMINAR FLOW 534—604
    10.1. Introduction 534
    10.2. Reynolds Experiment 535
    10.3. Navier-Stokes Equations of Motion 537
    10.4. Relationship between Shear Stress and Pressure Gradient 540
    10.5. Flow of Viscous Fluid in Circular Pipes—Hagen Poiseuille Law 541
    10.6. Flow of Viscous Fluid through an Annulus 567
    10.7. Flow of Viscous Fluid Between Two Parallel Plates 570
    10.7.1. One plate moving and other at rest—couette flow 570
    10.7.2. Both plates at rest 572
    10.7.3. Both plates moving in opposite directions 572
    10.8. Laminar Flow through Porous Media 582
    10.9. Power Absorbed in Bearings 583
    10.9.1. Journal bearing 58310.9.2. Foot-step bearing 585
    10.9.3. Collar bearing 586
    10.10. Loss of Head due to Friction in Viscous flow 587
    10.11. Movement of Piston in Dashpot 589
    10.12. Measurement of Viscosity 591
    10.12.1. Rotating cylinder method 591
    10.12.2. Falling sphere method 594
    10.12.3. Capillary tube method 595
    10.12.4. Efflux Viscometers 597
    Highlights 597
    Objective Type Questions 601
    Theoretical Questions 602
    Unsolved Examples 602
11. TURBULENT FLOW IN PIPES 605—637
    11.1. Introduction 605
    11.2. Loss of Head due to Friction in Pipe Flow–Darcy Equation 606
    11.3. Characteristics of Turbulent Flow 608
    11.4. Shear Stresses in Turbulent Flow 609
    11·4·1. Boussinesq’s theory 609
    11·4·2. Reynolds theory 610
    11·4·3. Prandtl’s mixing length theory 610
    11.5. Universal Velocity Distribution Equation 610
    11.6. Hydrodynamically Smooth and Rough Boundaries 612
    11·6·1. Velocity distribution for turbulent flow in smooth pipes 613
    11·6·2. Velocity distribution for turbulent flow in rough pipes 615
    11.7. Common Equation for Velocity Distribution for both Smooth
    and Rough Pipes 618
    11.8. Velocity Distribution for Turbulent Flow in Smooth Pipes by Power Law 620
    11.9. Resistance to Flow of Fluid in Smooth and Rough Pipes 621
    Highlights 633
    Objective Type Questions 635
    Theoretical Questions 636
    Unsolved Examples 637
12. FLOW THROUGH PIPES 638—724
    12.1. Introduction 638
    12.2. Loss of Energy (or Head) in Pipes 638
    12.3. Major Energy Losses 638
    12·3·1. Darcy-weisbach formula 639
    12·3·2. Chezy’s formula for loss of head due to friction 639
    12.4. Minor Energy Losses 64512·4·1. Loss of head due to sudden enlargement 645
    12·4·2. Loss of head due to sudden contraction 652
    12·4·3. Loss of head due to obstruction in pipe 656
    12·4·4. Loss of head at the entrance to pipe 657
    12·4·5. Loss of head at the exit of a pipe 657
    12·4·6. Loss of head due to bend in the pipe 657
    12·4·7. Loss of head in various Pipe Fittings 657
    12.5. Hydraulic Gradient and Total Energy Lines 657
    12.6. Pipes in Series or Compound Pipes 668
    12.7. Equivalent Pipe 671
    12.8. Pipes in Parallel 674
    12.9. Syphon 699
    12.10. Power Transmission through Pipes 703
    12.11. Flow through Nozzle at the End of a Pipe 706
    12·11·1. Power transmitted through the nozzle 707
    12·11·2. Condition for transmission of maximum power through nozzle 707
    12·11·3. Diameter of the nozzle for transmitting maximum power 708
    12.12. Water Hammer in Pipes 711
    12·12·1. Gradual closure of valve 711
    12·12·2. Instantaneous closure of valve in rigid pipes 712
    12·12·3. Instantaneous closure of valve in elastic pipes 713
    12·12·4. Time required by pressure wave to travel from the valve to the tank
    and from tank to valve 714
    Highlights 716
    Objective Type Questions 719
    Theoretical Questions 721
    Unsolved Examples 721
13. BOUNDARY LAYER THEORY 725—784
    13.1. Introduction 725
    13.2. Boundary Layer Definitions and Characteristics 726
    13.2.1. Boundary layer thickness (δ) 727
    13.2.2. Displacement thickness (δ*) 727
    13.2.3. Momentum thickness (θ) 728
    13.2.4. Energy thickness (δe) 729
    13.3. Momentum Equation for Boundary Layer by Von Karman 739
    13.4. Laminar Boundary Layer 742
    13.5. Turbulent Boundary Layer 766
    13.6. Total Drag due to Laminar and Turbulent Layers 769
    13.7. Boundary Layer Separation and its Control 774
    Highlights 778
    Objective Type Questions 780
    Theoretical Questions 782
    Unsolved Examples 78214. FLOW AROUND SUBMERGED BODIES—DRAG AND LIFT 785—824
    14.1. Introduction 785
    14.2. Force Exerted by a Flowing Fluid on a Body 785
    14.3. Expressions for Drag and Lift 786
    14.4. Dimensional Analysis of Drag and Lift 788
    14.5. Streamlined and Bluff Bodies 798
    14.6. Drag on a Sphere 798
    14.6.1. Terminal velocity of a body 799
    14.6.2. Applications of stokes’ law 800
    14.7. Drag on a Cylinder 804
    14.8. Circulation and Lift on a Circular Cylinder 804
    14.8.1. Flow patterns and development of lift 804
    14.8.2. Position of stagnation points 806
    14.8.3. Pressure at any point on the cylinder surface 807
    14.8.4. Expression for lift on cylinder (kutta- joukowski theorem) 807
    14.8.5. Expression for lift coefficient for rotating cylinder 809
    14.8.6. Magnus effect 810
    14.9. Lift on an Airfoil 815
    Highlights 818
    Objective Type Questions 820
    Theoretical Questions 822
    Unsolved Examples 823
14. COMPRESSIBLE FLOW 825—879
    15.1. Introduction 825
    15.2. Basic Thermodynamic Relations 825
    15.2.1. The characteristics equation of state 825
    15.2.2. Specific heats 826
    15.2.3. Internal energy 826
    15.2.4. Enthalpy 827
    15.2.5. Energy, work and heat 827
    15.3. Basic Thermodynamic Processes 827
    15.4. Basic Equations of Compressible Fluid Flow 829
    15.4.1. Continuity equation 829
    15.4.2. Momentum equation 829
    15.4.3. Bernoulli’s or energy equation 829
    15.5. Propagation of Disturbances in Fluid and Velocity of Sound 837
    15.5.1. Derivation of sonic velocity (velocity of sound) 837
    15.5.2. Sonic velocity in terms of bulk modulus 838
    15.5.3. Sonic velocity for isothermal process 839
    15.5.4 Sonic velocity for adiabatic process 839
    15.6. Mach Number 84015.7. Propagation of Disturbance in Compressible Fluid 841
    15.8. Stagnation Properties 844
    15.8.1. Expression for stagnation pressure (ps) in compressible flow 844
    15.8.2. Expression for stagnation density (ρs) 846
    15.8.3. Expression for stagnation temperature (Ts) 847
    15.9. Area-velocity Relationship and Effect of Variation of Area for Subsonic,
    Sonic and Supersonic Flows 850
    15.10. Flow of Compressible Fluid Through a Convergent Nozzle 852
    15.11. Variables of Flow in terms of Mach Number 857
    15.12. Flow Through Laval Nozzle (Convergent-Divergent Nozzle) 860
    15.13. Shock Waves 865
    15.13.1. Normal shock wave 866
    15.13.2. Oblique shock wave 868
    15.13.3. Shock strength 868
    15.14. Measurement of Compressible Flow 870
    15.15. Flow of Compressible Fluid Through Venturimeter 870
    Highlights 873
    Objective Type Questions 876
    Theoretical Questions 878
    Unsolved Examples 878
15. FLOW IN OPEN CHANNELS 880—958
    A. UNIFORM FLOW
    16.1. Introduction 880
    16.1.1. Definition of an open channel 880
    16.1.2. Comparison between open channel and pipe flow 880
    16.1.3. Types of channels 881
    16.2. Types of Flow in Channels 881
    16.2.1. Steady flow and unsteady flow 882
    16.2.2. Uniform and non-uniform (or varied) flow 882
    16.2.3. Laminar flow and turbulent flow 882
    16.2.4. Subcritical flow, critical flow and supercritical flow 882
    16.3. Definitions 883
    16.4. Open Channel Formulae for Uniform Flow 884
    16.4.1. Chezy’s formula 884
    16.5. Most Economical Section of a Channel 889
    16.5.1. Most economical rectangular channel section 890
    16.5.2. Most economical trapezoidal channel section 892
    16.5.3. Most economical triangular channel section 908
    16.5.4. Most economical circular channel section 910
    16.6. Open Channel Section for Constant Velocity at all Depths of Flow
    914B. NON-UNIFORM FLOW
    16.7. Non-uniform Flow Through Open Channels 917
    16.8. Specific Energy and Specific Energy Curve 917
    16.9. Hydraulic Jump or Standing Wave 923
    16.10. Gradually Varied Flow 938
    16.10.1. Equation of gradually varied flow 938
    16.10.2. Back water curve and afflux 940
    16.11. Measurement of Flow of Irregular Channels 948
    16.11.1. Area of flow 948
    16.11.2. Mean velocity of flow 948
    Highlights 951
    Objective Type Questions 954
    Theoretical Questions 956
    Unsolved Examples 957
16. UNIVERSITIES’ QUESTIONS (LATEST) WITH “SOLUTIONS” 959—994
    OBJECTIVE TYPE TEST QUESTIONS 995—1046PART – II
    HYDRAULIC MACHINES
17. IMPACT OF FREE JETS 1—51
    1.1. Introduction 1
    1.2. Force Exerted on a Stationary Flat Plate Held Normal to the Jet 1
    1.3. Force Exerted on a Stationary Flat Plate Held Inclined to the Jet 2
    1.4. Force Exerted on a Stationary Curved Plate 3
    1.5. Force Exerted on a Moving Flat Plate Held Normal to Jet 11
    1.6. Force Exerted on a Moving Plate Inclined to the Direction of Jet 12
    1.7. Force Exerted on a Curved Vane when the Plate Vane is Moving
    in the Direction of Jet 15
    1.8. Jet Striking a Moving Curved Vane Tangentially at One Tip and
    Leaving at the Other 22
    1.9. Jet Propulsion of Ships 40
    Highlights 48
    Objective Type Questions 49
    Theoretical Questions 50
    Unsolved Examples 50
18. HYDRAULIC TURBINES 52—176
    2.1. Introduction 52
    2.2. Classification of Hydraulic Turbines 53
    2.3. Impulse Turbines – Pelton Wheel 55
    2.3.1. Construction and working of Pelton wheel/ turbine 55
    2.3.2. Work done and efficiency of a Pelton wheel 57
    2.3.3. Definitions of heads and efficiencies 59
    2.3.4. Design aspects of Pelton wheel 61
    2.4. Reaction Turbines 81
    2.4.1. Francis turbine 81
    2.4.1.1. Work done and efficiencies of a Francis turbine 84
    2.4.1.2. Working proportions of a Francis turbine 85
    2.4.1.3. Design of a Francis turbine runner 86
    2.4.1.4. Advantages and disadvantages of Francis turbine over a
    Pelton wheel 87
    2.4.2. Propeller and Kaplan turbines—Axial flow reaction turbines 121
    2.4.2.1. Propeller turbine 122
    2.4.2.2. Kaplan turbine 122
    2.4.2.3. Kaplan turbine versus Francis turbine 124
    2.5. Deriaz Turbine 1292.6. Tubular or Bulb Turbines 130
    2.7. Runaway Speed 131
    2.8. Draft Tube 131
    2.8.1. Draft tube theory 132
    2.8.2. Types of draft tubes 133
    2.9. Specific Speed 138
    2.10. Unit Quantities 143
    2.11. Model Relationship 145
    2.12. Scale Effect 153
    2.13. Performance Characteristics of Hydraulic Turbines 154
    2.13.1. Main or constant head characteristic curves 154
    2.13.2. Operating or constant speed characteristic curves 156
    2.13.3. Constant efficiency or iso-efficiency or Muschel curves 157
    2.14. Governing of Hydraulic Turbines 157
    2.14.1. Governing of impulse turbines 157
    2.14.2. Governing of reaction turbines 158
    2.15. Cavitation 159
    2.16. Selection of Hydraulic Turbines 162
    2.17. Surge Tanks 164
    Highlights 166
    Objective Type Questions 169
    Theoretical Questions 171
    Unsolved Examples 172
19. CENTRIFUGAL PUMPS 177—247
    3.1. Introduction 177
    3.2. Classification of Pumps 177
    3.3. Advantages of Centrifugal Pump over Displacement (Reciprocating)
    Pump 178
    3.4. Component Parts of a Centrifugal Pump 179
    3.5. Working of a Centrifugal Pump 181
    3.6. Work done by the Impeller (or Centrifugal Pump) on Liquid 182
    3.7. Heads of a Pump 184
    3.8. Losses and Efficiencies of a Centrifugal Pump 186
    3.8.1. Losses in centrifugal pump 186
    3.8.2. Efficiencies of a centrifugal pump 186
    3.8.3. Effect of outlet vane angle on manometric efficiency 187
    3.9. Minimum Speed for Starting a Centrifugal Pump 217
    3.10. Effect of Variation of Discharge on the Efficiency 220
    3.11. Effect of Number of Vanes of Impeller on Head and efficiency
    2223.12. Working Proportions of Centrifugal Pumps 222
    3.13. Multi-stage Centrifugal Pumps 224
    3.13.1. Pumps in series 224
    3.13.2. Pumps in parallel 224
    3.14. Specific Speed 227
    3.15. Model Testing and Geometrically Similar Pumps 229
    3.16. Characteristics of Centrifugal Pumps 233
    3.17. Net Positive Suction Head (NPSH) 235
    3.18. Cavitation in Centrifugal Pumps 236
    3.19. Priming of a Centrifugal Pump 239
    3.20. Selection of Pumps 239
    3.21. Operational Difficulties in Centrifugal Pumps 240
    Highlights 241
    Objective Type Questions 243
    Theoretical Questions 245
    Unsolved Examples 246
20. RECIPROCATING PUMPS 248—287
    4.1. Introduction 248
    4.2. Classification of Reciprocating Pumps 248
    4.3. Main Components and Working of a Reciprocating Pump 249
    4.4. Discharge, Work Done and Power Required to Drive Reciprocating
    Pump 251
    4.4.1. Single-acting reciprocating pump 251
    4.4.2. Double-acting reciprocating pump 251
    4.5. Co-efficient of Discharge and Slip of Reciprocating Pump 252
    4.5.1. Co-efficient of discharge 252
    4.5.2. Slip 252
    4.6. Effect of Acceleration of Piston on Velocity and Pressure in the Suction
    and Delivery Pipes 256
    4.7. Indicator Diagrams 258
    4.7.1. Ideal indicator diagram 258
    4.7.2. Effect of acceleration in suction and delivery pipes on indicator
    diagram 259
    4.7.3. Effect of friction in suction and delivery pipes on indicator diagram 266
    4.7.4. Effect of acceleration and friction in suction and delivery pipes on
    indicator diagram 267
    4.8. Air Vessels 275
    Highlights 284
    Objective Type Questions 285Theoretical Questions 286
    Unsolved Examples 286
21. MISCELLANEOUS HYDRAULIC MACHINES 288—324
    5.1. Introduction 288
    5.2. Hydraulic Accumulator 288
    5.2.1. Simple hydraulic accumulator 288
    5.2.2. Differential hydraulic accumulator 289
    5.3. Hydraulic Intensifier 296
    5.4. Hydraulic Press 299
    5.5. Hydraulic Crane 303
    5.6. Hydraulic Lift 307
    5.7. Hydraulic Ram 310
    5.8. Hydraulic Coupling 317
    5.9. Hydraulic Torque Converter 318
    5.10. Air Lift Pump 320
    5.11. Jet Pump 320
    Highlights 321
    Objective Type Questions 322
    Theoretical Questions 323
    Unsolved Examples 324
22. WATER POWER DEVELOPMENT 325—358
    6.1. Hydrology 325
    6.1.1. Definition 325
    6.1.2. Hydrologic cycle 325
    6.1.3. Measurement of run-off 326
    6.1.4. Hydrograph 328
    6.1.5. Flow duration curve 329
    6.1.6. Mass curve 331
    6.2. Hydro-power Plant 335
    6.2.1. Introduction 335
    6.2.2. Application of hydro-electric power plants 335
    6.2.3. Advantages and disadvantages of hydro-electric power plants 336
    6.2.4. Average life of hydro-plant components 336
    6.2.5. Hydro-plant controls 337
    6.2.6. Safety measures in hydro-electric power plants 337
    6.2.7. Preventive maintenance to hydro-plant 338
    6.2.8. Calculation of available hydro-power 338
    6.2.9. Cost of hydro-power plant 3396.2.10. Hydro-power development in India 339
    6.2.11. Combined hydro and steam power plants 340
    6.2.12. Comparison of hydro-power station with thermal power station 341
    Highlights 356
    Theoretical Questions 357
    Unsolved Examples 358
23. FLUIDICS 359—370
    7.1. Introduction 359
    7.2. Advantages, Disadvantages and Applications of Fluidic Devices/Fluidics 360
    7.3. Fluidic (or Fluid Logic) Elements 361
    7.3.1. General aspects 361
    7.3.2. Coanda effect 361
    7.3.3. Classification of fluidic devices 362
    7.3.4. Fluid logic devices 363
    7.3.4.1. Bi-stable flip-flop 363
    7.3.4.2. AND gate 364
    7.3.4.3. OR-NOR gate 364
    7.3.5. Fluidic sensors 365
    7.3.5.1. Interruptible jet sensor 365
    7.3.5.2. Reflex sensor 366
    7.3.5.3. Back pressure sensor 366
    7.3.6. Fluidic amplifiers 366
    7.3.6.1. Turbulence amplifier 367
    7.3.6.2. Vortex amplifier 367
    7.4. Comparison Among Different Switching Elements 368
    Highlights 369
    Objective Type Questions 369
    Theoretical Questions 370
24. UNIVERSITIES’ QUESTIONS (LATEST) WITH “SOLUTIONS” 371—401
    OBJECTIVE TYPE TEST QUESTIONS 403—416
    LABORATORY PRACTICALS (Experiments: 1–26) 1—64
    Index i—viiiINDEX
    A
    Afflux, 940
    B
    Back water curve, 940
    length of, 940
    Bernoulli’s equation, 260
    for real fluid, 276
    practical applications of, 291
    – orificemeter, 303
    – pitot tube, 310
    – venturimeter, 291
    Bluff body, 798
    Boundary layer definitions, 726
    – boundary layer thickness, 727
    – displacement thickness, 727
    – energy thickness, 729
    – momentum thickness, 728
    Boundary layer separation, 774
    Buckingham’s π-method, 394
    Buoyancy, 160
    centre of, 160
    C
    Capillarity, 28
    Centre of pressure, 97
    Chezy’s formula, 639, 884
    Circulation and vorticity, 218
    Circulation, 804
    Compressibility and bulk modulus, 34
    Compound pipes, 608
    Compressible fluid flow, 825
    basic equations of, 829
    – continuity equation, 829
    – energy equation, 829
    – momentum equation, 829
    propagation of disturbances in, 837
    through a convergent nozzle, 852
    through a convergent-divergent nozzle, 860
    measurement of, 870
    through a venturimeter, 870
    Continuity equation, 207
    in cartesian co-ordinates, 209
    in polar co-ordinates, 211
    Coriolis co-efficients, 336
    Couette flow, 570
    Critical depth, 906
    Curved immersed surface, 129
    D
    Dams, 140
    possibility of dam failure, 142
    Darcy equation, 606, 639
    Density, 3
    – mass density, 3
    – weight density, 3
    Dimensional analysis, 386
    introduction to, 386
    methods of, 390
    Dimensions, 387
    Dimensional homogeneity, 389
    Dimensionless numbers, 418
    Discharge, 207
    Displacement thickness, 727
    Drag and lift, 785
    Drag on a sphere, 798
    Drag of a cylinder, 804
    E
    Efflux viscometers, 594
    Elbow meter, 309
    Energy thickness, 729
    Equivalent pipe, 671
    Eulerian method, 193
    Euler’s equation, 262
    Euler’s number, 419
    FLUID MECHANICSii Index
    F
    Falling sphere method, 594
    Fluid, 2
    Floating bodies, 165
    oscillation (rolling) of, 187
    types of equilibrium of, 165
    – neutral equilibrium, 165
    – stable equilibrium, 165
    – unstable equilibrium, 165
    Flownets, 231
    methods of drawing, 231
    uses and limitations of, 232
    Flow through nozzle, 706
    power transmitted, 707
    condition for maximum power
    transmission, 707
    Fluid flow, 195
    compressible and incompressible, 197
    laminar and turbulent, 197
    one, two and three-dimensional, 196
    rotational and irrotational, 197
    steady and unsteady, 195
    uniform and non-uniform, 196
    Forced vortex flow, 345
    Free liquid jet, 313
    Free vortex flow, 346
    Froude number, 412
    G
    Gradually varied flow, 938
    equation of, 938
    H
    Hazen Poiseuille law, 541
    Hydraulic co-efficients, 458
    co-efficient of contraction, 458
    co-efficient of velocity, 459
    co-efficient of discharge, 459
    co-efficient of resistance, 459
    experimental determination of, 460
    Hydraulic gradient and total energy
    lines, 657
    Hydraulic jump, 923
    I
    Impulse momentum equation, 320
    Inclined immersed surface, 116
    K
    Kinetic energy correction factor, 336
    Kutta-Joukowski theorem, 807
    L
    Laminar flow, 534
    between parallel plates, 570
    through an annulus, 567
    through porous media, 582
    Laminar boundary layer, 742
    Langrangian method, 192
    Liquids (properties of), 3
    Liquids in relative equilibriumn, 364
    Lock gates, 151
    M
    Mach number, 420
    Major energy losses, 638
    Magnus effect, 810
    Manning’s formula, 873
    Manometers, 54
    simple manometers, 54
    differential manometers, 63
    advantages and limitations of, 81
    Mechanical gauges, 81
    Metacentre, 165
    Metacentric height, 165
    determination of, 166
    – analytical method, 166
    – experimental method, 167
    Minor energy losses, 638
    at the entrance to pipe, 657
    at the exit of a pipe, 657
    due to sudden enlargement, 645
    due to sudden contraction, 652
    due to obstruction in pipe, 656
    due to bend in the pipe, 657
    in various pipe fittings, 657
    Model analysis, 415
    Model laws, 420
    Euler model law, 445Index iii
    Froude model law, 434
    Mach Model law, 447
    Reynolds model law, 420
    Weber model law, 446
    Models, 449
    distorted, 449
    scale effect in, 450
    undistorted, 449
    Momentum correction factor, 336
    Moment of momentum equation, 343
    Momentum thickness, 728
    Momentum equation for boundary layer, 739
    Most economical section, 889
    – circular channel, 910
    – rectangular channel, 890
    – trapezoidal channel, 892
    – triangular channel, 908
    Mouthpieces, 490
    N
    Navier-Stokes equations, 537
    Newton’s law of viscosity, 5
    Notches, 508
    rectangular, 509
    stepped, 514
    triangular, 511
    trapezoidal, 513
    O
    Open channels, 880
    formulae for uniform flow in, 884
    – Chezy’s formula, 884
    non-uniform flow through, 917
    types of, 881
    types of flow in, 881
    – laminar and turbulent flows, 882
    – steady flow and unsteady flow, 882
    – subcritical, critical and
    supercritical flows, 882
    Orifice, 457
    Classification of, 457
    Orificemeter, 303
    P
    Pascal’s law, 45
    Path line, 198
    Pipes in series, 668
    Pipes in parallel, 674
    Pitot tube, 310
    Potential head or energy, 259
    Power absorbed in bearings, 583
    collar bearing, 586
    foot-step bearing, 585
    journal bearing, 583
    Pressure, 43
    measurement of, 53
    Pressure head (of a liquid), 43
    R
    Rayleigh’s method, 390
    Reynolds number, 418
    Reynolds experiment, 535
    Rotating cylinder method, 591
    Rotameter, 308
    S
    Shock waves, 865
    Similitude, 416
    Specific volume, 3
    Specific gravity, 3
    Specific energy and specific energy curve, 917
    Steamline, 198
    Steam tube, 198
    Streak line, 199
    Stream function, 228
    Streamlined body, 798
    Stagnation properties, 844
    Surface tension, 25
    Syphon, 699
    T
    Terminal velocity of a body, 799
    Thermodynamic properties, 23
    Turbulent flow, 605
    characteristics of, 608
    shear stresses in, 609
    – Boussinesq’s theory, 609
    – Prandtl’s mixing length theory, 610iv Index
    – Reynolds theory, 610
    Turbulent boundary layer, 766
    V
    Vapour pressure, 37
    Velocity potential, 227
    Velocity head or kinetic energy, 259
    Venturimeter, 291
    – horizontal, 292
    – vertical and inclined, 298
    Viscosity, 4
    effect of temperature on, 8
    effect of pressure on, 8
    measurement of, 591
    – capillary tube method, 595
    – falling sphere method, 594
    – rotating cylinder method, 591
    Vorticity, 218
    Vortex motion, 345
    W
    Water hammer in pipes, 711
    Weber number, 419
    Weirs, 508
    broad-crested, 522
    cipolletti, 521
    ogee, 523
    norrow-crested, 523
    rectangular, 518
    submerged or drowned, 523Index v
    HYDRAULIC MACHINES
    A
    Air lift pump, 320
    Air vessels, 275
    B
    Bulb turbines, 130
    C
    Cavitation, 159
    Cavitation factor, 160
    Centrifugal pump, 177
    advantages, 178
    classification of, 177
    component parts of a, 179
    characteristics of, 233
    – constant efficiency curves, 234
    – constant head and constant
    discharge curves, 234
    – main characteristic curves, 233
    – operating characteristic curves, 234
    cavitation in, 236
    effect of variation of discharge on the
    efficiency, 220
    efficiencies of a, 186
    – manometric, 186
    – mechanical, 187
    – overall, 187
    – volumetric, 187
    head of a, 184
    – gross or effective head, 186
    – manometric head, 185
    – static head, 185
    losses of a, 186
    – hydraulic losses, 186
    – leakage loss, 186
    – mechanical losses, 186
    minimum speed for starting a, 217
    model testing, 229
    multistage, 224
    – pumps in series, 224
    – pumps in parallel, 224
    net positive suction head (NPSH), 235
    operational difficulties in, 240
    priming of a, 239
    selection of, 239
    work done by the impeller, 182
    working of a, 182
    working proportions of, 222
    D
    Deriaz turbine, 129
    Draft tube, 131
    theory of, 132
    types of, 133
    F
    Flow duration curve, 329
    Fluidics, 359
    fluidic elements, 361
    Force exterted by jet on
    a series of radial curved vanes, 24
    moving curved plate, 15
    moving flat plate, 11
    – held normal to the jet, 11
    – inclined to the jet, 12
    stationary curved plate, 3
    stationary flat plate, 1
    – held inclined to the jet, 2
    – held normal to the jet, 1
    Francis turbine, 81
    advantages and disadvantages of, 87
    design of runner of, 86
    work done and efficiency of, 84
    working proportions of, 85vi Index
    specific speed, 138
    I
    Impact of free jet, 1
    Impulse turbines, 55
    Indicator diagrams, 258
    J
    Jet pump, 320
    Jet propulsion of ships, 40
    K
    Kaplan turbine, 122
    versus Francis turbine, 124
    M
    Mass curve, 331
    Multistage centrifugal pumps, 224
    pumps in parallel, 224
    pumps in series, 224
    Muschel curves, 157
    N
    Negative slip, 252
    P
    Pelton wheel, 55
    construction and working of, 55
    design aspects of, 61
    work done and efficiency of a, 57
    Performance characteristics of turbines, 154
    constant efficiency, 157
    main or constant head, 154
    operating or constant speed, 156
    Pitting, 160
    Precipitation, 326
    Propeller turbine, 122
    R
    Reaction turbines, 81
    Reciprocating pumps, 248
    H
    Hydrograph, 328
    Hydrology, 325
    Hydraulic accumulator, 288
    differential, 289
    simple, 288
    Hydraulic coupling, 317
    Hydrologic cycle, 325
    Hydraulic crane, 303
    Hydraulic intensifier, 296
    Hydraulic lift, 307
    direct acting, 307
    suspended, 307
    Hydraulic press, 299
    Hydro-power plant, 335
    advantages and disadvantages of, 336
    application of, 325
    average life of plant components, 336
    controls, 337
    cost of, 339
    preventive maintenance, 338
    safety measures in, 337
    Hydraulic turbines, 52
    cavitation, 159
    cavitation factor, 160
    classification of, 53
    definitions, 59
    – efficiencies, 60
    – gross head, 59
    – net or effective head, 59
    governing of, 157
    – impulse turbine, 157
    – reaction turbine, 158
    model relationship, 145
    performance characteristics of, 154
    run away speed, 131
    scale effect, 153
    selection of, 162Index vii
    air vessels, 275
    classification of, 248
    co-efficient of discharge, 252
    discharge, work done and power required
    to drive, 251
    indicator diagrams, 258
    main components and woking, 249
    negative slip, 252
    Runaway speed, 131
    Run off, 326
    measurement of, 326
    – discharge observation method, 327
    – empirical formulae, 326
    – from rainfall records, 326
    – run off curves and tables, 327
    S
    Scale effect, 153
    slip, 252
    Specific speed, 138
    Surge tanks, 164
    T
    Tanspiration, 326
    Tubular turbines, 130

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