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 |  موضوع: كتاب A Textbook of Fluid Mechanics and Hydraulic Machines السبت 29 أكتوبر 2022, 2:40 am | |
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أحضرت لكم كتاب
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)
و المحتوى كما يلي :
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
15. 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
16. 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
17. UNIVERSITIES’ QUESTIONS (LATEST) WITH “SOLUTIONS” 959—994
OBJECTIVE TYPE TEST QUESTIONS 995—1046PART – II
HYDRAULIC MACHINES
1. 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
2. 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
3. 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
4. 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
5. 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
6. 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
7. 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
8. 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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