Fluid Mechanics: Basic Concepts and Principles (In SI Units)

Preface
Acknowledgements
Contents
1 Laminar Flow (Viscous Flow or Flow withLow Reynolds Number)
	1.1 INTRODUCTION
	1.2 LAMINAR AND TURBULENT FLOW
		1.2.1 Laminar Flow
		1.2.2 Turbulent Flow
	1.3 REYNOLDS EXPERIMENT
	1.4 EXPERIMENTAL DETERMINATION OF CRITICAL VELOCITY
	1.5 STEADY LAMINAR FLOW THROUGH A CIRCULAR PIPE
		1.5.1 Comparison between Hagen-Poiseuille Equation and Darcy’s Formula
	1.6 FLOW BETWEEN PARALLEL PLATES
		1.6.1 Both Plates are Fixed
	1.7 MOMENTUM CORRECTION FACTOR
	1.8 KINETIC ENERGY CORRECTION FACTOR
	1.9 POWER ABSORBED IN VISCOUS RESISTANCE
		1.9.1 Journal Bearing
		1.9.2 Foot-Step Bearing
		1.9.3 Collar Bearing
	1.10 DASH-POT MECHANISM: MOVEMENT OF A PISTON IN A DASH-POT
	1.11 STOKES’ LAW
	1.12 MEASUREMENT OF VISCOSITY
		1.12.1 Capillary Tube Viscometer
		1.12.2 Rotating Cylinder Viscometer
		1.12.3 Falling Sphere Viscometer
		1.12.4 Industrial Viscometers
	1.13 NAVIER-STOKES EQUATIONS OF MOTION
	1.14 FLUIDIZATION
		1.14.1 Conditions for Fluidization
		1.14.2 Types of Fluidization
	SUMMARY
	ASSIGNMENT - 1
	ASSIGNMENT - 2
2
Turbulent Flow
	2.1 INTRODUCTION
	2.2 TYPES OF VELOCITIES IN A TURBULENT FLOW
		2.2.1 Relation between Various Velocities
		2.2.2 Degree or Level of Turbulence
		2.2.3 Intensity of Turbulence
	2.3 CLASSIFICATION OF TURBULENCE
	2.4 SHEAR STRESS IN TURBULENT FLOW
		2.4.1 Reynolds Theory
		2.4.2 Boussinesq Eddy-viscous Theory
		2.4.3 Prandtl’s Mixing Length Theory
		2.4.4 Von-Karman’s Theory
	2.5 VELOCITY DISTRIBUTION LAW IN TURBULENT FLOW
		2.5.1 Velocity Distribution in Laminar Region: Zone-I
		2.5.2 Velocity Distribution in the Turbulent Region: Zone-II
		2.5.3 Relation between umax and u
	2.6 HYDRODYNAMICALLY SMOOTH AND ROUGH BOUNDARIES
		2.6.1 Hydrodynamically Smooth Boundary
		2.6.2 Hydrodynamically Rough Boundary
	2.7 VELOCITY DISTRIBUTION IN TERMS OF MEAN VELOCITY
	2.8 POWER LAW FOR VELOCITY DISTRIBUTION IN SMOOTH PIPES
	2.9 DETERMINATION OF COEFFICIENT OF FRICTION f
	2.10 THERMAL (HOT-WIRE AND HOT FILM) ANEMOMETERS
	2.11 LASER DOPPLER VELOCIMETRY
		2.11.1 Operating Principle
	SUMMARY
	ASSIGNMENT - 1
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3
Boundary Layer Theory
	3.1 INTRODUCTION
	3.2 BOUNDARY LAYER FORMATION OVER A FLAT PLATE
		3.2.1 Laminar Boundary Layer
		3.2.2 Transition Boundary Layer
		3.2.3 Turbulent Boundary Layer
		3.2.4 Laminar Sub-layer
	3 .3 BOUNDARY LAYER THICKNESS: δ
	3.4 DISPLACEMENT THICKNESS: δ*
	3.5 MOMENTUM THICKNESS: θ
	3.6 ENERGY THICKNESS: δ**
	3.7 DRAG FORCE ON A FLAT PLATE DUE TO BOUNDARY LAYER
	3.8 ESTIMATION OF THE LAMINAR BOUNDARY LAYER THICKNESS
	3.9 TURBULENT BOUNDARY LAYER ON A FLAT PLATE
	3.10 BOUNDARY LAYER ON ROUGH SURFACES
	3.11 SEPARATION OF BOUNDARY LAYER
	3.12 CONTROL OF BOUNDARY LAYER SEPARATION
		3.12.1 Suction Method
		3.12.2 By Pass Method
		3.12.3 Injection Method
		3.12.4 Rotating of Cylinder Method
		3.12.5 Streamlining of Body Shape
	SUMMARY
	ASSIGNMENT - 1
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4
Flow Through Pipe
	4.1 INTRODUCTION
	4.2 ENERGY LOSSES IN PIPES
		4.2.1 Major Losses
		4.2.2 Minor Losses
	4.3 SIPHON
	4.4 PIPES IN SERIES: COMPOUND PIPES
	4.5 CONCEPT OF EQUIVALENT LENGTH AND EQUIVALENT PIPE
		4.5.1 Equivalent Length
		4.5.2 Equivalent Pipe
	4.6 PIPES IN PARALLEL
		4.6.1 Three Pipes in Parallel
		4.6.2 Four Pipes in Parallel
	4.7 TRANSMISSION OF HYDRAULIC POWER THROUGH PIPELINES
		4.7.1 Condition for Maximum Transmission Power
		4.7.2 Maximum Efficiency of Transmission of Power
	4.8 WATER HAMMER
		4.8.1 Pressure Rise due to Gradual Closure of Valve
		4.8.2 Pressure Rise due to Instantaneous Closure of Valve
		4.8.3 Pressure Rise due to Instantaneous Closure of Valve in an Elastic Pipe
	4.9 PIPE NETWORKS
		4.9.1 Hardy Cross Method (HCM)
	4.10 SURGE TANK
		4.10.1 Types of Surge Tanks
	4.11 THREE RESERVOIR PROBLEM
		4.11.1 Exact Method
		4.11.2 Trial and Error Method
	SUMMARY
	ASSIGNMENT - 1
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5
Pipe Flow Measurement
	5.1 INTRODUCTION
	5.2 VENTURIMETER
	5.3 ORIFICE METER OR ORIFICE PLATE
	5.4 PITOT TUBE
	5.5 CURRENT METER
	5.6 ROTAMETER
	5.7 BEND METER
	SUMMARY
	ASSIGNMENT - 1
	ASSIGNMENT - 2
6
Orifices and Mouthpieces
	6.1 INTRODUCTION
	6.2 TYPES OF ORIFICES
	6.3 HYDRAULIC COEFFICIENTS
		6.3.1 Coefficient of Contraction: Cc
		6.3.2 Coefficient of Velocity: Cv
	6.4 EXPERIMENTAL DETERMINATION OF HYDRAULIC COEFFICIENTS
		6.4.1 Coefficient of Discharge: Cd
		6.4.2 Coefficient of Contraction: Cc
	6.5 SMALL AND LARGE ORIFICES
	6.6 DISCHARGE THROUGH A SMALL RECTANGULAR ORIFICE
	6.7 DISCHARGE THROUGH A LARGE RECTANGULAR ORIFICE
	6.8 DISCHARGE THROUGH FULLY SUBMERGED ORIFICE
	6.9 DISCHARGE THROUGH PARTIALLY SUBMERGED ORIFICE
	6.10 CLASSIFICATION OF MOUTHPIECES
		6.10.1 External Mouthpieces
		6.10.2 Internal Mouthpiece
	6.11 DISCHARGE THROUGH EXTERNAL CYLINDRICAL MOUTHPIECE
	6.12 DISCHARGE THROUGH A CONVERGENT MOUTHPIECE
	6.13 DISCHARGE THROUGH A CONVERGENT DIVERGENTMOUTHPIECE
	6.14 DISCHARGE THROUGH AN INTERNAL MOUTHPIECE (RE-ENTRANT OR BORDA’S MOUTHPIECE)
		6.14.1 Borda’s Mouthpiece Running Free
		6.14.2 Borda’s Mouthpiece Running Full
	SUMMARY
	ASSIGNMENT - 1
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7
Flow Past Submerged Bodies
	7.1 INTRODUCTION
	7.2 DRAG AND LIFT
	7.3 TYPES OF DRAG FORCE
		7.3.1 Streamlined and Bluff Bodies
	7.4 EXPRESSION FOR DRAG AND LIFT
		7.4.1 Drag Force: FD
		7.4.2 Lift Force: FL
		7.4.3 Co-efficient of Drag: CD
		7.4.4 Co-efficient of Lift: CL
	7.5 DRAG ON A SPHERE
	7.6 DRAG ON A CYLINDER
	7.7 LIFT AND CIRCULATION ON A CIRCULAR CYLINDER
	7.8 MAGNUS EFFECT: LIFT GENERATED BY SPINNING
	7.9 LIFT ON AN AIRFOIL
		7.9.1 Steady State of a Flying Object
	SUMMARY
	ASSIGNMENT - 1
	ASSIGNMENT - 2
8
Flow Through Open Channels
	8.1 INTRODUCTION
	8.2 GEOMETRICAL TERMINOLOGIES: FLOW THROUGH OPEN CHANNELS
	8.3 TYPES OF FLOW IN OPEN CHANNELS
		8.3.1 Steady and Unsteady Flow
		8.3.2 Uniform and Non-uniform Flow
		8.3.3 Laminar and Turbulent Flow
		8.3.4 Sub-critical, Critical and Super-critical Flow
	8.4 CHEZY’S FORMULA
	8.5 EMPIRICAL RELATIONS FOR DETERMINATION OF CHEZY CONSTANT
	8.6 MOST ECONOMICAL SECTION
		8.6.1 Most Economical Rectangular Channel
		8.6.2 Most Economical Trapezoidal Channel
	SUMMARY
	ASSIGNMENT - 1
	ASSIGNMENT - 2
9
Notches and Weirs
	9.1 INTRODUCTION
	9.2 DIFFERENCE BETWEEN NOTCH AND ORIFICE
	9.3 DIFFERENCE BETWEEN A NOTCH AND A WEIR
	9.4 CLASSIFICATION OF NOTCHES AND WEIRS
	9.5 DISCHARGE OVER A RECTANGULAR NOTCH OR WEIR
	9.6 TRIANGULAR NOTCH OR V-NOTCH
	9.7 DISCHARGE OVER A TRAPEZOIDAL NOTCH OR WEIR
	9.8 DISCHARGE OVER A STEPPED NOTCH
	9.9 ADVANTAGES OF TRIANGULAR NOTCH OVER RECTANGULAR NOTCH
	9.10 EFFECT ON THE DISCHARGE OVER A NOTCH DUE TO AN ERROR IN THE MEASUREMENT OF HEAD
		9.10.1 For a Rectangular Notch
		9.10.2 For a Triangular Notch
	9.11 CIPOLLETTI WEIR
	9.12 FRANCIS’S FORMULA FOR RECTANGULAR WEIR WITH END CONTRACTIONS
	9.13 VELOCITY OF APPROACH
	9.14 VENTILATION OF WEIRS
	9.15 DISCHARGE OVER A BROAD CRESTED WEIR
	9.16 DISCHARGE OVER A SUBMERGED WEIR
	9.17 OGEE WEIR
	SUMMARY
	ASSIGNMENT - 1
	ASSIGNMENT - 2
10
Compressible Flow
	10.1 INTRODUCTION
	10.2 EQUATION OF STATE
	10.3 THERMODYNAMIC PROCESSES
		10.3.1 Isothermal Process [T = c]
		10.3.2 Isobaric Process [ p = c]
		10.3.3 Isochoric Process (or Isometric Process) [V = c]
		10.3.4 Adiabatic Process [ pvγ = c ]
		10.3.5 Polytropic Process [pvn = c]
	10.4 STEADY AND UNSTEADY FLOW
	10.5 UNIFORM AND NON-UNIFORM FLOW
	10.6 COMPRESSIBLE AND INCOMPRESSIBLE FLOW
		10.6.1 Compressible Flow [ρ ≠ c]
		10.6.2 Incompressible Flow (ρ = c).
	10.7 RATE OF FLOW
	10.8 CONTINUITY EQUATION
	10.9 STEADY FLOW ENERGY EQUATION [SFEE]
	10.10 STAGNATION STATE
	10.11 VELOCITY OF SOUND WAVE IN COMPRESSIBLE FLUIDS
		10.11.1 Velocity of Sound (a) in terms of Bulk Modulus of Elasticity (K)
	10.12 VELOCITY OF SOUND IN AN IDEAL GAS
	10.13 PROPAGATION OF PRESSURE WAVES (OR DISTURBANCES IN A COMPRESSIBLE FLUID)
	10.14 NOZZLE AND DIFFUSER
	10.15 FLOW THROUGH NOZZLE
	10.16 NOZZLES OPERATING IN THE OFF-DESIGN CONDITION
	10.17 NORMAL SHOCKS
		10.17.1 Flow of Perfect Gases with Heat-transfer (Rayleigh Flow)
		10.17.2 Flow of Perfect Gases with Friction (Fanno Flow)
	SUMMARY
	ASSIGNMENT - 1
	ASSIGNMENT - 2
References
Appendices
Index