**1. BASIC CONCEPT RELATING TO FLUIDS**

1.1 Introduction

1.2 Definition of a Fluid

1.3 Fluid as a Continuum

1.4 Incompressible and Compressible Flow

1.5 Basic Definitions

1.5.1 Mass

1.5.2 Density

1.5.3 Specific Volume

1.5.4 Specific Weight

1.5.5 Relative density

1.6 Viscosity

1.6.1 Units of Viscosity

1.6.2 Dimensional Formula of Viscosity

1.6.3 Kinematic Viscosity

1.6.4 Units of Kinematic viscosity

1.6.5 Dimensional formula of kinematic viscosity

1.6.6 Newtonian and non Newtonian fluids

1.6.7 Effects of temperature and pressure on viscosity

1.6.8 Ideal Fluid

1.7 Compressibility and Elasticity of Fluids

1.8 Surface Tension

1.9 Capillarity

1.10 Pressure inside a Water Droplet, Soap and Bubble

Illustrative Examples

EXERCISES

A. Theory

B. Unsolved problems

**2. STATIC PRESSURE AND ITS MEASUREMENT**

2.1 Introduction

2.2 Pressure at a Point

2.3 Pascal's Law

2.4 Euler's Differential Equations

2.4.1 The basic equation of hydrostatics

2.4.2 Pressure head

2.4.3 The hydrostatic paradox

2.5 Atmospheric Pressure

2.5.1 Fortin barometer

2.6 Application of the Basic Equation of Fluid Statics

2.7 Manometers

2.7.1 Piezometer

2.7.2 Simple manometers

2.7.3 Differential Manometers

2.8 Measurement of Small Pressure Difference

2.8.1 Inclined gauge

2.8.2 Micromanometers

2.9 Pressure Variation in a Compressible Fluid

2.9.1 Variation under Isothermal conditions

2.9.2 Variation under adiabatic conditions

2.9.3 Variation of pressure and density with altitude for a constant temperature gradient

2.9.4 Variation of temperature and pressure in the atmosphere

ILLUSTRATIVE EXAMPLES

EXERCISES

A. Theory

B. Unsolved Problems

**3. FLUID STATICS**

3.1 Introduction

3.2 Total Pressure

3.3 Centre of Pressure

3.4 Total Pressure and Centre of Pressure on A Vertical Plane Surface

3.5 Total Pressure and Centre of Pressure for Inclined Surface

3.6 Pressure Diagrams

3.7 Pressure on Curved Surfaces

3.7.1 General case of pressure on curved surfaces

3.7.2 Pressure on cylindrical surfaces

Illustrative Examples

EXERCISES

A. Theory

B. Unsolved Problems

**4. BUOYANCY AND FLOATATION**

4.1. Introduction

4.2. Buoyancy

4.3. Centre of Buoyancy

4.4. Equilibrium of Floating Bodies

4.5. Metacentre

4.6. Metacentric Height

4.7. Stability of Floating Bodies Metacentre and Metacentric Height

4.8 Experimental Method of Determination of Metacentric Height

4.9 Analytical Method for Metacentric Height

4.10 The Period of Roll of a Vessel

Illustrative Examples

Exercises

A. Theory

B. Unsolved problems

**5. KINEMATICS OF FLUID**

5.1 Introduction

5.2 Description of Fluid Motion

5.3 Fluid Flow Classifications

5.3.1 Steady flow and unsteady flow

5.3.2 Uniform flow and non uniform flow

5.3.3 One, two and three dimensional flow

5.3.4 Laminar flow and turbulent flow

5.3.5 Rotational flow and Irrotational flow

5.4 Flow Lines

5.4.1 Streamline

5.4.2 Stream tube

5.4.3 Path line

5.4.4 Streak line

5.5 Velocity and Acceleration

5.5.1 Convective acceleration and Local acceleration

5.5.2 Tangential acceleration and normal acceleration

5.6 Principle of Continuity Conservation of Mass Flow

5.6.1 One dimensional continuity equation

5.6.2 Continuity equation for three dimensional flow using Cartesian Coordinates

5.7 Deformation of a Fluid Element

5.8 Circulation and Vorticity

5.8.1 Circulation for the rectangular element

5.8.2 Circulation for the circle

5.8.3 Vorticity

5.9 Stream Function and Velocity Potential

5.9.1 The stream function

5.9.2 Velocity Potential

5.10 Flow Net

5.10.1 Methods of drawing flow nets

5.10.2 Uses of flow net

5.10.3 Limitations of flow net

ILLUSTRATIVE EXAMPLES

EXERCISES

A. Theory

B. Unsolved problems

**6. DYNAMICS OF FLUID FLOW**

6.1 Introduction

6.2 Euler's Equation of Motion

6.2.1 Bernoull's equation Integration of Euler's equation along a streamline for steady flow

6.2.2 Limitations on Bernoulli's equations

6.2.3 Modification to Bernoulli's equation

6.2.4 The physical significance of Bernoulli's equation

6.3 Applications of Bernoulli's Equation

6.3.1 Venturimeter

6.3.1.1 Venturimeter analysis

6.3.1.2 Vertical/Inclined Venturimeter

6.3.1.3 Use of differential manometer in venturimeter

6.3.2 Orifice meter

6.3.3 Flow nozzle or Nozzle meter

6.3.4. Flow tubes

6.3.5 Pressure recovery

6.4 Velocity Measurements

6.4.1 Static, stangnation and dynamic pressures

6.4.2 Pitot tube

6.4.3 Pitot static tube

6.5 Momentum Equation

6.5.1 Impulse-Momentum equation

6.5.2 Momentum equation for two and there dimensional flow along a stream line

6.5.3 Momentum correction factor

6.5.4 Application of the momentum equation

6.5.4.1 Forces on a pipe bend

6.5.4.2 Force due to the diflection of a jet by a curved vane

6.5.4.3 Force at a nozzle

6.5.4.4 Reaction of a jet

6.6 Navier Stokes Equations

6.2.1 Navier Stokes equation in vector form and meaning of each term

6.2.2 Navier Stokes in cylindrical polar coordinates

Illustrative Examples

EXERCISES

A. Theory

B. Unsolved Problems

**7. FLOW THROUGH ORIFICES AND MOUTH PIECES**

7.1 Introduction

7.2 Sharp Edged Orifice Discharging Free

7.3 Hydraulic Coefficients

7.3.1 Coefficient of contraction (Cc)

7.3.2 Coefficient of velocity (Cv)

7.3.3 Coefficient of discharge (Cd)

7.3.4 Coefficient of resistance (Cr)

7.4 Experimental Determination of Hydraulic Coefficients for an Orifice

7.4.1 Experimental determination of coefficient of contraction

7.4.2 Determination of coefficient of velocity Cv

7.4.2.1. Jet distance measurement method (Trajectory method)

7.4.3 Determination of coefficient of discharge

7.5 Submerged Orifice

7.6 Partially Submerged Orifice

7.7 Sharp Edged Large Vertical Orifice with Rectangular Shape

7.8 Mouthpieces or Tubes

7.8.1 External cylindrical mouthpiece running full

7.8.2 Flow through convergent divergent mouthpiece

7.8.3 Borda's or Re entrant mouthpiece

7.8.3.1 Borda's mouthpiece running free

7.8.3.2 Borda's mouthpiece running full

7.9 Flow through an Orifice or a Mouthpiece under variable heads

7.9.1 General procedure for calculating time of emptying a tank through an orifice /mouthpiece at its bottom

7.9.2 Time of emptying cylindrical tank

7.9.3 Determine the constant head under a head falling

7.10 Time of Emptying (or Filling) A Tank with Inflow

7.11 Flow of Liquid from One Vessel to Another

Illustrative Examples

EXERCISES

A. Theory

B. Unsolved problems

**8. FLOW OVER NOTCHES AND WEIRS**

8.1 Introduction

8.2 Rectangular Weirs

8.2.1 Flow over rectangular weir

8.2.2 Flow over rectangular weir with velocity of approach

8.2.3 Empirical formulae for discharge over rectangular weir

8.3 Flow over a Triangular Weir (V Notch)

8.4 Flow over a Trapezoidal Weir or Notch

8.4.1 Cippoletti weir

8.5 Long Based Weirs

8.5.1 Broad crested weir

8.5.2 Round nosed weirs

8.5.3 Crump weirs

8.6 Submerged Weirs

8.7 Ventilation of Weir

Illustrative Examples

EXERCISES

A. Theory

B. Unsolved problems

**9. FLOW THROUGH PIPES**

9.1 Introduction

9.2 Reynolds Experiments

9.2.1 Reynolds number and its Significance

9.2.2 Laminar and turbulent flow

9.2.3 Critical Reynolds number

9.3 Fluid Friction

9.4 Head Lost Due to Friction in Pipes Darcy's Weisbach Equation

9.4.1 Proof of the Darcy's Weisbach equation

9.4.2 Chezy's formula

9.4.3 Manning's formula

9.4.4 Hazen William's formula

9.5 Minor Losses

9.5.1 Head loss due to sudden enlargement

9.5.2 Head loss due to sudden contraction

9.5.3 Head loss at entrance to pipe

9.5.4 Exit loss

9.5.5 Head loss due to obstruction

9.5.6 Head loss due to bends, valves, Non symmetrical sections, etc.

9.6 Total Energy Line and Hydraulic Gradient

9.6.1 Total energy line (TEL)

9.6.2 Hydraulic gradient line (HGL)

9.7 Flow Through Pipe Lines

9.8 Flow through Pipes Connected in Series

9.9 Method of Equivalent Lengths

9.10 Flow through Pipes Connected in Parallel

9.11 Power Transmission through Pipes

9.11.1 Maximum power transmission efficiency

9.12 Flow through Nozzle at the End of a Pipe

9.12.1 Efficiency of Power transmission through nozzle

9.12.2 Condition for maximum power transmission through nozzle

9.12.3 Diameter of nozzle for maximum transmission of power through nozzle

9.13 Water Hammer

9.14 Water hammer analysis

9.14.1 Rigid Water Column theory

9.14.2 Elastic pipe theory

Illustrative examples

EXERCISES

A. Theory

B. Unsolved problems

**10. LAMINAR VISCOUS FLOW**

10.1 Introduction

10.2. Hagen-Poiseuille Flow

10.3. Plane Poiseuille Flow

10.4 Coutte Flow

Illustrative Examples

EXERCISES

A. Theory

B. Unsolved Problems

**11 TURBULENT FLOW THROUGH PIPES**

11.1 Introduction

11.2 Turbulent Shear Stress

11.3 Boussines Eddy Viscosity

11.4. Prandtl's Mixing Length Theory

11.5 Shear Velocity or Friction Velocity

11.6 Prandtl's Universal Velocity Distribution Equation for Turbulent Pipe Flow

11.7 Hydrodynamically Smooth and Rough Boundaries

11.8 Velocity Distribution for Turbulent Flow in Smooth and Rough Pipes Prandtl Karman Velocity Distribution Equation

11.8.1 Velocity distribution in smooth pipes

11.8.2 Velocity distribution in rough pipes

11.9 Velocity Distribution for Turbulent Flow in Terms of Average Velocity

11.9.1 Turbulent flow in smooth pipes

11.9.2 Turbulent flow in rough pipes

11.9.3 Difference between point velocity and average velocity for smooth and rough pipes

11.10 Turbulent Pipe Coefficient

11.11 The Chronological Development of Turbulent Pipe Flow Theories

11.11.1 Smooth pipes and Blasius equation

11.11.2 Stanton and Pannell

11.11.3 Nikuradse experimental results using artificially rough pipes

11.11.4 The smooth and rough laws of Prandtl and von Karman

11.10.5 The Colebrook White transition formula

11.11.6 Moody diagram for commercial pipes

11.11.7 Hydraulic Research station charts (HRS) Acketes

11.11.8 Barr explicit formula

11.11.9 Murdock formula

11.11.10 Swamee and Jain's explicit equation

11.11.11 S.E. Haaland's formula

11.12 Non Circular Pipes

11.13 Roughness of Pipes with Age (Old Pipes)

Illustrative Examples

Exercises

A. Theory

B. Unsolved Problems

**12. DIMENSIONAL ANALYSIS AND SIMLITUDE**

12.1 Introduction

12.2 Dimensions, Dimensional Homogeneity and Units

12.3 Dimensional Analysis

12.3.1 The Buckingham - theorem

12.3.2 Selection of repeating variables

12.3.3 Determining the groups

12.3.4 Some additional comments about dimensional analysis

12.3.5 Uniqueness of terms

12.3.6 Limitations of dimensional analysis selection of variables superfluous and omitted variables

12.4 Modeling and Similitude

12.4.1 Geometric Similarity

12.4.2 Kinematic similarity

12.4.3 Dynamic similarity

12.4.4 Standard dimensionless numbers

12.4.4.1 Reynold's number (Re)

12.4.4.2 Froude's number ( )

12.4.4.3 Mach's number (M)

12.4.4.4 Euler's number (Eu)

12.4.4.5 Weber's number (Wb)

12.5 Model Laws

12.5.1 Reynold's model law

12.5.2 Froude's model law

12.5.3 Mach model law

12.5.4 Euler's model law

12.5.5 Weber's model low

12.6 Undistorted and Distorted Models

12.7 Scale Effect

12.8 Comments on Model Testing

Illustrative Examples

EXERCISES

A. Theory

B. Unsolved problems

**13. BOUNDARY LAYER THEORY**

13.1 Introduction

13.2 Description of the Boundary Layer

13.3 Boundary Layer Thicknesses

13.3.1 Boundary layer thicknesses

13.3.2 Boundary layer displacement thickness

13.3.3 Momentum thickness

13.3.4 Energy thickness **

13.4 Local Skin Friction and Average Skin Friction Drag Coefficient

13.4.1 Local skin friction drag coefficient Cf

13.4.2 Average skin friction drag coefficient CD

13.5 The Prandtl Boundary Layer Equations

13.6 Blasius Solution

13.7 Momentum Integral Boundary Layer Equation for Flat Plate or VON Karman Integral Equation

13.7.1 Momentum integral equation for zero pressure gradient

13.8 Momentum Integral Method for Laminar Flow over a Flat Plate

13.9 Turbulent Boundary Layer

13.10 Combined Laminar and Turbulent Boundary Layers

13.11 Coefficient of Drag for Turbulent Boundary Layer for Rough Plate

13.12 Flow with a Pressure Gradient

13.13 Separation of Boundary Layer Flow

13.13.1 Examples of separation of boundary layer flow

13.13.2 Separation control

Illustrative Examples

EXERCISES

A. Theory

B. Unsolved Problems

**14 FLOW OVER IMMERSED BODIES**

14.1. Introduction

14.2 Forces on Immersed Bodies Drag and Lift

14.3 Drag on Immersed Bodies

14.4 Types of Drag

14.4.1 Skin friction drag

14.4.2 Pressure drag

14.4.3 Profile drag

14.4.4 Deformation drag

14.4.5 Wave drag

14.4.6 Induced drag

14.5 Streamlined and Bluff Bodies

14.6 Drag on Sphere

14.6.1 Dynamics of sports ball

14.7 Drag on Cylinder

14.7.1 von Karman vortex street

14.7.2 Summary of flow regimes in flow past a circular cylinder

14.8 Lift

14.8.1 Magus effect and the circulation theory of lift (Kutta Joukowski theorem)

14.9 Lift of an Aerofoil

14.10 Aerofoil Terminology

14.11 Inviscid Flow Past a Two Dimensional Aerofoil

14.12 Real (Viscous) Fluid Past A Two Dimensional Aerofoil

14.13 Aerofoil Characteristics

Illustrative Examples

EXERCISES

A. Theory

B. Unsolved Problems