**1 DIMENSIONAL ANALYSIS AND SIMLITUDE**

1.1 Introduction

1.2 Dimensions, Dimensional Homogeneity and Units

1.3 Dimensional Analysis

1.3.1 The Buckingham - theorem

1.3.2 Selection of repeating variables

1.3.3 Determining the groups

1.3.4 Some additional comments about dimensional analysis

1.3.5 Uniqueness of terms

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

1.4 Modeling and Similitude

1.4.1 Geometric Similarity

1.4.2 Kinematic similarity

1.4.3 Dynamic similarity

1.4.4 Standard dimensionless numbers

1.4.4.1 Reynold's number (Re)

1.4.4.2 Froude's number ( )

1.4.4.3 Mach's number (M)

1.4.4.4 Euler's number (Eu)

1.4.4.5 Weber's number (Wb)

1.5 Model Laws

1.5.1 Reynold's model law

1.5.2 Froude's model law

1.5.3 Mach model law

1.5.4 Euler's model law

1.5.5 Weber's model low

1.6 Undistorted and Distorted Models

1.7 Scale Effect

1.8 Comments on Model Testing

Illustrative Examples

Exercises

A. Theory

B. Unsolved Problems

**2 LAMINAR VISCOUS FLOW**

2.1 Introduction

2.2. Hagen-Poiseuille Flow

2.3. Plane Poiseuille Flow

2.4 Coutte Flow

Illustrative Examples

Exercises

A. Theory

B. Unsolved Problems

**3 TURBULENT FLOW THROUGH PIPES**

3.1 Introduction

3.2 Turbulent Shear Stress

3.3 Boussines Eddy Viscosity

3.4. Prandtl's Mixing Length Theory

3.5 Shear Velocity or Friction Velocity

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

3.7 Hydrodynamically Smooth and Rough Boundaries

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

3.8.1 Velocity distribution in smooth pipes

3.8.2 Velocity distribution in rough pipes

3.9 Velocity Distribution for Turbulent Flow in Terms of Average Velocity

3.9.1 Turbulent flow in smooth pipes

3.9.2 Turbulent flow in rough pipes

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

3.10 Turbulent Pipe Coefficient

3.11 The Chronological Development of Turbulent Pipe Flow Theories

3.11.1 Smooth pipes and Blasius equation

3.11.2 Stanton and Pannell

3.11.3 Nikuradse experimental results using artificially rough pipes

3.11.4 The smooth and rough laws of Prandtl and von Karman

3.10.5 The Colebrook White transition formula

3.11.6 Moody diagram for commercial pipes

3.11.7 Hydraulic Research station charts (HRS) Ackeres

3.11.8 Barr explicit formula

3.11.9 Murdock formula

3.11.10 Swamee and Jain's explicit equation

3.11.11 S.E. Haaland's formula

3.12 Non Circular Pipes

3.13 Roughness of Pipes with Age (Old Pipes)

Illustrative Examples

EXERCISES

A. Theory

B. Unsolved Problems

**4 OPEN CHANNEL FLOW**

4.1 Introduction

4.2 Flow Classification

4.2.1 Steady uniform flow

4.2.2 Steady non uniform flow

4.2.3 Unsteady flow

4.2.4 Laminar and turbulent flows

4.2.5 Subcritical, critical and supercriticial flows

4.3 Geometric Elements of Channel Section

4.4 Velocity Distribution in A Channel Section

4.5 Uniform Channel Flow

4.5.1 The Chezy's formula

4.5.2 The Ganguillet and Kutter formula

4.5.3 The Manning's formula

4.6 Most Economical Section of Channel

4.6.1 Rectangular channel section

4.6.2 Trapezoidal channel section

4.6.3 Triangular channel section

4.6.4 Circular channel section

4.7 Open Channel Section for Constant Velocity at all Depths of Flow

4.8 Specific Energy and Critical Depth

4.8.1 Total energy and specific energy

4.8.2 Relationship between specific energy and depth

4.8.3 Critical depth (yc)

4.8.4 The general equation of critical flow

4.8.5 An application of the critical depth line

4.8.6 Channel Transitions

4.8.7 Critical depth meters

4.9 Determination of Average (Mean) Velocity in Flow through Channels

4.10 Gradually Varied Flow

4.10.1 General equation of gradually varied flow or Dynamic equation gradually varied flow

4.10.2 Special values of varied flow equation

4.10.3 Classification of surface profiles

Illustrative Examples

EXERCISES

A. Theory

**5 RAPIDLY VARIED FLOW**

5.1. Introduction

5.1.1 Hydraulic jump

5.1.2 Forms of the hydraulic jump

5.1.3 Uses of the hydraulic jump

5.1.4 Analysis of the hydraulic jump

5.1.5 Energy loss across a hydraulic jump

5.1.6 Significance of the hydraulic jump equations

5.1.7 Height and length of the hydraulic jump

5.1.8 Location of hydraulic jump

Illustrative Examples

Exercises

A. Theory

B. Unsolved Problems

**6 WAVES AND SURGES IN OPEN CHANNEL**

6.1 Introduction

6.2. Waves and their Classification

6.2.1 Celerity of small solitary wave

6.2.2 Monoclinal waves

6.2.3 Surges

6.2.4 The upstream positive surge

6.2.5 The downstream positive surge

6.2.6 Negative surge waves

Illustrative Examples

EXERCISES

A. Theory

B. Unsolved Problems

**7 IMPACT OF FREE JETS**

7.1. Introduction

7.2. Force Exerted by Fluid Jet on Stationary Flat Plate

7.2.1. Flat plate normal to the jet

7.2.2. Flat plate inclined at an angle θ to the jet

7.3. Force Exerted by Fluid Jet on Moving Flat Plate

7.3.1. Flat plate normal to jet

7.3.2. Flat plate inclined to jet

7.3.3. Flat plate moving in series

7.4. Force exerted by a Fluid Jet on Stationary Curved Vane

7.4.1. Jet striking a symmetrical stationary curved vane at the centre

7.4.2. Jet striking an unsymmetrical stationary curved vane tangentially at one of the tips

7.5. Force Exerted by a Fluid Jet on Moving Curved Vane

7.5.1. Curved vane, jet striking at the centre

7.5.2. Jet striking on unsymmetrical curved vane tangentially at one of the tips

7.6. Flow Over Radial Vanes

7.7. Euler’s Equation of Fluid Machines (Moment of Momentum or angular momentum equation)

7.7.1. The physical concept of Eulers equation

Illustrative Examples

Exercises

A. Theory

B. Unsolved Problems

**8 HYDRAULIC PRIME MOVERS**

8.1. Introduction

8.2. Heads

8.2.1. Gross Head

8.2.2. Net Head

8.3. Component of Hydropower Plants

8.3.1. Water Reservoir

8.3.2. Head Works

8.3.3. Dams

8.3.4. Water Ways

8.3.5. Tail Race and Outlet Water Way

8.3.6. Turbine Governors

8.3.7. Generators

8.3.8. Transformer and transmission lines

8.4. Hydraulic Turbines and their Selection

8.4.1. Impulse and Reaction turbines

8.4.2. Classification according to direction of flow

8.4.3. Classification according to specific speed and speed factor

8.4.4. Operating or normal speed N

8.4.5. Turbine rating and performance

8.4.6. Runaway speed

8.4.7. Cavitation in turbines, and turbine setting

8.4.8. Selecting the turbine type and number of units

8.5. Types of Energy Loss and Efficiencies

8.5.1. Efficiencies

Exercises

A. Theory

**9 IMPULSE TURBINES**

9.1. Introduction

9.2. The Pelton Wheel

9.2.1. Main Components and their functions

9.3. Pelton Wheel Losses and Efficiencies

9.4. Theory of Pelton Wheel

9.5. Working Proportions of Pelton Wheel

9.6. Number of Jets and Wheels Per Unit

9.7. Selection of Jet Ratio and Bucket width to Jet Diameter

9.8. Selection of Speed

9.9. Selection of High Head

9.10. Relation between Specific Speed and Jet Ratio

9.11. Limitations of the Pelton Turbine

Illustrative Examples

Exercises

A. Theory

B. Unsolved Problems

**10 REACTION TURBINES**

10.1. Introduction

10.2. The Francis Turbine

10.2.1. Scroll casing or spiral casing

10.2.2. Speed rings

10.2.3. Guide vanes or wicket gates

10.2.4. Runner

10.2.5 Draft tubes

10.3. Work done and Efficiencies of Francis Turbine

10.4. Velocity Diagrams for Francis Turbine

10.5. Working Proportions of A Francis Turbine

10.6. Design of Francis Turbine Runner

10.7. Axial Flow Reaction Turbines

10.9. Choice between Propeller and Francis Turbines

10.10. Choice of Kaplan and Propeller Turbines

10.11. Kaplan and Propeller Turbines

10.11.1. Scroll casing

10.11.2. Stayring

10.11.3. Wicket gates

10.11.4. Runner

10.11.5. The turbine cover

10.11.6. The air valve

10.11.7. Draft tube

10.11.8. Cavitation

10.12. Working Proportions of Kaplan and Propeller Turbines

10.13. Draft Tubes

10.13.1. The function of draft tubes

10.13.2. Hydraulic characteristics of draft tubes

10.13.4. The efficiency of a draft tube

10.14. Types of Draft Tubes

10.15. Cavitation

10.15.1. Definition of Cavitation

10.15.2 Causes of cavitation

10.15.3. Effects on hydraulic machines

10.15.4. Cavitation Erosions

10.15.5. Prevention of Cavitation

Illustrative Examples

Exercises

A. Theory

B. Unsolved Problems

**11 GOVERNING OF HYDRAULIC TURBINES**

11.1. Introduction

11.2. The Main Elements of Governor

11.3. Action of A Governor

11.4. Governing of Impulse Turbine

11.4.1. Combined spear and deflector control

11.5. Governing of Francis Turbines

11.5.1. Relief valve or pressure regulator

11.6. Governing of Kaplan Turbine

11.8. Surge Tanks

11.8.1. The main functions

11.8.2. Working

11.8.3. Types of surge tank

11.8.4. Multiple surge tanks

11.8.5. Necessity of a tank

11.8.6. Location

11.8.7. Size of tank

Illustrative Examples

Exercises

A. Theory

B. Unsolved Problems

**12 PERFORMANCE OF HYDRAULIC TURBINES**

12.1. Introduction

12.2. Performance Under Unit Head

12.2 Performance under Specific Conditions

12.2.1 Specific speed

12.3 Performance Characteristic Curves

12.3.1 Main characteristic curves

12.3.2 Operating characteristics curves

12.3.3. Isoefficiency or Muschel curves

12.4 Model Testing of Turbines

Illustrative Examples

Exercises

A. Theory

B. Unsolved Problems

**13 CENTRIFUGAL PUMPS**

13.1 Introduction

13.2 Classification of Centrifugal Pumps

13.2.1 Operating head

13.2.2 Specific speed

13.2.3 Types of casing

13.2.4 Number of impellers per shaft

13.2.5 Disposition or layout of shaft

13.2.6 Number of entrances to the impeller

13.2.7 Relative direction of flow through impeller

13.3 Centrifugal Pump

13.3.1 Types of vanes

13.3.2 Work done and action of centrifugal pump

13.3.3 Head of a Pump

13.3.4 Efficiencies of centrifugal pump

13.3.5. Losses in centrifugal pump

13.4 Minimum Starting Speed

13.5 Minimum Diameter of Impeller

13.6 Specific Speed

13.7 Affinity Laws for Centrifugal Pumps

13.8 Cavitation in Centrifugal Pumps

13.9 Model Testing of Centrifugal Pump

13.10 Multistage Centrifugal Pumps

13.10.1 Pumps in series

13.10.2. Pumps in Parallel

13.11 Characteristic curves of Centrifugal Pumps

13.11.1 Main and operating characteristics

13.11.2 Constant efficiency or Muschel curves

13.11.3 Constant head and Constant discharge curves

13.12 Pump Selection

Illustrative Examples

Exercises

A. Theory

B. Unsolved problems