## Description

This book is specially designed for the undergraduate students of civil engineering and AMIE. The text covers the syllabi requirements of almost all technical universities in India and abroad. A lucid pattern, both in terms of language and content, has been adopted throughout the text. This book will prove to be a boon to the students preparing for engineering, AMIE and other competitive examinations.

## Table of Content

**Chapter 1 PRESSURE MEASUREMENTS**

1.1 Introduction

1.2 Pressure at a Point

1.2.1 Forces Acting on a Fluid Element

1.2.2 Definition of Stress

1.2.3 Sign Convention

1.2.4 Stress at a Point

1.3 Absolute, Gauge, Atmospheric and Vacuum Pressures

1.4 Pascal’s Law

1.5 Pressure Variation in a Static Incompressible Fluid

1.6 Pressure Equivalents and its Units

1.7 Measurement of Pressure

1.8 Measurement of Gauge Pressure at a Point −Piezometer

1.9 Manometer

1.9.1 U-tube Manometer

1.9.2 Multitude Manometer

1.9.3 Differential Manometer

1.9.4 Single-column Manometer

1.9.5 Inclined Single-column Manometer

1.9.6 Micro Manometer

1.10 Hydraulic Press or Bramah’s Press

1.11 Mechanical Gauges

1.11.1 Bourdon Gauge

1.11.2 Diaphragm Pressure Gauge

1.11.3 Deadweight Pressure Gauge

**Chapter 2 FLOW MEASUREMENTS**

2.1 Practical Application of Bernoulli’s Theorem

2.1.1 Venturimeter

2.1.2 Derivation of Discharge Equation for Venturimeter

2.2 Orifice Meter

2.2.1 Derivation of Discharge Equation for Orifice Meter

2.3 Flow Nozzle or Nozzle Meter

2.4 Pitot Tube

2.5 Floats

**Chapter 3 FLOW OVER NOTCHES**

3.1 Introduction

3.2 Types of Notches

3.3 Discharges over a Rectangular Notch

3.4 Time of Emptying the Tank Through a Rectangular Notch

3.5 Effect on Discharge over a Rectangular Notch due to Error in Measurement of Head

3.6 Discharges over a Triangular Notch or V-Notch

3.7 Advantages of V-Notch over Rectangular Notch

3.8 Time of Emptying a Tank over a Triangular Notch

3.9 Effect on Discharge over a Triangular Notch due to Error in the Measurement of Head

3.10 Discharges over Trapezoidal Notch

3.11 Discharges over Stepped Notch

3.12 Effect of Velocity of Approach

**Chapter 4 FLOW OVER WEIRS**

4.1 Introduction

4.2 Classifications of Weirs

4.3 Discharges over Rectangular Weir

4.4 Francis Formula for Discharge over a Rectangular Weir

4.5 Bazin’s Formula for Discharge over a Rectangular Weir

4.6 Rehbock Formula

4.7 Ventilation of Rectangular Weirs

4.8 Time Required for Emptying a Reservoir with a Rectangular Weir

4.9 Discharges over a Triangular Weir

4.10 Time of Emptying a Tank over a Triangular Notch

4.11 Discharges over a Trapezoidal Weir

4.12 Discharges over a Narrow Crested Weir

4.13 Discharges over a Broad-Crested Weir

4.14 Discharges over a Submerged or Drowned Weir

4.15 Discharges over a Sharp Crested Weir

4.16 Discharges over an Ogee Weir

4.17 Proportional Weir

4.18 Experimental Determination of Weir Constants

**Chapter 5 OPEN CHANNEL FLOW AND ITS CLASSIFICATIONS**

5.1 Description

5.2 Comparison of Open Channel Flow and Pipe Flow

5.3 Influence of Gravity and Viscosity on the Flow in an Open Channel

5.4 Flow Regimes

5.5 Classification of Flow in Open Channels or Types of Flow in Open Channels

5.6 Basic Flow Equations

5.6.1 Comparison between Energy and Momentum Principles

**Chapter 6 OPEN CHANNELS AND THEIR PROPERTIES**

6.1 Introduction

6.1.1 Natural and Artificial Channels

6.1.2 Rigid and Mobile Boundary Channels

6.1.3 Prismatic and Non-prismatic Channels

6.1.4 General Classification

6.2 Geometric Elements

6.2.1 Geometric Elements for Different Channel Cross Sections

6.3 Velocity Distribution

6.3.1 Pitot Tube

6.4 Energy and Momentum Correction Factors

6.4.1 Derivation of Energy and Momentum Correction Factors (α and β)

6.5 Pressure Distribution in Channels with Small Slope

6.6 Pressure Distribution in Channels with Large Slope

6.7 Pressure Distribution in Curvilinear Flows

**Chapter 7 UNIFORM FLOW**

7.1 Introduction

7.2 Resistance Equation or Shear Stress on the Boundary

7.3 Chezy’s Equation

7.3.1 Derivation of Chezy’s Equation

7.4 Empirical Formula for the Value of Chezy’s Constant

7.5 Factors Affecting Manning’s n

7.6 Estimating the Value of Manning’s n

**Chapter 8 MOST ECONOMICAL SECTION**

8.1 Definition

8.1.1 Most Economical Rectangular Section

8.1.2 Most Economical Trapezoidal Channel

8.1.3 Most Economical Circular Channel Section

8.1.4 Most Economical Triangular Section

8.1.5 Isosceles Triangular Channel Section (Sides at 45◦ with the Base)

**Chapter 9 COMPUTATION OF UNIFORM FLOW**

9.1 Introduction

9.2 Conveyance of a Channel Section

9.3 Non-Dimensional Forms of the Conveyance Curves

9.4 Problems of Uniform Flow Computation

9.5 Calculation of Normal Depth or Uniform Flow Depth

9.6 Hydraulic Exponent (N) for Uniform Flow Computation

9.7 Graphical Method to Find Hydraulic Exponent

**Chapter 10 APPLICATION OF ENERGY PRINCIPLE**

10.1 Energy Principle for Open Channel Flow

10.2 Specific Energy (or Specific Energy Head)

10.2.1 Specific Energy Curve or Variation of Specific Energy (Q = Constant)

10.3 Criterion for Critical State of Flow(Constant Discharge Situation)

10.3.1 Mathematical Expression for Critical Depth for Different Channel Sections

10.3.2 Mathematical Expression for Critical Velocity in a Rectangular Section

10.3.3 Mathematical Expression for Minimum Specific Energy in Terms of Critical

Depth for Rectangular Section

10.3.4 Discharge Diagram

10.3.5 Condition for Maximum Discharge for a Given Value of Specific Energy

10.4 Computation of Critical Flow

10.5 Hydraulic Exponent for Critical Flow Computation

10.6 Open Channel Transitions

10.6.1 Channel Transition from a Wider to a Narrower Channel (Throat) without

Change in Bed Level

10.6.2 Channel Transition without Change in Width but with Rise in Bed Level

**Chapter 11 GRADUALLY VARIED FLOW**

11.1 Introduction

11.2 Assumptions of Gradually Varied Flow

11.3 Dynamic Equations of Gradually Varied Flow

11.4 Different Forms of the Dynamic Equations

11.5 Recap of Section Factor, Conveyance and Hydraulic Exponents M and N

11.6 General Expression for Hydraulic Exponents M and N

11.7 Continuation of Different Forms of Gradually Varied Flow Equations

11.8 Classification of Channel Slopes and Flow Conditions

11.9 Classification of Flow Profiles

11.10 Classification of Surface Profiles

**Chapter 12 GRADUALLY VARIED FLOW COMPUTATION**

12.1 Introduction

12.2 Computation of Gradually Varied Flow

12.3 Graphical Integration Method

12.4 Numerical Integration Method

12.5 Direct Integration Method

12.6 Bresse’s Method

12.7 Bakhmeteff’s Method

12.8 Vente Chow’s Method

12.9 Direct Step Method

12.10 Standard Step Method

**Chapter 13 APPLICATION OF MOMENTUM PRINCIPLE**

13.1 Momentum Principle in Open Channel

13.2 Specific Force

13.2.1 Expression for Specific Force

13.3 Criterion for Critical State of Flow

13.4 Interpretation of Local Phenomena

13.5 Types of Hydraulic Jump (USBR Classification)

13.6 Analysis of the Hydraulic Jump

13.7 Hydraulic Jump in a Horizontal Rectangular Channel

13.7.1 Relation between Pre Jump and Post Jump Froude Numbers

13.8 Loss of Energy due to Hydraulic Jump

13.8.1 Height and Length of the Jump

13.8.2 Length of the Jump

13.8.3 Power Lost

13.8.4 Relative Loss (ΔE/E1)

13.8.5 Efficiency of the Hydraulic Jump (η)

13.9 Hydraulic Jump in a Triangular Channel

13.10 Gauging Flumes

13.10.1 Non-modular Flume or the Venturi Flume

13.10.2 Modular Flume or the Standing Wave Flume

**Chapter 14 REVIEW OF PUMPS**

14.1 Introduction

14.1.1 Selection of Centrifugal Pumps based on Specific Speed

14.2 Pump Classification

**Chapter 15 CENTRIFUGAL PUMP**

15.1 Introduction to Centrifugal Pumps

15.2 Priming of a Centrifugal Pump

15.3 Main Parts of a Centrifugal Pump

15.3.1 Working of a Centrifugal Pump

15.3.2 Operational Difficulties in Centrifugal Pumps and their Remedies

15.4 Classification of Centrifugal Pumps

15.4.1 Casing

15.4.2 According to Relative Direction of Flow through Impeller

15.4.3 Number of Entrances to the Impeller

15.4.4 According to Working Head

15.5 Classification of Impeller

15.5.1 Shrouded or Closed Impeller

15.5.2 Semi-open Impeller

15.5.3 Open impeller

15.6 Comparison of Properties of Impeller and Displacement Type Pumps

15.7 Radial Flow Between two Parallel Discs

15.8 Circulation of Velocity around a Closed Circuit

15.9 Circulation of Velocity in an Impeller Pump

15.10 Flows Through Straight Conduits of Constant Cross Section

15.11 Flows Through Closed Conduits with a Variable Cross Section and a Curved Centre

Line

15.12 Velocity Distribution in Nozzles and Diffusers

15.13 Expression for the Work Done on the Impeller/Fundamental Equation of a Centrifugal

Pump

15.13.1 Working Proportions of Centrifugal Pump

15.14 Head Capacity Relationship

15.15 Pressure Changes in Centrifugal Pump

15.16 Ideal Efficiency of a Pump

15.17 Maximum Suction Lift

15.18 Definitions of Heads and Efficiencies of a Centrifugal Pump

15.18.1 Head of a Pump

15.18.2 Efficiencies of Centrifugal Pump

15.19 Minimum Starting Speed

15.20 Shut-Off Head

15.21 Pump Laws

15.22 Effect of Variation in Speed

15.23 Specific Speed

15.23.1 Expression for Specific Speed for a Pump

15.24 Pump Similarity

15.25 Characteristic Curves of Centrifugal Pumps

15.25.1 Main Characteristic Curves

15.25.2 Operating Characteristics

15.25.3 Constant Efficiency Curves

15.25.4 Constant Head and Constant Discharge Curves

15.26 Multistage Centrifugal Pump

15.26.1 Multistage Centrifugal Pump for High Heads

15.26.2 Multistage Centrifugal Pump for High Discharge

15.27 Effect of Number of Blades

15.28 Net Positive Suction Head (NPSH)

15.29 Cavitation in Pumps

15.30 Head Lost Due to Changes in Discharge

**Chapter 16 POSITIVE DISPLACEMENT PUMPS**

16.1 Introduction

16.2 Types of Reciprocating Pump

16.3 Working of a Reciprocating Pump

16.4 Theory of the Reciprocating Pump

16.4.1 Discharge of Reciprocating Pump

16.5 Simple Indicator Diagram

16.6 Effect of Acceleration

16.7 Maximum Speed of the Rotating Crank of a Reciprocating Pump

16.8 Effect of Acceleration and Friction

16.9 Effect of Air Vessel

16.10 Work Saved by Fitting Air Vessel

16.11 Multiple Cylinder Pumps

16.11.1 Double Cylinder Pump

16.11.2 Triple Cylinder Pump

16.12 Performance Characteristics

**Chapter 17 HYDRAULIC MACHINES−TURBINES**

17.1 Introduction

17.2 Classification of Turbines

17.3 Layout of a Hydro-Electric Power Plant

17.4 Definitions of Heads

17.4.1 Head Loss due to Friction

17.4.2 Head Loss in the Nozzle

17.5 Power Produced by a Turbine

17.6 Efficiencies of a Turbine

**Chapter 18 PELTON WHEEL TURBINE**

18.1 Component Parts of Pelton Wheel

18.2 Velocity Triangle and Work Done for Pelton Wheel

18.3 Working Proportion of a Pelton Wheel

18.4 Radial Flow Impulse Turbine

**Chapter 19 REACTION TURBINE-FRANCIS TURBINE**

19.1 Reaction Turbine

19.2 Classification of Reaction Turbine

19.3 Main Components of a Radial Flow Reaction Turbine

19.3.1 Draft Tube Theory

19.4 Expression for Work Done in an Inward Radial Flow Turbine

19.5 Outward Flow Reaction Turbine

19.6 Mixed Flow Turbine

19.7 Power and Efficiency

19.8 Runaway Speed

19.9 Surge Tanks

**Chapter 20 AXIAL FLOW REACTION TURBINE-KAPLAN TURBINE**

20.1 Propeller Turbine and Kaplan Turbine

**Chapter 21 PERFORMANCE OF HYDRAULIC TURBINES**

21.1 Performance of Hydraulic Turbines

21.2 Performance Under Unit Head-Unit Quantities

21.3 Performance Under Specific Conditions

21.4 Characteristics of Turbines

21.5 Cavitation

21.6 Governing of Turbines

21.6.1 Governing of Pelton Wheel Turbine

21.6.2 Governing of Reaction Turbines

**• Index**

## About The Author

**P N Chandramouli** is Professor, Department of Civil Engineering, The National Institute of Engineering, Mysore. He received his B.E in Civil Engineering from University of Mysore, M.E from Indian Institute of Science, Bangalore and Ph.D from Indian Institute of Technology, Roorkee. He has over 30 years of teaching experience at The National Institute of Engineering. He is a life member of ISTE and ACCE.

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