Preface to the first edition

Mochica (1) South American civilization (AD 200-1000) living in the Moche River Valley, Peru along the Pacific coastline; (2) The language of Yuncas. Known for the visit of the Queen of Sabah (or Sheba) to the King of Israel around 950 BC and for the construction of the Marib Dam (115 BC to 575 AD).

Fig. 1.1. Flow beneath a sluice gate: which is the correct free-surface profile?

List of symbols

Tij component of the shear stress (Pa) of /-momentum transport in the direction of the average shear stress (Pa). TO)C critical shear stress (Pa) for initiation of sediment movement TQ skin fiiction shear stress (Pa). Bed shear stress (Pa) Ti yield stress (Pa). T*)C critical Shields parameter for initiation of sediment movement Subscript.

Introduction

PRESENTATION
FLUID PROPERTIES
STATIC FLUIDS
OPEN CHANNEL FLOW .1 Definition

Applications
Discussion

EXERCISES

When considering a fluid at rest (Fig. 1.1), the pressure at any point in the fluid follows Pascal's law. For an air-water mixture flow (called 'white water') the definition of the free surface (i.e. the interface between the flowing mixture and the surrounding atmosphere) becomes somewhat complicated (e.g. Wood, 1991; Chanson, 1997) .

Fig. 1.1 Pressure variation in a static fluid.

Fundamental equations

INTRODUCTION
THE FUNDAMENTAL EQUATIONS .1 Introduction

The continuity equation
The momentum equation The Navier-Stokes equation

The fundamental equations 15

The energy equation

EXERCISES

In equation (2.9), the term on the left is the sum of the momentum accumulation d(pV)/dt plus the momentum flux Vd(pV)/dx. The energy of the system is the sum of (1) the potential energy term gz, (2) the kinetic energy term F^/2 and (3) the internal energy e.

Fig. 2.1 Sketch of control volume for a two- two-dimensional flow.

Applications of the Bernoulli equation to open channel flows

INTRODUCTION

APPLICATION OF THE BERNOULLI EQUATION - SPECIFIC ENERGY .1 Bernoulli equation

Influence of the velocity distribution Introduction
Specific energy Definition
Limitations of the Bernoulli equation

The kinetic energy term F^/2g is very small and the specific energy tends to the flow depth d (i.e. the asymptote E = d). The upstream and downstream values of the specific energy are equal (by applying Bernoulli's equation).

Fig. 3.1 Sketch of open chan- chan-nel flow: (a) general case and (b) steep channel flow

FROUDE NUMBER .1 Definition

Similarity and Froude number
Critical conditions and wave celerity
Analogy with compressible flow
Critical flows and controls

In all flow situations where the gravitational effects are significant, the appropriate dimensionless number (that is, the Froude number) should be considered. The main limitations of the compressible flow/open channel flow analogy are: a) The specific heat ratio must be equal to 2. As a result, the Froude number increases and when Fr = I critical flow conditions arise for a channel width B^^ ^^.

Fig. 3.9 Overflow above a broad-crested weir (weir height: 0.067 m, channel width: 0.25 m, crest length: 0.42 m):

PROPERTIES OF COMMON OPEN-CHANNEL SHAPES .1 Properties

Critical flow conditions

As a result, the Froude number decreases and when Fr = I critical flow conditions occur for a particular channel width downstream ^min-. With B

EXERCISES

Application: The upstream flow conditions are: di = 0.05 m, Bi = lm, Q = 101/s and the downstream channel width is B2 = 0.8 m. Calculate the downstream flow depth and the downstream Froude number. Flow depth above the weir Upstream specific energy Velocity above the crest Specific energy above the crest Downstream flow depth Downstream Froude number Downstream specific energy. We will assume that critical flow conditions (and hydrostatic pressure distribution) occur at the top of the weir (i.e. section 2).

Applications of the momentum principle: hydraulic jump, surge

MOMENTUM PRINCIPLE AND APPLICATION .1 Introduction

Momentum principle
Momentum function

Calculate the pressure force acting on the vertical face of the step and indicate the direction of the force (ie upstream or downstream). The downstream depth is derived from the definition of specific energy (in a rectangular channel assuming a hydrostatic pressure distribution): .. where B is the channel width. The solution to the moment equation is F = +205 kN (recall F is the force exerted by the step on the fluid).

Fig. 4.1 Application of the momentum equation to a negative step.

HYDRAULIC JUMP .1 Presentation

Basic equations
Discussion Types of hydraulic jump

-Baptiste Belanger was the first to propose the application of the momentum principle to hydraulic jump flow (Belanger, 1828). Recent studies have shown that the flow properties (including air entrainment) of hydraulic jumps are functions not only of the upstream Froude number, but also of the upstream flow conditions: for example, Chov^ (1973) has proposed some guidelines for determining the roll length of hydraulic estimate jumps. jump as a function of upstream flow conditions.

Fig. 4.2 Hydraulic jump in a natural waterway: Bald Rock Creek at the Junction Qld,Australia (9 November 1997)-flowfrom the left to the right

SURGES AND BORES .1 Introduction

Equations
Discussion
Positive and negative surges Definitions

-STEADY FLOW ANALOGY Positive wave. as seen by an observer traveling at peak velocity). Note that Fg^g must be greater than Vx as the wave moves downstream in the direction of the initial current. For an observer traveling with the flow upstream of the wavefront (that is, at a velocity Fj), the velocity of the wave (relative to the upstream flow) is:

Fig. 4.7 Photograph of tidal bore. Tidal bore at Truro, Nova Scotia, Canada (Courtesy of Larry Smith) -Cobequod Bay (Indian name), being called Salmon River upstream - looking downstream at the incom-ing bore

FLOW RESISTANCE IN OPEN CHANNELS .1 Presentation and definitions

Another difference is the driving force acting in the direction of the flow, in closed pipes, the flow is driven by a pressure gradient along the pipe, while, in open channel flows, the fluid is pushed by the weight of the water flowing loosely down a slope. The author of the present text believes that it is preferable to use the hydraulic diameter instead of the hydraulic radius, since the calculations of the fixation factor are made with the hydraulic diameter (and not the hydraulic radius). A graphical solution of the Colebrook-White formula is the Moody diagram (Moody, 1944) given in Fig.

IMI \

34;"K J TfLI

Flow resistance of open channel flows

Equation (4.19b) is not valid for non-uniform equilibrium flows, for which equation (4.22) must be used. The Chezy equation is valid for uniform equilibrium and nonuniform (gradually varied) turbulent flows. The Gauckler-Manning equation is valid for uniform equilibrium and non-uniform (gradually varied) flows.

Fig. 4.11 Application of the momentum equation to uni-form equilibrium open channel flow

FLOW RESISTANCE CALCULATIONS IN ENGINEERING PRACTICE .1 Introduction

Selection of a flow resistance formula
Flow resistance in a flood plain

Note: Because the flow is not exactly rough turbulent, the Gauckler-Manning equation should not be used. Note: Since the flow is not rough and turbulent, the Gauckler-Manning equation should not be used. Estimate the uniform equilibrium flow depth using both the Darcy friction factor and the Gauckler-Manning coefficient (if the flow is rough and turbulent).

Fig. 4.12 Examples of natural rivers and flood plains, (a) Lance Creek and it's flood plain, looking upstream (by H.E

EXERCISES Momentum equation

The bed of the channel is horizontal and smooth (both upstream and downstream of the weir). Considering a river channel with a floodplain on each side (Fig. E.4.3), the river channel is lined with precast concrete. The left bank plain (Flood Plain No. 2) is a grass area (millipede grass, ^Manning ~ 0-06 SI units). The longitudinal bed slope of the river is 3.2 m/km.

Uniform flows and gradually varied flows

UNIFORM FLOWS .1 Presentation

Uniform flows 95

Discussion Mild and steep slopes
Uniform flow depth in non-rectangular channels

Even in artificial channels of uniform cross-section (e.g. Figs. 5.1 and 5.2), the occurrence of uniform flows is not effective due to the existence of controls (e.g. weirs and locks) that determine the relationship between depth and discharge . Since the normal depth is greater than the critical depth, the uniform equilibrium flow is subcritical. Since the normal depth is greater than the critical depth, the channel slope is gentle.

Fig. 5.1 Cross-sections of maximum flow rate: i.e.

NON-UNIFORM FLOWS .1 Introduction

Equations for GVF: backwater calculation
Discussion
Backwater computations

It is customary to designate d true depth (i.e. non-uniform flow depth), d^ normal depth (i.e. uniform flow depth), and d^ critical depth. An example is the flow downstream of a lock gate in a steep embankment when the gate opening is smaller than normal depth. The uplift profiles are obtained by combining the differential equation (5.6), the drag calculations (i.e. fictional slope) and the boundary conditions.

Figure 5.3 illustrates typical longitudinal free-surface profiles. Upstream and downstream control can induce various flow patterns

EXERCISES

Note: If steady flow conditions are subcritical, a transition from supercritical to subcritical flow is expected between the end of the flow and the end of the channel. In the channel downstream of the spillway, the first calculations predict the occurrence of a hydraulic jump. In this case, we can assume that the flow depth behind the hydraulic jump is equal to the uniform flow depth.

Revision exercises

Calculate and state the values (and units) of the indicated quantities in the following list:. Calculate and state the values (and units) of the following quantities:. f) Current velocity at section 2. The channel bed is horizontal and smooth (both upstream and downstream of the step).

Appendices to Part 1

For a perfect gas, the specific heat at constant pressure Cp and the specific heat at constant volume Cy are related to the gas constant as:. A fluid's compressibility is a measure of the change in volume and density when the fluid is subjected to a change in pressure. Unit symbols are written in lowercase letters (ie m for metres, kg for kilos), but a capital is used for the first letter when the name of the unit is derived from a surname (eg

Table Al.l Distributions of air temperature and air pressure as fiinctions of the altitude (for dry air and standard acceleration of gravity)

A1.3.3 Differential and differentiation

In the latter case, the two possible current depths d' and d" are called alternating depths (Fig. Al. 1).

Fig. A1.1 Definition sketch: alternate depths across a sluice gate.

Introduction to sediment transport in open channels

INTRODUCTION
SIGNIFICANCE OF SEDIMENT TRANSPORT .1 Sediment transport in large alluvial streams

Failures caused by sediment-transport processes

TERMINOLOGY
STRUCTURE OF THIS SECTION
EXERCISES

In the early 1960s, the restoration of the railway line to Mount Isa (a mining town in the Australian desert) required the construction of several bridges over streams. Bridges have collapsed due to the inability of (overseas) engineers to understand local hydrology and associated sediment movement. In the 2nd part, the material of the lectures is grouped into a series of definitions (Chapter 7), basic concepts of sediment movement (Chapters 8 and 9), calculations of sediment transfer capacity. Chapters 10 and 11) and applications to natural alluvial flows, including the concepts of erosion, accretion, and bed movement (Chapter 12).

Fig. 6.1 Aerial view of Camas Creek flowing into the North Fork of the Flathead River, Montana, USA (12 July 1981) (by P

Sediment transport and sediment properties

BASIC CONCEPTS .1 Definitions

Bed formation

The channel forms to the left after a maximum flow of 8000 m^/s-flow from left to right, (e) Gravel counterbank at Brigalow Bend, Burdekin River, Australia August 1995 (courtesy of Dr C. Fielding). The bed is formed after a maximum flow of 8000 m^/s - viewed downstream, with a dug observation ditch in the foreground. Anticips and standing waves are rarely seen in natural streams because channel shapes are often not preserved between flood retreat stages.

Fig. 7.1 Bed forms in movable boundary hydraulics: (a) typical bed forms and (b) bed form motion

PHYSICAL PROPERTIES OF SEDIMENTS .1 Introduction

Property of single particles
Properties of sediment mixture The density of a dry sediment mixture equals
Particle size distribution

The nominal diameter is the size of a sphere of the same density and mass as the actual particle. It is defined as the ratio of the weight of the sediment to the weight of the mixture of water and sediment, multiplied by a million. The characteristic sediment size d^Q is defined as the size at which 50 wt. % of finer material.

Table 7.2 Sediment size classification Class name

PARTICLE FALL VELOCITY .1 Presentation

Settling velocity of a single particle in still fluid

The buoyant force on a submerged body is the difference between the vertical component of the pressure force on its lower side and the vertical component of pressure on its upper side. Since the pressure below him/her is greater than that directly above, a reaction force (i.e. buoyancy force) acts on the diver in a vertical direction. In the balance of forces, the drag force is opposite to the direction of motion of the particles, and the buoyant force is positive (upward).

Table 7.3 Computed settling velocity of sediment particles in still water (equation (7.10))

I k QAyp

Effect of sediment concentration
Effect of turbulence on the settling velocity
ANGLE OF REPOSE
LABORATORY MEASUREMENTS .1 Particle size distribution

Concentration of suspended sediments

EXERCISES Bed forms

Nielsen (1993) suggested that the fall velocity of sediment particles increases or decreases depending on the turbulence intensity, the particle density, and the characteristic length scale and time scale of the turbulence. The angle of repose is a function of the particle shape, and on a flat surface it increases with angularity. Calculate (and give units) (a) the porosity of the sand mixture and (b) the wet density of the mixture.