CVEN90051 CIVIL HYDRAULICS

Learning objectives

To revise previous knowledge acquired during Fluid Mechanics and consolidate basic understanding of flow in open channels. Specifically:

•       To understand the fundamental concepts of uniform flow

•       To understand the concept of normal depth

•        To know how to apply Manning’s equation to analyse flow in simple and compound channels

•        Identify regions of critical, subcritical & supercritical flow in field situations.

•         Use the specific energy concept to explain transitions between critical, subcritical & supercritical flow.

•         Explain and quantify the effect of channel structures and transitions on water depths.

Introduction

“Fluid mechanics” is the general title given to the study of all aspects of the behaviour of fluids which are relevant to engineers. Within this very broad discipline, a number of subsections have developed. Of these subsections, hydraulics is the branch which concentrates on the study of liquids. Civil engineers are largely, though not exclusively, concerned with one liquid, namely water. The development of the industrial society rests largely on the ability of civil engineers to provide adequate water services, such as the supply of potable water, drainage, flood control, etc. An efficient network of water service would rely on open channel flow, which refers to the flow of liquids in channels open to the atmosphere or in partially filled conduits and is characterized by the presence of a liquid–gas interface called the free surface.

FOOD-FOR-THOUGHT: Is potable water distributed through open channel flow? Yes, no? Why? FOOD-FOR-THOUGHT: Are sewer lines open channels? Yes, no? Why?

The most natural flows encountered in practice are the flow of water in creeks, rivers, and floods, as well as the draining of rainwater off highways,  parking  lots, and roofs.  Human-made open channel flow systems include irrigation systems, sewer lines, drainage ditches, and gutters, and the design of such systems is an important application area of engineering.  Module#1  will focus on hydraulic  structures. These are structures that are fully or partially submerged in water to either divert, disrupt, store, or completely stop the natural flow of water bodies.

QUESTION: Can you name a hydraulic structure?

To design any type of hydraulics structure (see an example of structure in Figure 1 belwo), you would need an accurate knowledge of the environmental conditions, i.e. the water flow. This knowledge includes water velocity, water  level  (depth),  discharge,  etc …  You  have  studied  most  of  the  key  properties  of  open channel flows  in  the  subject “Fluid  Mechanics”,  remember?  You  will  need  this  past  knowledge  to  survive Module#1. The objective of the firt week of the subject (Topic 1) is to refresh your knowledge of open channel flow.

Figure 1: Weir in river

Questions to guide your reading

•    What is uniform flow?

•    What is the hydraulic radius, R?

•    In uniform flow, what determines the depth of water in the channel?

•     How do Chezy C and Manning’s n relate?

•     Is Manning’s n a constant at a given site?

•     Can the Manning equation be used in a compound channel? in a natural channel?

•     What is the Froude number, and how is relevant to open channel flow? What is the value of the Froude number for subcritical, critical and supercritical flows?

•     How do we calculate the critical depth in open channel flow?

•     What is specific energy? How is it different from total energy? How does the specific energy of a channel flow vary with the depth?

•     Why does the water surface dip over a hump in the channel bed? Does it always do this?

Reading guide

The purpose of the reading guide is to (i) highlight contents that are fundamental for the subject (i.e. contents that you need to  study and   understand well), (ii) identify contents that are marginal  and   can be  studies more superficially and, if necessary, (iii) provide further explanation on contents that we believe are not well explained in the reading material. Occasionally, the guide may provide extra information to complement the reading. What this guide does NOT is to explain contents in the reading material. This will be done during lectures and consultations.

The reading material is the primary source to understand the subject. The material for Topic #1 is available through “Reading Online”  in   LMS.  The   material  is  extrapolated  from  the  textbook:   Hamill,   L.,  2011.  Understanding hydraulics. Macmillan International Higher Education. Read part on uniform Flow pp. 226-266.

NOTE: Topic#1  is  a  revision  of  a  prerequisite.  Therefore,  you  may  already  have  useful material  from  the Fluid Mechanics subject. If you want to use your own material to refresh your knowledge, that is fine.

The first concept that you should refresh is that of uniform flow (Section 8.1.1). In open channels of constant slope and constant cross section, the liquid accelerates until the head loss due to frictional effects equals  the  elevation  drop.  The   liquid  at  this   point  reaches  its  terminal  velocity,  and   uniform flow  is established (see schematic in figure 2 below). The flow remains uniform as long as the slope, cross section and  surface  roughness  of  the  channel  remain  unchanged.  The  flow  depth  in  uniform  flow  is called  the normal depth. (Normal Depth is denoted as D in suggested reading materis). In other words, normal depth occurs when gravitational force of the water is equal to the friction drag and there is no acceleration of flow .

Figure 2: From non-uniform to uniform flow.

FOOD-FOR-THOUGHT: So, what is a non-uniform flow?

Cross  section  of  a  channel  can   be  anything  from  a  simple   rectangular  shape  to  very  complex geometry. Key geometrical properties are introduced in Section 8.1.2. The variable that you need are:

•    Cross section area: A;

•    Wetted perimeter (the length of contact between water and the channel): P;

• The hydraulic radius: R = A / P;

•    The surface width of the water in the channel: Bs

•    The  hydraulic  mean  depth (mean depth of flow in an irregular, non-rectangular channel where the depth varies across the width of the cross-section): DM = A / Bs;

•     Bed slope S0.

SUGGESTION:  Should  you   remember  the  symbol  of  the  variable   (A,  B, a,  etc   …)  or  the  concept?   My experience tells me that you are doomed if you try to remember the symbol only! Any book, lecture material, tutorial, paper, etc … introduces its own symbol for the same variable. Do not get confused if, for example, you encounter water depth expressed as D or d or h or whatever.  It  is fundamental you  understand  the meaning of the variable.

NOTE: Look at how I presented the variables above. I called all variables that are needed, defining both the simplest  (the  area  of  the   cross  section)  and  the   more  complex  (e.g  the  hydraulic  radius  which  is  a combination  of  different  variables).   If  you  state  the   name  of  your  variables  at  the   beginning  of  your assignment, report, exercise, etc … any reader understands!

Besides geometrical parameters, there is a variable that play a fundamental role in hydraulics. This

is the Froud Number:

where V is the water velocity and g is the acceleration due to gravity. The reason why the Froud Number is fundamental will become clear later.

If you have a cross section and have a water depth, how much water can be discharged over the unit time? To answer this question, you will need to compute the discharge Q = A V. So, the question shifts to: what is the water velocity? This can be calculated with the Chezy equation:

where C is the Chezy coefficient. (See details in Section 8.2.1).

NOTE: I often receive the feedback that a book published in e.g. 1990 is outdated. Is it really??? The Chezy equation was derived by Antoine Chézy sometime in the 18th  century. All fundamentals knowledge for civil hydraulics was derived centuries ago. So, any book you use to study hydraulics is definitively not outdated!

In 1890, the Irish engineer Robert Manning proposed a modification of the Chezy equation that is used is still currently used to compute the water velocity (Section 8.2.1):

The coefficient n is the Manning’s coefficient and it incorporate effect of surface roughness into the computation of the velocity. Table 1 below provides values for this coefficient.

Table 1: Typical values of Manning’s n for different types of surface

What about discharge? It can be computed easily following the Manning’s equation:

So, if you want to compute the discharge Q give a water depth, this is easy right? If you want to compute the water depth given a discharge?? This si not so easy as water depth appears at both side of the equal in the equation above. Details to compute the depth are reported in Section 8.2.3. If the cross section is a wide rectangular geometry, calculation is straightforward. If not, a trial-and-error method is need.

TRIAL-AND-ERROR: This is the favourite method to solve many problems in hydraulics. Get familiar with it!

What is the best cross section to get the maximise the discharge? This is discussed in Section 8.3.

Section 8.4 discusses compound sections. These are cross section of complex geometry.  In  my view the topic discussed in this rection is straightforward. But revise it, if you don’t remember it clearly.

Section 8.5 is interesting, but not fundamental.

Section 8.6 introduces a fundamental concept: specific energy and critical depth. So, make sure you revise this section well as it will be critical for understanding topics of Module#1. The section start with the concept of specific energy (E):

where the coefficient a = 1. Note that the specific energy is similar to the total energy head, but with the omission of the “z” term  because specific energy (head) is calculated above the bed of the channel not above an arbitrary datum. This makes the specific energy much more manageable.

The  specific  energy  allows  introducing  a  key  graph,  which  is  reported  in figure  8.6. This  is  a fundamental tool to identify between critical, subcritical and supercritical flows and transitions between them.

NOTE: Specific energy and figure 8.6 will  return  in  Topic  2, when  we will  discuss  how  to  compute the different water profiles in the proximity of obstacles and hydraulics structure.

SUGGESTION:  Pay  attention to the figure  below  (extracted  from figure 8.17).  It  shows water across an obstacle. How does the water profile change above the obstacle? To answer this question you will need to consider changes to specific energy and correlate them to figure 8.6.

Figure 3: Water surface above a locally raised bed.

Section 8.7 explains how to compute the critical depth. For a given discharge, this is the depth of minimum specific energy; or, for a given specific energy, is the depth of maximum discharge. Calculating the critical depth is the first step towards understanding whether you flow is super or sub critical.

FOOD-FOR-THOUGHT:   Undeniably,  you   have  come  across  the  concept  of   hydraulic  jump.   Do  you remember what is it? This will be discussed in the next topic. Although it is part of your prerequisite, the hydraulic jump will be fundamental in many hydraulic structures. So, it will be revised in Topic 2.