Unit 421-316 Engineering Hydrology
421-316 Engineering Hydraulics and Hydrology
December 11, 2005
Open channel hydraulics
John Fenton
Department of Civil and Environmental Engineering
University of Melbourne, Victoria 3010, Australia
Abstract
This course of 15 lectures provides an introduction to open channel hydraulics, the generic name for the study of flows in rivers, canals, and sewers, where the distinguishing characteristic is that the surface is unconfined. This means that the location of the surface is also part of the problem, and allows for the existence of waves – generally making things more interesting!
At the conclusion of this subject students will understand the nature of flows and waves in open channels and be capable of solving a wide range of …show more content…
This reminds us that we are obtaining approximate solutions to approximate problems, but it does allow some simplifications to be made.
The basic approximation in open channel hydraulics, which is usually a very good one, is that variation along the channel is gradual. One of the most important consequences of this is that the pressure in the water is given by the hydrostatic approximation, that it is proportional to the depth of water above.
In Australia there is a slightly non-standard nomenclature which is often used, namely to use the word
”channel” for a canal, which is a waterway which is usually constructed, and with a uniform section.
We will use the more international English convention, that such a waterway is called a canal, and we will use the words ”waterway”, ”stream”, or ”channel” as generic terms which can describe any type of irregular river or regular canal or sewer with a free surface.
1.1 Types of channel flow to be studied
(a) Steady uniform flow dn d n Normal depth
(b) Steady gradually-varied flow
(c) Steady rapidly-varied …show more content…
In most hydraulic applications the discharge is a more important quantity than the velocity, as it is the volume of water and its rate of propagation, the discharge, which are important.
1.2.2 A generalisation – net discharge across a control surface
Having obtained the expression for volume flux across a plane surface where the velocity vector is normal to the surface, we introduce a generalisation to a control volume of arbitrary shape bounded by a
ˆ
control surface CS. If u is the velocity vector at any point throughout the control volume and n is a unit vector with direction normal to and directed outwards from a point on the control surface, then u · n on
ˆ
the control surface is the component of velocity normal to the control surface. If dS is an elemental area of the control surface, then the rate at which fluid volume is leaving across the control surface over that
5
Open channel hydraulics
John Fenton
elemental area is u · n dS , and integrating gives
ˆ
Total rate at which fluid volume is leaving across the control surface =
Z
CS
(1.1)
u · n dS.
ˆ
If we consider a finite length of channel as shown in Figure 1-3, with the control surface made up of
ˆ
n1
December 11, 2005
Open channel hydraulics
John Fenton
Department of Civil and Environmental Engineering
University of Melbourne, Victoria 3010, Australia
Abstract
This course of 15 lectures provides an introduction to open channel hydraulics, the generic name for the study of flows in rivers, canals, and sewers, where the distinguishing characteristic is that the surface is unconfined. This means that the location of the surface is also part of the problem, and allows for the existence of waves – generally making things more interesting!
At the conclusion of this subject students will understand the nature of flows and waves in open channels and be capable of solving a wide range of …show more content…
This reminds us that we are obtaining approximate solutions to approximate problems, but it does allow some simplifications to be made.
The basic approximation in open channel hydraulics, which is usually a very good one, is that variation along the channel is gradual. One of the most important consequences of this is that the pressure in the water is given by the hydrostatic approximation, that it is proportional to the depth of water above.
In Australia there is a slightly non-standard nomenclature which is often used, namely to use the word
”channel” for a canal, which is a waterway which is usually constructed, and with a uniform section.
We will use the more international English convention, that such a waterway is called a canal, and we will use the words ”waterway”, ”stream”, or ”channel” as generic terms which can describe any type of irregular river or regular canal or sewer with a free surface.
1.1 Types of channel flow to be studied
(a) Steady uniform flow dn d n Normal depth
(b) Steady gradually-varied flow
(c) Steady rapidly-varied …show more content…
In most hydraulic applications the discharge is a more important quantity than the velocity, as it is the volume of water and its rate of propagation, the discharge, which are important.
1.2.2 A generalisation – net discharge across a control surface
Having obtained the expression for volume flux across a plane surface where the velocity vector is normal to the surface, we introduce a generalisation to a control volume of arbitrary shape bounded by a
ˆ
control surface CS. If u is the velocity vector at any point throughout the control volume and n is a unit vector with direction normal to and directed outwards from a point on the control surface, then u · n on
ˆ
the control surface is the component of velocity normal to the control surface. If dS is an elemental area of the control surface, then the rate at which fluid volume is leaving across the control surface over that
5
Open channel hydraulics
John Fenton
elemental area is u · n dS , and integrating gives
ˆ
Total rate at which fluid volume is leaving across the control surface =
Z
CS
(1.1)
u · n dS.
ˆ
If we consider a finite length of channel as shown in Figure 1-3, with the control surface made up of
ˆ
n1