This document discusses open channel flow, which is the flow of liquid through a conduit with a free surface driven only by gravity. It compares open channel flow to pipe flow, describes different types of open channel flows, parameters used in analysis like hydraulic radius and Froude number, and formulas like Chezy's and Manning's equations used to analyze open channel flow characteristics. Examples are provided to demonstrate how to apply these concepts and formulas to calculate quantities like velocity, discharge, slope, and critical depth in open channel flow problems.
Uniform Flow: Basic concepts of free surface flows,
velocity and pressure distribution,
Mass, energy and momentum principle for prismatic and non-prismatic channels,
Review of Uniform flow: Standard equations,
hydraulically efficient channel sections,
compound sections,
Energy-depth relations:
Concept of specific energy, specific force,
critical flow, critical depth,
hydraulic exponents, and
Channel transitions.
Uniform Flow: Basic concepts of free surface flows,
velocity and pressure distribution,
Mass, energy and momentum principle for prismatic and non-prismatic channels,
Review of Uniform flow: Standard equations,
hydraulically efficient channel sections,
compound sections,
Energy-depth relations:
Concept of specific energy, specific force,
critical flow, critical depth,
hydraulic exponents, and
Channel transitions.
PPT contains
Open Channel Flow-Comparison between open channel flow and pipe flow,
geometrical parameters of a channel,
classification of open channels, classification of open channel flow,
Velocity Distribution of channel section.
Uniform Flow-Continuity Equation,
Energy Equation and Momentum Equation,
Characteristics of uniform flow,
Chezy’s formula, Manning’s formula.
Computation of Uniform flow.
Specific energy, critical flow, discharge curve,
Specific force, Specific depth, and Critical depth.
Measurement of Discharge and Velocity – Broad Crested Weir.
Gradually Varied Flow Dynamic Equation of Gradually Varied Flow.
Hydraulic Jump and classification - Elements and characteristics- Energy dissipation.
Uniform Flow: Basic concepts of free surface flows,
velocity and pressure distribution,
Mass, energy and momentum principle for prismatic and non-prismatic channels,
Review of Uniform flow: Standard equations,
hydraulically efficient channel sections,
compound sections,
Energy-depth relations:
Concept of specific energy, specific force,
critical flow, critical depth,
hydraulic exponents, and
Channel transitions.
An open channel is a conduit in which a liquid flows with a free surface.
The free surface is actually an interface between the moving liquid and an overlying fluid medium and will have constant pressure.
In civil engineering applications; water is the most common liquid with air at atmospheric pressure as the overlying fluid.
The prime motivating force for open channel flow is gravity.
An open channel is a conduit in which a liquid flows with a free surface.
The free surface is actually an interface between the moving liquid and an overlying fluid medium and will have constant pressure.
In civil engineering applications; water is the most common liquid with air at atmospheric pressure as the overlying fluid.
The prime motivating force for open channel flow is gravity.
An open channel is a conduit in which a liquid flows with a free surface.
The free surface is actually an interface between the moving liquid and an overlying fluid medium and will have constant pressure.
In civil engineering applications; water is the most common liquid with air at atmospheric pressure as the overlying fluid.
The prime motivating force for open channel flow is gravity.
PPT contains
Open Channel Flow-Comparison between open channel flow and pipe flow,
geometrical parameters of a channel,
classification of open channels, classification of open channel flow,
Velocity Distribution of channel section.
Uniform Flow-Continuity Equation,
Energy Equation and Momentum Equation,
Characteristics of uniform flow,
Chezy’s formula, Manning’s formula.
Computation of Uniform flow.
Specific energy, critical flow, discharge curve,
Specific force, Specific depth, and Critical depth.
Measurement of Discharge and Velocity – Broad Crested Weir.
Gradually Varied Flow Dynamic Equation of Gradually Varied Flow.
Hydraulic Jump and classification - Elements and characteristics- Energy dissipation.
Uniform Flow: Basic concepts of free surface flows,
velocity and pressure distribution,
Mass, energy and momentum principle for prismatic and non-prismatic channels,
Review of Uniform flow: Standard equations,
hydraulically efficient channel sections,
compound sections,
Energy-depth relations:
Concept of specific energy, specific force,
critical flow, critical depth,
hydraulic exponents, and
Channel transitions.
An open channel is a conduit in which a liquid flows with a free surface.
The free surface is actually an interface between the moving liquid and an overlying fluid medium and will have constant pressure.
In civil engineering applications; water is the most common liquid with air at atmospheric pressure as the overlying fluid.
The prime motivating force for open channel flow is gravity.
An open channel is a conduit in which a liquid flows with a free surface.
The free surface is actually an interface between the moving liquid and an overlying fluid medium and will have constant pressure.
In civil engineering applications; water is the most common liquid with air at atmospheric pressure as the overlying fluid.
The prime motivating force for open channel flow is gravity.
An open channel is a conduit in which a liquid flows with a free surface.
The free surface is actually an interface between the moving liquid and an overlying fluid medium and will have constant pressure.
In civil engineering applications; water is the most common liquid with air at atmospheric pressure as the overlying fluid.
The prime motivating force for open channel flow is gravity.
Flow Equations for sluice gate.Introduces different flow equations to students which are widely utilized for the design of sluice gates connected to open channel.This tutorial will help to understand and articulate the basic flow equation utilized by designers all over the world.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
1. OPEN CHANNEL FLOW
Open channel flow is a flow of liquid, basically water in a conduit with a free surface. The open
channel flows are driven by gravity alone, and the pressure gradient at the atmospheric interface
is negligible.
Closed duct flows are full of fluid, have no free surface within, and are driven by a pressure
gradient along the duct axis.
That is a surface on which pressure is equal to local atmospheric pressure.
Open channel flows are characterized by the presence of a liquid-gas interface called the free
surface. Some are natural flows such as rivers, creeks and floods, some are human made
systems such as fresh water aquaducts, irrigation, sewers and drainage ditches.
2.
3. An open channel always has two sides and a bottom, where the flow satisfies the no-slip
condition. Therefore even a straight channel has a three-dimensional velocity distribution. Some
measurements of straight channel velocity contours are shown below.
The profiles are quite complex, with maximum velocity typically occurring in the midplane
about 20% below the surface.
4. COMPARISON OF OPEN CHANNEL FLOW AND PIPE FLOW
OPEN CHANNEL FLOW PIPE FLOW
Open channel flow must have a free surface. No free surface in pipe flow.
A free surface is subject to atmospheric
pressure.
No direct atmospheric pressure, hydraulic
pressure only.
Flow area is determined by the geometry of the
channel plus the level of free surface, which is
likely to change along the flow direction and
with as well as time.
Flow area is fixed by the pipe dimensions. The
cross section of a pipe is usually circular.
The cross section may be of any from circular
to irregular form of natural streams, which may
change along the flow direction and as well as
with time.
The cross section of a pipe is usually circular.
The depth of flow, discharge and the slopes of
channel bottom and of the free surface are
interdependent.
No such dependence.
5. TYPES OF OPEN CHANNEL FLOWS
The most common method of classifying open channel flow is by the rate of change of the free
surface depth. The simplest and most widely analyzed case in uniform flow.
Type of flow Description
Steady flow When discharge (Q) does not change with time.
Uniform flow When depth of fluid does not change for a selected length or section of
the channel.
Uniform steady flow When discharge does not change with time and depth remains constant
for a selected section. Cross section should remain unchanged, referred
to as a prismatic channel.
Varied steady flow When depth changes but discharge remains the same.
Varied unsteady flow When both depth and discharge change along a channel length of
interest.
Rapidly varying flow Depth change is rapid.
Gradually varying
flow
Depth change is gradual.
6. 1. Rapidly varying flow
2. Gradually varying flow
3. Hydraulic jump
4. Weir and waterfall
5. Gradually varying
6. Hydraulic drop due to change in channel slope
7. PARAMETER USED IN OPEN CHANNEL FLOW ANALYSIS
Hydraulic radius, R of open channel flow
R is a ratio of flow cross sectional area, A and wetted perimeter (WP)
WP
A
R =
R : Hydraulic radius
A : Flow cross sectional area
WP : Wetted perimeter
8.
9. Reynolds number for open channel flow.
υμ
ρ VRVR
==Re
Re < 500 – laminar flow
Re > 2000 – turbulent flow
Reynolds number for pipe flow
υμ
ρ VDVD
==Re
Re < 2000 – laminar flow
Re > 4000 – turbulent flow
10. Froude number, Fr
The Froude number (Fr) is a dimensionless number defined as the ratio of channel velocity to
the speed of propagation of a small disturbance wave in the channel.
For a rectangular or very wide constant depth channel, Froude number can be defined as :
hgy
V
Fr ==
speedwaveSurface
velocityFlow
where,
V = Velocity
g = gravity
yh = Hydraulic depth
T
A
yh =
A = Area
T = Top width of the channel
Fr < 1.0 → Sub-critical flow
Fr = 1.0 or when hgyV = → Critical flow
Fr > 1.0 → Super-critical flow
A combination of both numbers is used to describe channel flow conditions.
11. THE CHEZY FORMULA
Uniform flow can occur in long straight runs of constant slope and constant channel cross
section. The water depth is constant at nyy = , and the velocity is constant at 0VV = . The slope be
θtan0 =S , where θ is the angle the bottom makes with the horizontal, considered positive for
downhill flow. From Bernoulli equation, the head loss becomes:
LSzzhf 021 =−=
where L is the horizontal distance between section 1 and 2.
Head loss from Darcy-Weisbach is:
g
V
D
L
fh
h
f
2
2
=
radiusHydraulic
diameterHydraulic
44
=
=
×==
h
h
hh
R
D
WP
A
RD
2
1
0
2
12
1
0
8
SR
f
g
V h ⋅⋅⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
For a given shape and bottom roughness, the quantity
2
1
8
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
f
g
is constant and can be denoted by C.
2
1
8
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
f
g
C
12. Finally, the velocity V0 can be expressed as :
( )2
1
0
2
1
0
2
1
2
1
0
8
SRCSR
f
g
V hh ⋅=⋅⋅⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
( )2
1
0SRCAQ h⋅=
These are called Chezy formulas, first developed by the French engineer Antoine Chezy in
conjuction with his experiments on the Saine River and the Courpalet Canal in 1769.
The quantity C, called the Chezy coefficient, varies about 60 ft½
/s for small rough channels to
160 ft½
/s for large smooth channels (30 m½
/s to 90 m½
/s in SI units).
13. EXAMPLE
A straight rectangular channel is 6 ft wide and 3 ft deep and laid on a slope of 2°. The friction
factor is 0.022.
SOLUTION
sft108
022.0
2.3288 2
1
=
×
==
f
g
C
2
ft1836 =×=A
ft5.1
363
18
=
++
==
WP
A
Rh
°= 2tan0S
( ) ( )( ) ( )( ) /sft4502tan5.118108 3
2
1
2
1
0 =°×=⋅= SRCAQ h
For SI units, it can be used directly.
14. Uniform steady flow and Manning’s equation
When discharge remain the same and depth does not change, then we have uniform steady flow.
In this condition, the surface of water is parallel to the bed of the channel. To make sure water
(liquid) flow inside the channel, it must have certain angle of inclination, or the channel’s slope.
The slope of the channel (S) can be expressed as :-
• An angle = 1 degree
• As percent = 1%
• As fraction = 0.01 or 1 in 100
15. Manning’s equation is used to estimate the velocity of flow in a channel.
The SI units form of Manning’s equation:-
2
1
3
2
0.1
SR
n
V ⋅⋅=
V = Velocity of flow in a channel (m/s)
n = Channel surface roughness. Values developed through experimentation.
R = Hydraulic radius (A/WP) in meter
S = Slope of the channel
The English units form of Manning’s equation:-
2
1
3
2
49.1
SR
n
V ⋅⋅=
V = Velocity of flow in a channel (ft/s)
R = Hydraulic radius (A/WP) in feet
17. The flowrate of a channel could be determined by :-
2
1
3
2
0.1
SAR
n
AVQ ⋅⋅==
where Q is in m3
/s.
For uniform flow, Q is referred to as normal discharge.
The above equation can also be re-arranged such that :-
2
1
3
2
S
nQ
AR =
The left hand side equation is based on channel geometry.
18. Example #01
Determine normal discharge for a 200 mm inside diameter common clay drainage tile running
half-full if the slope drops 1m over 1000m.
2
1
3
2
0.1
SAR
n
Q ⋅⋅=
013.0=n
2
2
m0157.0
42
1
=×=
D
A
π
m3142.0
2
1
perimeter,Wetted =×= DWP π
m05.0
3142.0
0157.0
===
WP
A
R
001.0=S
/sm1018.5
0.1 332
1
3
2
−
×=⋅⋅= SAR
n
Q
19. Example #02
Calculate slope of channel if normal discharge is 50 ft3
/s. Channel is formed, unfinished
concrete.
English unit !!!
2
1
3
2
49.1
SAR
n
Q ⋅⋅= →
3
2
2
1
49.1 AR
Qn
S =
017.0
ft24.1
WP
A
R
ft66.9
ft12 2
=
==
=
=
n
WP
A
00169.0=S
(Channel should drop 1.69 feet for every 1000 feet length.
20. Example #03
Design a rectangular channel in formed, unfinished concrete with below mention specifications.
Normal flowrate = 5.75 m3
/s
S = 1.2%
Normal depth = half of the width of the channel.
Since we have to design the channel, use this equation.
2
1
3
2
S
nQ
AR =
Y=B/2
B
( )
892.0
012.0
75.5017.0
2
1
2
1
3
2
=
×
==
S
nQ
AR
22
2
BB
BBYA =×==
BYBWP 22 =+=
4
B
WP
A
R ==
892.0
42
3
2
2
3
2
=⎟
⎠
⎞
⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
BB
AR
m88.0
m76.1
=
=
Y
B
21. Example #04
In a rectangular channel as mention in Example #03, the final width was set at 2m and the
maximum discharge is 12m3
/s. Find the normal depth for this maximum discharge.
2
1
3
2
S
nQ
AR =
Y=B/2
2
( )
862257.1
012.0
12017.0
2
1
2
1
3
2
=
×
==
S
nQ
AR
YA 2=
YWP 22 +=
Y
Y
WP
A
R
22
2
+
==
( ) 862257.1
22
2
2
3
2
3
2
=⎟
⎠
⎞
⎜
⎝
⎛
+
=
Y
Y
YAR
Cannot solve directly. Use trial and error method. Can use MS Excel datasheet.
From Excel,
The normal depth must be 1.348 meter.
23. CONVEYANCE AND MOST EFFICIENT CHANNEL SHAPES
2
1
3
2
0.1
SAR
n
Q ⋅⋅=
Other than the S term, all other terms are related to channel cross section and its features.
These terms together are referred to as the Conveyance (K) of the channel.
3
2
0.1
AR
n
K ⋅=
Then,
2
1
SKQ ⋅=
WP
A
R =
K is maximum when wetted perimeter (WP) is the least for a give area. This is also the most
efficience cross section for conveying flow.
For circular section, half full flow is the most efficient.
24.
25. COMPOUND SECTIONS
It is occurs when channel shape changes with flow depth. It is a typical idea in natural stream
sections during flooding.
At normal condition, water flows in the main channel. During floods, water spills over the flood
plain.
We need to know the flowrate, Q at various depths or vice-versa. So that we could design
channels or determine channel safety for various flood magnitudes.
26. Example #05
Channel type: Natural channel with levees.
Slope: 0.00015
Determine the normal discharge, Q for depth 3 ft and 6 ft.
27.
28. COMPOUND SECTION
This is more realistic situation, where the channel roughness (value of n) may be different for
floodplain than the main channel.
In this case, we need to determine velocity for each sub-section, and then sum up the discharges
for the sections.
Example #06
Slope: 0.5%
n for bank = 0.06
n for main channel = 0.03
Calculate discharge for depth of 8 feet?
30. ENERGY PRINCIPLES FOR OPEN CHANNEL FLOW
Energy at particular point in the channel is potential energy and kinetic energy.
Specific energy:
2
22
22 gA
Q
y
g
V
yE +=+=
areaflowsectionalCross
Discharge
Velocity
flowofDepth
=
=
=
=
A
Q
V
y
Total energy:
2
22
22 gA
Q
zy
g
V
zyE ++=++=
datumthefrombottomchanneltheofHeight=z
31. Example:
Rectangular channel width = 2 m
Depth = 1 m
Q = 4.0 m3/s 2 m
1 m
2 m
Height above datum = 2 m
Determine the specific energy and total energy.
Specific energy:
( )( )( )
m20.1
281.92
4
1
2 2
22
=+=+=
g
V
yE
Datum
Total energy:
E = datum height + specific energy = 2.0 + 1.2 = 3.2 m
32. Specific energy diagram
The specific energy can be plotted graphically as a function of depth of flow.
k
s
E
gA
Q
Ey
gA
Q
y
g
V
yE
energy,Kinetic
2
energy)(potentialenergy,Static
22
2
2
2
22
=
=
+=+=
Relationship between y and static energy, Es
33. Relationship between y and kinetic energy, Ek
2
2
2gA
Q
Ek =
For a rectangular channel;
Substitute Q with specific discharge (discharge per unit width),
B
Q
q =
Substitute area, A with, yBA ⋅=
2
2
2
2
22 gy
q
gA
Q
Ek ==
34. EXAMPLE
A rectangular channel, width is 4 m, flowrate is 12 m3
/s and depth of flow is 2.5 m.
Draw specific energy diagram
Find critical and alternate depth?
2
2
2
2
2
2
gy
q
yE
gA
Q
yE
+=
+=
/sm3
4
12 2
===
B
Q
q
37. 1. The diagram applies for a given cross section and discharge.
2. As the depth of flow increases, the static energy increases, and the kinetic energy
decreases
3. The total energy curve approaches the static energy curve for high depths and the
kinetic energy curve for small depths
4. The specific energy is minimum (Emin) for a particular depth – this depth happens to
be the critical depth – Depth for which the Froude’s number = 1.0. velocity = Vc.
5. Emin – only energy value with a singular depth!
6. Depths less than the critical depths – supercritical flow. Froude Number > 1.0. V > Vc.
7. Depths greater than the critical depths – subcritical flow. Froude Number < 1.0. V < Vc.
8. For all other energy values – there are two depth associated – one greater than the
critical depth and one less than the critical depth.
9. The two depths associated with the same energy values are referred to as – Alternate
depths
10. As discharge increases, the specific energy curves move to the upper right portion of
the chart.
38.
39. 2
2
2
2
2
2
gy
q
yE
gA
Q
yE
+=
+=
There is a minimum value of E at a certain value of y called the critical depth.
3
2
2
2
10
gy
q
dy
dE
−==
It shows that Emin occurs at yc
3
1
2
23
1
2
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
gb
Q
g
q
yc
The associated minimum energy is ;
( ) cc yyEE
2
3
min ==
The depth, yc corresponds to channel velocity equal to the shallow-water wave propagation
speed, C0.
gy
V
Fr =
( ) 22232
ccccc yVygygyq ===
40. By comparison it follows that the critical channel velocity is:
( ) 0
2
1
CgyV cc ==
1=Fr
For , no solution exists.minEE <
For , two solutions are possible:minEE >
(1) Large depth with cVV < , called sub-critical.
(2) Small depth with , called super-critical.cVV >
In sub-critical flow, disturbances can propagate upstream because wave speed .VC >0
In super-critical flow, waves are swept downstream: Upstream is a zone of silence, and a small
obstruction in the flow will create a wedge-shape wave exactly analogous to the Mach waves.
The angle of these waves must be:
( )
V
gy
V
C 2
1
101
sinsin −−
==μ
The wave angle and the depth can thus be used as a simple measurement of super-critical flow
velocity.
41.
42. Critical depth, yc
m971.0
81.9
3 3
1
23
1
2
=⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
g
q
yc
Minimum specific energy, Emin
( ) m457.1971.0
2
3
2
3
min === cyE
Since given depth was 2.5 m > 0.971 m, the given depth is sub-critical and the other depth
should be super-critical.
Now, determining alternate depths (Energy at 2.5 m)
m57.2
5.281.92
3
5.2
2 2
2
2
2
=
××
+=+=
gy
q
yE
This energy value is the same for the other alternate (super-critical) depth, so;
2
2
81.92
3
57.2
y
y
××
+=
Determine value of y by trial and error method. (use Excel ok)
45. HYDRAULIC JUMP
In open channel flow a supercritical flow can change quickly back to a subcritical flow by
passing through a hydraulic jump
The upstream flow is fast and shallow.
The downstream flow is slow and deep.
The hydraulic jump is quite thick, ranging in length from 4 to 6 time the downstream depth.
It is very important that such jumps be located on specially designed aprons; otherwise the
channel bottom will be badly scoured by the agitation.
Jumps also mixed fluids very effectively and have application to sewage and water treatment
designs.