Application of Specific Energy in Open Channels to Various Forms of
Channel Constriction
RATNA MUSA1*, TRIFFANDY M.W2, AMALIA RUSALDY3
1Civil Engineering Program, Muslim University of Indonesia, South Sulawesi, INDONESIA
2Great Hall of the Pompengan Jenneberang River Region, South Sulawesi, INDONESIA
3Department of Civil and Environmental Engineering, Gadjah Mada University, Yogyakarta, INDONESIA
Abstract: - Planning of water structures such as dams, irrigation canals, and other water structures requires a
description of these buildings' hydraulic flow phenomenon. Each flow condition, moderate, and after passing
through each building has its characteristics or tendencies. The aim of the study was to analyze the flow
characteristics through several channel constrictions (sudden, transition, and radius) and verify the relationship
between the results of laboratory tests with other research results. Understanding the flow characteristics in a
narrow channel can be used to consider the design of channel engineering, especially irrigation canals. The
results of the analysis show that the flow of water through the constriction undergoes a specific energy change.
The maximum specific energy occurs at the sudden constriction type of 0.1339 m. The predicted results
correlated moderately with experimental data from this and other studies. The application of specific energy for
channel narrowing with upstream Es = downstream Es with Q = 0.0025 m3/s, then the maximum downstream
water level elevation occurs in the form of a sudden narrowing of 0.1200 m. This value deviates from the
results of laboratory tests with an elevation of 0.1310 m by 8%. This is due to setting and measurement errors
during laboratory tests.
Key-Words: Channel narrowing, Flow velocity, Froud Numbers, Specific Energy
Received: April 21, 2021. Revised: January 22, 2022. Accepted: February 24, 2022. Published: March 26, 2022.
1 Introduction
An open channel is a free-flowing water channel.
Open channels can be distinguished into two types,
namely artificial and natural. Open channels are
found both on irrigation channels, technical, semi-
technical, and natural channels in non-prismatic
conditions. In a channel with a non-prismatic
drainage channel, water flow changes such as
altitude, velocity, channel width, water discharge,
and other flow behavior. Some of the causes of the
non-prismatic cross-section are the connection of
two cross-sections, other buildings such as bridge
pillars, or other causes that alter the channel's cross-
section. Flow analysis of non-prismatic channels
requires precision due to changes in flow
characteristics. One example is channel narrowing,
which causes altitude, velocity, and energy in the
flow to change. The flow of energy affects the
channel's smooth flow, which can disrupt water flow
distribution that can harm. This fact needs attention.
The discussion of the flow in the case of channel
narrowing in this paper tries to disentangle the
problem through measurement and testing on an
open channel in the presence of constriction.
Referring to the law of continuity, when the flow of
water flows on a narrow section of the channel, it
can increase the flow rate and energy. The
narrowing of the channel cross-section becomes one
of the factors to increase the flow and energy
velocity. From previous research, [1] project is to
establish general design criteria for optimal
hydraulic conditions to avoid sediment depositions
in the tunnel and keep the resulting abrasion
damages at a minimum. In [2] propose a depth-
discharge relationship and energy-loss coefficient
for a subcritical, equal-width, right-angled dividing
flow over a horizontal bed in a narrow aspect ratio
channel. [3] Used abrupt type of narrowing by using
several different channel widths; hence previous
research has been used as a benchmark in this study,
which used three types of narrowing types
constriction, transition constriction type, and the
narrowing Radius of the same channel width. This
study focuses on analyzing changes in flow
characteristics due to channel narrowing (sudden,
transition, and radius). We argue that applying it to
the inspection model should solve the following two
problems: (1) How to know the flow characteristics
of different types of constriction, and (2) How to
apply specific energy in determining the
downstream water level (after constriction) with the
assumption that upstream Es = downstream Es, then
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this result is verified by laboratory test results with
other research results.
The results of previous research that are (Analysis
of Changes in the Effect Flow Rate on the Open
Channel) [4] produces a difference in energy loss at
the beginning of the narrowing, and after the
narrowing, the change in energy before and after the
narrowing is commonly called the specific energy
loss. We tried to refine the results by designing open
channels on a uniform flow, assuming the specific
energy of the upstream part is equal to the specific
energy of the downstream part to determine the
depth of water downstream resulting from the
narrowing of the channel.
2 Problem Formulation
2.1 Research Methodology and Procedure
According to the generation type of assumptions, we
divided the existing work into three narrowing.
2.1.1 Research Methodology
The research method is a scientific way to get data
with a specific purpose and usefulness. The natural
channel cross-section is generally very irregular,
usually varying from parabolic to trapezoidal forms.
The term channel section is perpendicular to the
flow direction, while the vertical channel section is
the vertical cross-section through the lowest or
lowest point of the cross-section. Therefore, the
horizontal channel of the cross-section is always a
vertical cross-section (Figure 1):
Fig. 1: Cross-section of rectangular channels
Wide (A) = b x h (1)
Wet Round (P) = b + 2h (2)
Hydraulic Radius (R) = A/P = b x h / (b+2h) (3)
With b = channel base width (m) and h = high
water level (m).
The material used is water. The tools used are a
set of open channel models with a bottom of a
channel and a wall made of fiber, ruler, current
meter FL 03, stopwatch, pumping ball, 90o
constrictions, 45o constrictions, and Radius
constriction. The cross-section in abrupt type
refinement are presented in Figure 2 and Figure 3.
Also, Figure 4 presents the cross-section on the
narrowing of the Radius
Fig. 2: Cross-section in abrupt type refinement. [4]
Fig. 3: Cross-section on Transitional type
refinement. [4]
Fig. 4: Cross-section on the narrowing of the
Radius. [4]
2.1.2 Research Procedures
a. Laboratory Testing
(1) prepare tools and materials, (2) regulate flow
rate, (3) calibrate tools and flow rate, (4) Setting the
discharge with Q = 0.0025 m3/s (one of the
variations of the discharge used for each type of
narrowing), (5) measuring the water level before
and after constriction, (6) measuring the flow
velocity assuming the average flow velocity in the
vertical direction is measured only at a few points
and then calculated with mathematical results.
Measurements were carried out using the one-point
and two-point methods. The one-point method of
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measurement is carried out at a depth of 0.2 h or 0.6
h (h = Depth), at 0.6 h it is carried out when the
flow depth is between 2.5-7.5cm (V = 0.6 h). And
the two-point method was carried out at a depth of
0.2 h and 0.8 h. The average flow velocity is
obtained by the formula (V= 0.5(0.2h+0.8h)), (7)
calculate the Froude number, (8) calculate the
Specific Energy for each type of narrowing, (9)
compare the results of the three forms of narrowing
type (h and Es) which is greater than the results of
the three forms of narrowing type.
b. Application of Specific Energy in Irrigation
Channel Design
(1) determine the discharge (according to the
variation of the discharge used in laboratory
testing), (2) determine the channel width before and
after narrowing (according to laboratory tests) for
each type of narrowing, (3) determine the elevation
of the upstream water table according to the results
of laboratory tests (h1), (4) calculate the discharge
per unit width (q) before and after constriction for
each type of narrowing, (5) calculate the Froude
number, (6) calculate the specific energy upstream,
(7) calculate the water level in the downstream
assuming upstream Es = downstream Es, (8)
compare the water level elevation (h2) laboratory
tests with other tests, (9) describe the results of the
analysis obtained.
2.2 Our Contribution
This paper present analyses the flow changes due to
the narrowing of the open channel. From previous
research, Cristian Auel et al. [1] discusses
Turbulence Characteristics in Supercritical Open
Channel Flows: Effects of Froude Number and
Aspect Ratio, Chieh Hsu et al. [2] discussing
Subcritical 90° Equal-Width Open-Channel
Dividing Flow, and Jhonson et al. [3] used abrupt
type of narrowing by using several different channel
widths, hence previous research has been used as a
benchmark in this study which used three types:
sudden narrowing type, transitional narrowing type,
and radius narrowing type with the same channel
width. Understanding the flow characteristics of a
narrowed channel is used to consider canals'
technical design, especially irrigation channels.
2.3 Open Channels
Channels that drain water with a free surface are
called open channels. Open channels can occur
considerably, ranging from ground-level flows
during rain until continuous water flow in the
prismatic channel. Channels are classified into two
types: natural existing and artificial channels.
Natural channels include all water channels
naturally occurring on earth, from small gutters in
the mountains, small rivers, and large rivers to river
mouths. Artificial channels are human-made
channels for specific purposes and interests.
Nature's hydraulic properties are very uncertain.
Artificial channels have a regular cross-section and
are easier to analyse than natural channels. Artificial
channels include roadside drainage, irrigation canals
to irrigate rice fields, sewers, drains to carry water
to hydroelectric power, drinking water supply
channels, floodway. In some ways, it can be
assumed that the approach is sufficiently consistent
with actual observations. Thus, the flow
requirements of this channel are acceptable for the
completion of theoretical hydraulics analysis.
2.4 System Classification
The open channel flow can be classified into several
types and described in various ways as follows. The
flow-through constriction can be supercritical or
subcritical. Critical depth can be formulated by
Rangga Raju [5].
2.4.1 Steady Flow And Unsteady Flow
A flow in an open channel is steady when variables
of flow (such as velocity V, pressure P, mass
density ρ, flow face A, debit Q) and so on, across
the point of the liquid, do not change with time. The
flow is said to be unstable (unsteady) if the flow
variable at each point changes with time. Most open
channel problems generally require only research on
flow behavior in steady-state. The equation
expresses debit Q on a channel cross-section for any
flow:
Q=VA (4)
With V = average velocity and A = The cross-
sectional area is perpendicular to the flow direction.
Most steady-flow problems, based on consideration,
are assumed to remain along a large section of the
channel, in other words, a steady flow of continuous
steady flow, from equation (4):
2.4.2 Critical and Supercritical Flow
The Stream is critical if the Froude number (F) is
equal to one (1), whereas the subcritical flow is
sometimes called (tranquil flow) when F < 1 and
supercritical or (rapid flow) when F > 1. The flow
velocity ratio with the force of gravity (per unit
volume) is known as the Froude number and can be
formulated as follows [6] so that F can be written as
Boris.A [7], Ven Te Chow [8], Osman Akan [9]:
=
(5)
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With T = width of the water face, q = debit per
unit channel width
The specific energy diagram is presented in Figure
5.
Fig. 5: Specific energy diagram [9]
Fig. 6: Expression for top width T [9]
A channel changes its width from B1 to B2 assuming
that the channel bottom is constant. Since steady
flow Q is constant, due to changes in channel width,
the equation for the unit discharge q can be written:
Q = B1.q1 = B2. q2 (6)
Because B1 > B2 then q1 < q2. Equation (6) states
that the flow condition that occurs has a constant
flow rate (steady flow) but the unit of discharge (q)
changes due to changes in channel width from B1 to
B2. The specific image of the energy can be seen in
Figure 6.
Fig. 7: E and y relationships for channel
width changes [10]
For the example above E1 = E2, and from Figure 7 y1
> y2. Equation 6 can be written as
Q = B1. y1.v1 = B2. y2. v2 (7)
Because B1 > B2 and y1 > y2, then to fulfill the
above equation the magnitude of v2 > v1
2.4.3 The Flow is Changing Gradually
The specific energy is equal to the sum of the water
depth and the high velocity. On a channel basis, it is
assumed to have a sloping slope or no slope. Z is the
base height above the selected reference line, H is
the flow depth, and the energy correction factor (α)
is equal to one. The specific energy of the Stream at
each particular cross-section is calculated as the
total energy at that cross-section by using the
bottom of the channel as a reference, Budi Santoso
[11] For small slopes, ϴ = 0. Then the amount of
energy at the channel cross-section is:
(8)
This equation applies to streams aligned or changed
irregularly. That is Bernoulli's energy equation
Hunter Rouse and Simon Ince [12]. The criteria of
flow in a critical state of a stream have been defined
as a condition in which the Froude number is equal
to one. A more general definition is the flow state in
which the specific energy for a given discharge is
minimum, Paul Boss [13]. The following definition
can elaborate on a criterion for critical flow. The
amount of specific energy can be formulated as
follows [8], [10] for flat channels (θ = 90o = 0)
(9)
With E = Specific Energy
Associated Q = A x v then the Specific
Energy becomes [14], [15]:
(10)
(11)
(12)
3 Result dan Discussion
3.1 Results
3.1.1 Change in Flow Speed
Analysis of changes in flow speed can be seen
in Table 1:
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Table 1. Change of Flow Velocity Result
From the result of Table 1, flow velocity before
constriction with b1 = 0.08 m occurs before the
narrowing using the comparison of the continuity
formula and the Current meter in the form of sudden
narrowing and the Radius not experiencing a
significant change in flow rate. The transition
narrowing form has a significant change where the
current meter's velocity is 0.0 m/s, and the
continuity formula is 0.2 m/s. In comparison, the
velocity that occurs before the narrowing shows that
the constriction area's velocity for the three forms of
narrowing does not experience a significant change
where the current meter velocity and the continuity
formula are almost the same.
3.1.2 Wide Cross-Section
The cross-sectional area for each point can be
seen on Table 2:
Table 2. Broad cross-sectional results
3.1.3 Froude Number
The calculation of Froude numbers can be seen in
Table 3:
Table 3. The Froude Number Result
From the results of Table 2 and Table 3, it appears
that the flow that occurs before the narrowing is a
subcritical flow and flows. That occurs in the area of
sudden narrowing for a point distance review of 0.0
m, 0.11 m, 0.21 m, 0.23 m, and 0.46 m experiencing
subcritical flow. For a point distance review of 2.95
m experiences flow critical and for an overview, the
point distance of 3.58 m experiences supercritical
flow. In the transition narrowing area for the review,
point distances of 0.0 m, 0.21 m, 0.23 m, and 0.46 m
experience subcritical flow, a point-distance view of
0.11 m and 3.58 m experience critical flow. In the
confinement area, Radius for point distance review
of 0.0 m, 0.21 m, 0.23 m, 0.46, and 2.95 m
experienced subcritical flow. For point distance
review 0.11 m and 3.58 m experienced supercritical
flow.
3.1.4 Specific Energy
The results of specific energy calculations can
be seen in Table 4
Table 4. The Specific Energy Result
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From the results of Table 4 before the narrowing, it
appears that the maximum specific energy in the
form of sudden constriction (0.1339 m), moving
(0.1235 m), and Radius (0.1225 m) is due to
crushing in the narrowing.
Fig. 8: Specific Energy and water level with a
sudden constriction with a discharge of 0.0025 m3/s,
0.0020 m3/s, and 0.0015 m3/s.
Fig. 9: Specific Energy and water level with a
transition with a discharge of 0.0025 m3/s, 0.0020
m3/s, and 0.0015 m3/s.
Fig. 10: Specific Energy and water level with a
radius type with a discharge of 0.0025 m3/s, 0.0020
m3/s, and 0.0015 m3/s.
From Table 3 and Figure 8, Figure 9 and Figure 10
show that maximum specific energy occurs
at sudden constriction.
3.1.5 Application of Specific Energy
It is known that a rectangular channel is almost
horizontal with a width of 0.08 m and flows a
discharge of 0.0025 m3/s. its width is reduced to
0.04 m. and Es (upstream) = Es (downstream) or E1
= E2. determine what is the water level downstream
if the water level upstream of the narrowing of the
channel bottom is known.
Table 5. Calculation of Energy Principle
In Figure 11, Figure 12 and Figure 13 below,
we can see the specific energy difference in
the three form of narrowing, namely sudden
narrowing, transition narrowing, and Radius
narrowing with a fixed discharge (Q) of 0.0025
m3/sec
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0 0.5 1 1.5 2 2.5 3 3.5 4
Water Level (m)
Distance of review points on the flow profile (m)
Specific Energy Q = 0,0025 m^3/s
Specific Energy Q = 0,002 m^3/s
Specific Energy Q = 0,0015 m^3/s
specific energy Q = 0.0025 m
3
/s
spesific energy Q = 0.0020 m3/s
Spesific energy Q = 0.0015 m3/s
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0 0.5 1 1.5 2 2.5 3 3.5 4
Water Level (m)
Distance of review points on the flow profile (m)
specific energy Q = 0.0025 m
3
/s
spesific energy Q = 0.0020 m3/s
Spesific energy Q = 0.0015 m3/s
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0 0.5 1 1.5 2 2.5 3 3.5 4
Water Level (m)
Distance of review points on the flow profile (m)
specific energy Q = 0.0025 m
3
/s
spesific energy Q = 0.0020 m3/s
Spesific energy Q = 0.0015 m3/s
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Fig. 11: Specific energy at sudden constriction with
Q = 0.0025 m3/s
Figure 11 shows that the depth (h) at points A-A'
and B-B' has the same specific energy of 0.1339 m.
Prior to construction a depth of 0.1310 m is a
subcritical flow and a depth of 0.0210 m is a
supercritical flow for the same discharge of 0.0312
m3/s. in the constriction area to a depth of 0.1200 m
is a subcritical flow and a depth of 0.0480 m is a
supercritical flow with the same discharge 0.0625
m3/s.
Fig. 12: Specific energy at transition constriction
with Q = 0.0025 m3/s
Figure 12 shows that the depth (h) at points A-A'
and B-B' has the same specific energy of 0.1235 m.
Before narrowing the depth of 0.1200 m is a
subcritical flow and a depth of 0.0220 m is a
supercritical flow for the same discharge of 0.0312
m3/s. in the constriction area for a depth of 0.1056
m is a subcritical flow and a depth of 0.0520 m is a
supercritical flow with the same discharge of 0.0625
m3/s.
Fig. 13: Specific energy at radius constriction with
Q = 0.0025 m3/s
Figure 13 shows that the depth (h) at points A-
A' and B-B' has the same specific energy of 0.1225
m. Before narrowing the depth of 0.1190 m
is a subcritical flow and a depth of 0.0230 m
is a supercritical flow for the same discharge of
0.0312 m3/s. in the narrowing area for a depth of
0.1042 m is a subcritical flow and a depth of
0.0540 m is a supercritical flow with the same
discharge of 0.0625 m3/s.
3.2 Discussion
Based on Table 5 and Figure 11, Figure 12 and
Figure 13, if q increases from q upstream to q
downstream, then:
a) in the flow of supercross the water level must
rise, while in the subcritical flow, the water
level must go down
b) At the time of criticism, then the narrowing
becomes maximum. If it is narrowed again, then
the water level upstream (A) changes to add Es.
c) if the narrowing equals or exceeds the
narrowing of the criticism, then downstream (B)
narrowing will occur the flow of criticism so
that the depth of the downstream channel (B) is
H criticism
d) if the narrowing exceeds the narrowing of the
criticism, then the water level next to the upper
(A) narrowing will change.
e) The downstream water level of the three
narrowing forms studied It appears that the
maximum water level occurs in the sudden
narrowing form of 0.1200 m.
f) Comparison of water level downstream between
laboratory tests (0.1310 m) and analytical
results (0.1200 m) with a difference of 8%. This
indicates the presence of storage that may be
caused by measurements during laboratory tests.
4 Conclusion
Based on the research that has been done, it can be
concluded that the flow of water through the
constriction undergoes specific energy changes. The
maximum specific energy occurs at the sudden
constriction type of 0.1339 m. The predicted results
correlated moderately with experimental data from
this and other studies. The application of specific
energy for channel narrowing with upstream Es =
downstream Es with Q = 0.0025 m3/s, then the
maximum downstream water level elevation occurs
in the form of a sudden narrowing of 0.1200 m. This
value deviates from the results of laboratory tests
with an elevation of 0.1310 m by 8%. This is due to
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.11
0.12
0.13
0.14
0.0000 0.0200 0.0400 0.0600 0.0800 0.1000 0.1200 0.1400 0.1600 0.1800 0.2000 0.2200
h
E
Spesific energy at sudden constriction
Q = 0.0025 m3/s
q1 q2
A
B
B'
A'
0,1310
0,0480
0,0210
0,1200
supercritical flow interval
subcritical flow interval
q1
q2
0,12009
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.11
0.12
0.13
0.14
0.0000 0.0200 0.0400 0.0600 0.0800 0.1000 0.1200 0.1400 0.1600 0.1800 0.2000 0.2200
h
E
Spesific energy at transition constriction
Q = 0.0025 m3/s
q1 q2
A
B
B'
A'
0.1200
0.0520
0.0220
0.1056
supercritical flow interval
subcritical flow interval
q1
q2
0,12009
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.11
0.12
0.13
0.14
0.0000 0.0200 0.0400 0.0600 0.0800 0.1000 0.1200 0.1400 0.1600 0.1800 0.2000 0.2200
h
E
specific energy at radius constriction
Q = 0.0025 m3/s
q1 q2
A
B
B'
A'
0.1190
0.0540
0.0230
0.1042
supercritical flow interval
subcritical flow interval
q1
q2
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setting and measurement errors during laboratory
tests.
5 Suggestions
Further research used a larger channel change model
so that measurement and flow behavior are more
comfortable to observe and adding several variables
or objects that are not included in this study, for
example, sedimentation measurements.
Acknowledgments:
This work was supported by the Hydrological
Laboratory of Civil Engineering Program, Muslim
University of Indonesia, South Sulawesi, Indonesia.
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WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2022.17.6
Ratna Musa,
Triffandy M. W., Amalia Rusaldy
E-ISSN: 2224-3429
46
Volume 17, 2022
Contribution of individual authors to
the creation of a scientific article
(ghostwriting policy)
Ratna Musa has has organized this paper
and submitted and also executed the
experiments of Section 4 .
Triffandy M.W was responsible for the
Statistics and proofreading this article .
Amalia Rusaldy was responsible for the analyses .
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this
study.
Conflicts of Interest
The authors have no conflicts of interest to
declare .
Creative Commons Attribution License 4.0
(Attri-bution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
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