Espirales. Revista multidisciplinaria de investigación científica, Vol. 7, No. 47
October - December 2023. e-ISSN 2550-6862. pp 22-34
DOI https://doi.org/10.31876/er.v47i7.848
Development of a specific software for the calculation of
open channels with uniform flow considering energy
principles
Desarrollo de un software específico para el cálculo de canales abiertos de
flujo uniforme considerando los principios de energía
Liliana Lizbeth López López*
María Fernanda Pico Núñez*
Bernarda Estefanía Abril Gavilanes*
Received: July 13, 2023
Approved: September 22, 2023
Abstract
The purpose of this research project is the codification of a specific
software for the calculation of open channels of uniform flow
considering the energy principles, which allows to obtain quickly and
safely the normal and critical tie, geometric elements, flow rate,
optimal hydraulic section of the sections proposed by Ven Te Chow,
rectangular, trapezoidal, triangular, circular, parabolic, rectangular
with rounded corners and triangular with rounded bottom, in addition
to the geometric elements for any equation of the parabola, the
hydraulic headroom and weirs. To verify the veracity of the developed
program "SN CANALES v2.0", the results obtained were checked
with the existing HCANALES software and manually; obtaining a
margin of error of less than 1.5%, thus verifying that the values
obtained by the software are reliable.
Keywords:
Software, Open channels, Uniform flow.
Cite this:
López, L., Pico, M., Abril, B., (2023).
Desarrollo de un software específico
para el cálculo de canales abiertos
de flujo uniforme considerando los
principios de energía. Espirales
Revista Multidisciplinaria de
investigación científica, 7 (47),
Magister en Ingeniería Civil Mención Estructuras
Metálicas, Universidad Técnica de Ambato,
ll.lopez@uta.edu.ec, https://orcid.org/0009-0004-
7730-3162
Magister en Ingeniería Civil Mención Estructuras
Metálicas, Universidad Técnica de Ambato,
mf.pico@uta.edu.ec, https://orcid.org/0000-0002-
8468-3026
Magister en Ingeniería Civil Mención Estructuras
Metálicas, Gobierno Autónomo Descentralizado
Municipal de Ambato, eprilab@hotmail.com,
https://orcid.org/0000-0003-0788-0824
Liliana Lizbeth López López, María Fernanda Pico Núñez, Bernarda Estefanía Abril Gavilanes
Espirales. Revista multidisciplinaria de investigación científica, Vol. 7, No. 47
October - December 2023. e-ISSN 2550-6862. pp 22-34
23
Introduction
Water is a substance of vital importance for human beings, so there has been a need to
quantify and efficiently use water resources for human consumption, industry,
agriculture, energy regeneration, etc., due to this, human beings have always been in
search of how to measure it (Barragán Mendoza et al., 2007).
At the beginning of the application of knowledge on hydraulic engineering, there were
no technological tools like the current ones and therefore a lot of time was spent in the
process of performing mathematical calculations or in turn in the design of a structure,
since tables or nomograms were used. This repetitive process could unintentionally
cause errors (Acosta Lozada & Naranjo Bustos, 2016).
At present, there are softwares that allow the calculation of open channels, but not all
the sections proposed by Ven Te Chow are available, so the need arose to develop a
software where all these sections are available in order to contribute to the reduction of
the calculation time and to provide reliability in the results.
Thus, the project is composed of two approaches: theoretical and practical. Within the
theoretical approach, important issues in canal hydraulics are addressed and as for the
practical approach, the development of a specific software for the calculation of open
canals in which the energy principles are considered.
Based on the research, it can be mentioned that the flow of water in a conduit can be
open channel flow or pipe flow. These two types of flow are very similar, but they differ
Resumen
El presente proyecto de investigación tiene como propósito la
codificación de un software específico para el cálculo de canales
abiertos de flujo uniforme considerando los principios de energía, el
cual permite obtener de manera rápida y segura el tirante normal,
tirante crítico, elementos geométricos, caudal, sección hidráulica
óptima de las secciones planteadas por Ven Te Chow, rectangular,
trapezoidal, triangular, circular, parabólica, rectangular con esquinas
redondeadas y triangular con fondo redondeado, además los
elementos geométricos para cualquier ecuación de la parábola, el
resalto hidráulico y vertederos. Para comprobar la veracidad del
programa desarrollado "SN CANALES v2.0", los resultados
obtenidos fueron comprobados con el software existente HCANALES
y mediante la forma manual; obteniendo un margen de error menor
al 1.5%, con lo que se pudo verificar que los valores obtenidos por el
software son confiables.
Palabras clave:
Software, Canales abiertos, Flujo uniforme.
Development of a specific software for the calculation of open channels with uniform flow considering the energy
principles
Espirales. Revista multidisciplinaria de investigación científica, Vol. 7, No. 47
October - December 2023. e-ISSN 2550-6862. pp 22-34
24
in the fact that open channel flow must have a free surface and pipe flow does not
(Barragán Mendoza et al., 2007).
Figure 1.
Difference between pipes and channels.
A. Open Channels
An open channel is defined as one that does not completely enclose a liquid stream
between solid boundaries and is therefore in direct contact with the atmosphere.
Figure 2.
Open channels.
B. Geometry of a Channel
A natural channel is generally very irregular in shape and varies from place to place,
from approximately a parabola to approximately a trapezoid. Artificial channels are
designed with regular geometric shapes, a channel constructed with an invariable cross
section and a constant bottom slope is known as a prismatic channel. The term section
of a channel refers to the cross section taken perpendicular to the direction of flow
(Rodriguez Ruiz, 2008).
The most common cross sections are:
Trapezoidal section: Used in earth channels because they provide the necessary slopes
for stability, and in lined channels.
Rectangular section: Because the rectangle has vertical sides, it is generally used for
canals built with stable materials, wooden aqueducts, for canals excavated in rock and
for lined canals.
Triangular section: Used for lined ditches on highways, also in small earth channels,
mainly for ease of layout. They are also used as lined road culverts.
Parabolic section: This is sometimes used for lined channels and is the approximate
shape of many natural and old earth channels.
Liliana Lizbeth López López, María Fernanda Pico Núñez, Bernarda Estefanía Abril Gavilanes
Espirales. Revista multidisciplinaria de investigación científica, Vol. 7, No. 47
October - December 2023. e-ISSN 2550-6862. pp 22-34
25
Circular section: The circle is the most common section for small and medium size
sewers and culverts.
C. Geometric elements of a section
Geometric elements are the properties of the section of a channel that can be defined
by the geometry of the section and the depth of flow. These elements are very
important for flow calculation.
Figure 3.
Detail of the geometric elements of the cross section of a channel.
1. Flow depth: The vertical distance from the lowest point of a channel section to
the free surface, i.e. the maximum depth of water in the channel. This term is
often interchanged with the flow depth of the section (D).
2. Surface width or water mirror "T": The width of the free surface of the water, in
meters.
3. Wetted area "A": The wetted area (A) is the cross-sectional area of the flow
perpendicular to the flow direction.
4. Wetted Perimeter "P": The wetted perimeter (P) is the length of the line of the
intersection of the wetted channel surface and a transverse plane perpendicular
to the direction of flow.
D. Geometric elements of a parabolic channel
To calculate the geometric elements of a parabolic channel based on the equation of
the parabola, it is necessary to know the general equation of a parabola.
General equation of the parabola:
𝑓𝑥 = $𝑎 𝑥
!
+ 𝑏𝑥 + 𝑐 (1)
E. Flow Classification
The classification of flow in open channels is summarized as:
A)
Permanent flow
1) Permanent uniform flow
2) Permanent varied flow
• Gradually varied flow
• Rapidly varying flow
Development of a specific software for the calculation of open channels with uniform flow considering the energy
principles
Espirales. Revista multidisciplinaria de investigación científica, Vol. 7, No. 47
October - December 2023. e-ISSN 2550-6862. pp 22-34
26
B)
Non-permanent flow
1) Uniform unsteady flow
2) Non-steady flow
• Gradually varied non-permanent flow
• Rapidly varying non-permanent flow.
• Uniform Flow in Open Channels
Uniform flow occurs when the mean velocity is constant over any part of the channel
section.
Figure 4.
Uniform flow
In uniform flow the slope of the friction energy line (Sf), the slope of the free surface of
the water (Sa) and the geometric slope of the channel (So) are equal. If the mean velocity
remains constant, it has to do with the fact that the flow has a constant velocity at each
point of the cross section along the channel, that is, the velocity distribution of each
section does not alter.(Acosta Lozada & Naranjo Bustos, 2016).
Uniform flow is an ideal state that is difficult to achieve, however, in most cases
(especially in straight and long channels of constant cross section and bottom slope)
(Sotelo, 1887).
G. Manning's Roughness Coefficient
The value of n (Manning's roughness coefficient) is variable and depends on several
factors. The factors that have the greatest influence on the Manning's roughness
coefficient in either artificial or natural channels are:
1) Surface roughness.
2) Vegetation.
3) Irregularity of the channel.
4) Channel alignment.
5) Sedimentation.
6) Scour.
7) Obstruction.
8) Channel size and shape.
Liliana Lizbeth López López, María Fernanda Pico Núñez, Bernarda Estefanía Abril Gavilanes
Espirales. Revista multidisciplinaria de investigación científica, Vol. 7, No. 47
October - December 2023. e-ISSN 2550-6862. pp 22-34
27
H. Uniform Flow Calculation
In a channel the volumetric flow is calculated by the continuity equation:
Q=A*V (2)
Where:
Q= Flow rate
V= Flow velocity
A= Area
I. Energy
Energy is the capacity required to do work. Work is the result of applying a force along
a certain path and is usually defined as the product of a force times the length of the
path in the direction of application. Energy and work are expressed in the same units,
i.e. kpm or N m.
Figure 5.
Energy in a channel
J. Specific Energy
The specific energy is therefore the sum of the flow and the velocity load. The bottom
of the channel will change each time it rises or falls, in short the specific energy depends
on the water flow.
The following equation is used to determine the specific energy:
𝐸 = $𝑦$ +$
"
!
!#
(3)
K. Critical Flow
If the critical state of flow exists along the entire length of the channel or along a section
of the channel, the flow in the channel is a critical flow. The channel slope that maintains
a given flow at a uniform, critical depth is known as the critical slope (Sc). A channel
slope less than the critical slope will produce a slower flow of a subcritical nature for the
Development of a specific software for the calculation of open channels with uniform flow considering the energy
principles
Espirales. Revista multidisciplinaria de investigación científica, Vol. 7, No. 47
October - December 2023. e-ISSN 2550-6862. pp 22-34
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given flow and is therefore known as a gentle or subcritical slope. A slope greater than
the critical slope will produce a faster flow of a supercritical nature and is known as a
steep or supercritical slope.
1. Critical Flow Conditions
• Specific energy is minimum for a given flow rate
• The flow rate is maximum for a given specific energy.
• The specific strength is minimum for a given flow rate.
• The velocity head is equal to half the hydraulic depth in a low slope channel.
• The Froude number is equal to unity.
• The flow velocity in a low-slope channel with uniform velocity distribution is
equal to the celerity of small gravity waves in shallow water caused by local
disturbances.
Critical Flow Determination
For a critical flow state to occur, the condition must be met in which the Froude number
is equal to one, under this flow state, the specific energy is minimal for a given flow rate
and the current is unstable and subject to fluctuations in the depth of the liquid.
(Barragán Mendoza et al., 2007).
The following equation is used to determine the critical flow:
$
!
#%
"
𝑇 = 1 (4)
L. Hydraulic Highlight
The hydraulic jump is defined as the abrupt elevation of the liquid surface, when the
permanent runoff passes from the supercritical to the subcritical regime. It is a local
phenomenon very useful for dissipating hydraulic energy. This abrupt change of regime
is characterized by a rapid change in the curvature of the flow paths, which produces
vortices (turbulence) on the horizontal axis, including the appearance of velocities in the
opposite direction to the flow that cause collisions between particles in a more or less
chaotic manner, resulting in a large dissipation of energy.
Liliana Lizbeth López López, María Fernanda Pico Núñez, Bernarda Estefanía Abril Gavilanes
Espirales. Revista multidisciplinaria de investigación científica, Vol. 7, No. 47
October - December 2023. e-ISSN 2550-6862. pp 22-34
29
Figure 6.
Hydraulic Resalt
M. Types of Hydraulic Resalt
The hydraulic headwater can be classified according to the Froude number of the flow
upstream of the jump.
● For Froude number F=1,
The flow is critical, and no jump is formed here.
● For a Froude number F>1 and F<1.7
The surface of the water shows ripples and a jump called undulatory jump occurs.
● For a Froude number F>1.7 and F<2.5
We have a weak jump. This is characterized by the formation of a series of eddies on
the jump surface, but the water surface downstream remains uniform (Rodríguez Ruiz,
2008).
● For a Froude number F>2.5 and F<4.5
An oscillating jump occurs.
● For Froude number F>4.5 and F<8.0
A permanent or stable jump occurs
● For Froude number F=8.0 and greater
The strong jump is produced.
N. Hydraulic Resalt Calculation
a.
Energy Loss
The loss of energy in the shoulder is equal to the difference of the specific energies
before and after the shoulder (Rocha Felices, 2017).
Energy loss according to BERNOULLI:
Development of a specific software for the calculation of open channels with uniform flow considering the energy
principles
Espirales. Revista multidisciplinaria de investigación científica, Vol. 7, No. 47
October - December 2023. e-ISSN 2550-6862. pp 22-34
30
∆E= E1-E2 (5)
b.
Height of the Highlight
The height of the hydraulic jump is defined as the difference between the tie rods after
and before the jump.
H= Y2-Y1 (6)
O. Landfills
According to Balloffet, a weir is an open contour opening, located in the wall of a
reservoir, or in a barrier placed in a channel or river, through which the water contained
in the reservoir drains or overflows (Netto et al., 1988).
Weirs are structures formed by placing a thin or thick wall perpendicular to the flow over
which runoff occurs. Their operation is based on the theory of rimless orifices for thin-
walled weirs and critical flow conditions for thick-walled weirs.
Figure 7.
Landfill
Where:
H = Load on the landfill
L = Length of the weir crest
B = Approach channel width
P. Types of Landfills
In the most diverse forms and arrangements, landfills present the most diverse
behaviors, with several factors serving as the basis for the present classification (Netto
et al., 1988):
1) By shape
a) Simple (rectangular, trapezoidal, triangular, etc).
b) Composites (combined sections).
Liliana Lizbeth López López, María Fernanda Pico Núñez, Bernarda Estefanía Abril Gavilanes
Espirales. Revista multidisciplinaria de investigación científica, Vol. 7, No. 47
October - December 2023. e-ISSN 2550-6862. pp 22-34
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2) Relative sill height
a) Complete or free landfills p > p'
b) Incomplete or drowned landfills p < p'
3) Wall thickness
a) Thin-walled landfills.
b) Thick wall landfills ( e > 0.66 H)
4) Ridge length
a) Landfills without lateral contractions (L = B).
b) Contracted landfills (L < B) (with one or two contractions).
Materials and methods
The present project is based on an explanatory research, due to the search of the cause-
effect relationship in the calculation of open channels of uniform flow that considers the
principles of energy, within a manual process and the use of a software. In addition, it
is considered an applied research since the knowledge of channel hydraulics will be put
into practice to develop this specific software that will decrease the calculation time for
both students and engineers. Then, the data will be taken from three sources: by the
manual method that consists of the application of the relevant definitions and
equations; by the method with existing software where it will be supported by
HCANALES and finally by the software developed SN CANALES v2.0L.
Results
Table 1.
Error percentages obtained in the developed software compared to the
manual process and the existing HCANALES software, for different types of sections:
SECTION TYPE
ERROR RATE
1
Parabolic section
< 0.1%
2
Rectangular session
0.01% - 1.5%
3
Trapezoidal section
0.01% - 0.6%
4
Triangular session
0.01% - 0.2%
5
Rectangular session with rounded
corners
0.01% - 0.4%
6
Triangular session with rounded
bottom
0.01% - 0.5%
Development of a specific software for the calculation of open channels with uniform flow considering the energy
principles
Espirales. Revista multidisciplinaria de investigación científica, Vol. 7, No. 47
October - December 2023. e-ISSN 2550-6862. pp 22-34
32
7
Thin-walled rectangular weir
0.01% - 0.1%
8
Triangular landfill
0.01% - 1.01%
9
Trapezoidal weir
0.01% - 0.1%
10
Circular landfill
0.01% - 0.1%,
11
Submerged landfill
0.01%
After having carried out an analysis of the results obtained by the following methods:
manual, with the HCANALES Software and the developed software SN CANALES v2.0L,
we obtained an error of less than 1% between the results obtained, giving veracity to
the stated hypothesis. Having verified that the developed software has a significant
influence on the calculation time of open channels of uniform flow in which the energy
principles are considered", it is determined that evidently having a software significantly
decreases the time it takes to calculate them, while having more accurate values than
when performing a manual calculation because the software uses all the decimals for
the calculation.
In the developed software there is the main screen, where we can access the main
functions by means of drop-down menus.
From the drop-down menus you have access to the different screens that allow the
calculation of the
• Normal brace
• Critical tie rod
• Flow rate
• Geometric elements
• Optimum hydraulic section
• Hydraulic Highlight
• Landfills
In the different calculation screens, the numerical values corresponding to the data
necessary to perform the calculations must be entered.
A reference image is incorporated in each calculation screen according to the cross
section to be calculated.
The units of the input and output data depend on the system of units chosen for the
calculation, for which we have the metric and English system, which must be selected
before calculating.
To start the calculation, the "CALCULATE" button must be pressed, there is also a
"CLEAR" button which allows the user to clear the input and output data, and a "MAIN
MENU" button which allows the user to exit the current window and return to the main
screen.
Liliana Lizbeth López López, María Fernanda Pico Núñez, Bernarda Estefanía Abril Gavilanes
Espirales. Revista multidisciplinaria de investigación científica, Vol. 7, No. 47
October - December 2023. e-ISSN 2550-6862. pp 22-34
33
Conclusions
Since water is the vital liquid for human beings, it must be ensured that all people have
access to this element and that the means of transportation is adequate.
The results of the calculation of the geometric elements of a parabolic section obtained
by manual resolution and those obtained by means of the developed application have
an error rate of less than 0.1%, so it is deduced that the use of the software is reliable
and valid.
The results of the calculation of the hydraulic head of the different sections proposed
by Ven Te Chow, obtained by manual resolution and those obtained by means of the
developed application, have an error percentage between 0.01% and 1.5%, and since
this is the allowed range, it can be deduced that the use of the software is reliable and
valid.
The results of the landfill calculation obtained by means of the developed application
have an error percentage between 0.05% and 1%, this range of error is allowed so it is
deduced that the use of the software is reliable and valid.
Therefore, the results obtained with the software developed have an error of less than
1% compared to the values obtained with the calculation performed in HCANALES, so
the use of this program is valid for the different calculations it presents.
The error that occurs between the results of the manual calculations and those of the
software is due to the number of decimal places with which you are working.
..........................................................................................................
References
Acosta Lozada, R., and Naranjo Bustos, C. (2016).
Development of a software for the calculation
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PIPELINES AND CANALS.
Development of a specific software for the calculation of open channels with uniform flow considering the energy
principles
Espirales. Revista multidisciplinaria de investigación científica, Vol. 7, No. 47
October - December 2023. e-ISSN 2550-6862. pp 22-34
34
https://www.academia.edu/36993564/HIDRA
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