Broad-Crested Wire Assignment
Introduction
The area of study
that is directly connected with the open channel hydraulics mainly focuses on
the flowing liquid of the surface that is exposed to atmospheric pressure. This
is very useful in areas like rivers, canals and drainage. Unlike pressure pipe
systems, open channel flow is affected mainly by the force of gravity and the
shape of the channel. Knowledge of how water flows through such systems is
important for constructing networks for transporting water; flood control,
irrigating crops; or removing waste-bearing water. One of the critical
characteristics in these systems that engineers must define is the discharge,
namely, the amount of water moving through it per unit time.
This
type of weir is classified into a broad-crested weir with a horizontal crest
that has dimensions suited to measure the upstream and downstream water level
in the experiment. When designing this experimental setting, four different
points of water depth is measured; y₀ at the upstream of the channel, y₁ at the
gate features of the weir, y₂ right after the weir then lastly, y₃ at a
distance where flow is stable. Thus, the setup enables one to have an overall
understanding of the behaviour of water as it flows over the weir and the
changes in energy.
A broad crested
weir, with sharp-crested weirs, are distinguished by its crest, which is flat
and horizontal, and most of the length is along the direction of the flow. Such
geometry helps the cross-sectional structure of the flow change gradually as it
crosses the crest and avoids erosion and energy expenditure (Kulkarni and
Hinge, 2022). While nappe formation is used in precisely sharp, crested weirs,
broad crested weirs provide more stable flow conditions, useful if one wants
Subcritical flow. They are mostly applied in laboratory flumes as well as in
real channels with high measurement precision and long-lasting structures.
Aims and Objectives
The main aim of
this experiment is to study the hydraulic behavior of a broad-crested weir. To
assess its ability to measure the rate of flow in open channel conditions. In
the study, the actual and theoretical discharge over the weir will be measured
using a flow meter while the coefficient of discharge is calculated and one can
determine energy loss during flow transition (Singh and Sen, 2023). Through the
effectiveness of this experiment conducted under a laboratory setup, the study
will improve practical appreciation for flow over weirs to facilitate their
usage in the designing and implementation of hydraulic standards within civil
and environmental engineering practices.
The objectives are
●
To measure the heights of water
surface upstream and downstream of a broad creeping weir in a channel
●
To determine the actual discharge
and the theoretical discharge over the weir using standard hydraulic equations.
●
To assess the value of Cd when the
flow conditions are changed.
●
To compare the theoretical and
experimental numerical values to estimate where power can be wasted.
Theories
Evaluating the
behavior of flow over a broad crested weir presupposes wielding of open channel
hydraulics and basic principles of fluid mechanics. In this section, an
overview of the experimental theory as well as the theoretical equations that
describe the flow behaviour and results are discussed.
Bernoulli’s Principle
The open channel
flow is the flow of a fluid which has its surface in contact with the
atmosphere and this include rivers, canals, and flumes used in laboratories.
These flows are not pressurized pipe systems and are dependent on the channel
shapes in their operation. Bernoulli’s equation is also used in order to explain
distribution of energy in such flows (Kulkarni and Hinge, 2024). To assume
steady, incompressible, and non-viscous flow, it can be stated that the total
mechanical energy per weight remains constant along a streamline. As in open
channel conditions, pressure at the free surface is equal to atmospheric
pressure, which is negligible, Bernoulli’s equation to reduce as follows:
P/γ+v2/2g+z=H=constant
Where
P is pressure,
γ is the specific
weight of water,
v is flow velocity,
g is gravitational
acceleration, and
z is elevation
head.
The pressure at
free surface is atmospheric and cancels out simplified equations
H=v2/2g+z
Flow Over a Broad Crested Weir
A broad-crested
weir is a hydraulic structure that features a long crest through which the
water flows over gradually. This results in a flow slowing down, temporarily
halting, then speeding up as it moves over the crest, frequently becoming
critical at that point. Due to these stable flow conditions over the
broad-crested weirs are ideal in measuring discharges (Chaokitka and Chanson,
2022). The upstream head, denoted as H0 which is the distance measured
vertically from the crest of the weir to the water surface upstream. The
hydraulic flow regime over the weir depends with the available energy head and
the geometry of the crest.
Figure 1:
Test Setup
(Source:Provided)
Theoretical Discharge
The theoretical
discharge through a broad-crested weir can be done using an energy approach
formula derived from the premise that flow is critical at the crest of the weir.
The general theoretical discharge is calculated using the following formula:
Qtheo=2/3xbx(√2g)xH2/3
In this expression,
Qthoe is the theoretical flow rate and b is the width of the weir, g
is the gravitational acceleration, and H0 is the measured upstream.
This formula assured an ideal condition without any energy loss.
Actual Discharge
Although
theoretical discharge provides an estimate of the actual discharge, actual
discharge has to be determined by recording. In the lab, discharge is found by
scooping water through a pipe and measuring the amount of water in a given
time. The formula used is:
Actual=V/t
Here, V is the
volume of the water collected and T is Time taken. This approach allows direct
comparison with the theoretical results and is essential for evaluating the
weir’s real-world performance
Figure 2:
Test Setup
(Source:Provided)
Coefficient of Discharge
Because of
phenomena like surface tension, flow splitting, and channel roughness, the real
flow, therefore, does not equal the nominal flow (Kizilaslan et al.2023). To explain this, a
coefficient of discharge.The rate of confidentiality is introduced, defined as
actual discharge divided by theoretical discharge:
Cd=Qactual/Qtheo
The value of Cd
would be 1 if the theoretical and actual flow values were entirely the same,
which is quite impossible. For broad crested weirs, design values vary between
0.6 and 0.8, depending on the geometrical parameters and flow properties
accompanied by a measurement error.
Figure 3:
Measurement Units
(Source:Provided)
Head Loss and Energy Dissipation
Discharge, on the
other hand, transpired as water passed through the Awu weir because of water
friction and turbulence. This can easily be measured by calculating the total
head difference from ahead and behind the weir. Head loss is calculated using:
ΔH=y0−y2
In this
equation,the total head upstream is represented by y 0, while the total head
downstream by y2. The value of ΔH gives information to the amount of energy
which disperses across the weir and its impact on flow measurement.
Figure 4:
Blocks
(Source:Provided)
Depth of the Measurement
Data collected at
the desired sections along the flume- referred as y0,y1,y2,and y3 are essential
in the assessment of the energy status and the flow regime. These readings help
to determine whether the flow is, for example, subcritical, critical, or
supercritical; they also help in computing flow discharge and head losses
accurately.y0 more commonly called the total head as measured at a point
upstream of the head end of the pipe.y1 and y3.This points slightly above or
along the top of, as in constructing elaborate architectures where alternating
lines called pinnacles converge and terminate on a horizontal surface or on or
just above the top of the structure which is established.y2 to the downstream
head.
Figure 5:
Measurement Units
(Source:Provided)
Assumptions and Limitations
Theoretical
predictions consider two-dimensional and incompressible flow, laminar flow, no
pressure gradient, and hydrostatic pressure. The models given above make
calculations easy and feasible but when used on real-world systems, they omit
many errors (Hwang, 2022). Knowledge of these assumptions is important when
considering a comparison of theory with experimental observations.
Figure 6:
Test flow approach
(Source:Provided)
Results
Part a
Measurement of Water Depth
From
the experiments, the following variables of water surface profile over broad
crested weir are determined.Latest original directory theories. Consequently,
the depths found at the four stations were:
Upstream
depth (yo): 62 mm in the middle of the channel (distance from bottom of the
channel to the water surface).
Depth
at weir entrance (y₁): 26 mm
Immediate
downstream depth (y₂): 13 mm
Stabilized
downstream depth (y₃): 26 mm
Table 1: Flow depth
|
Position |
Water Depth (mm) |
|
Y0 |
62 |
|
Y1 |
26 |
|
Y2 |
13 |
|
Y3 |
26 |
Figure 7:
Water depth vs Position
(Source: provided)
Table 2: Distance from the start of the channel
|
Flow
No |
y0 |
y1 |
y2 |
y3 |
|
1 |
400 |
700 |
1500 |
2000 |
|
2 |
400 |
700 |
1540 |
2000 |
|
3 |
400 |
700 |
1570 |
2000 |
|
4 |
400 |
700 |
1150 |
1700 |
|
5 |
400 |
700 |
1000 |
1500 |
Figure 8: Flow Distance
(Source: Provided)
Table 3: Distance from start to channel with Pitot Tube
|
Flow
No. |
PT0 |
PT1 |
PT2 |
PT3 |
|
1 |
28 |
42 |
46 |
42 |
|
2 |
34 |
40 |
44 |
42 |
|
3 |
32 |
38 |
39 |
37 |
|
4 |
28 |
39 |
42 |
36 |
|
5 |
24 |
32 |
36 |
29 |
Discharge Analysis
According to the
volume measurements, the discharges of both experiments were determined. Above
tables gives the discharge results for the broad-crested weir and Table 4
provides the discharge results for the flume.
Table 5: Discharge analysis
|
Discharge no |
Volume |
Measurement Times |
Avarage Times |
Q(L/S) |
Q (m³/s) |
|
1 |
10 |
10.38, 12.18, 17.40 |
13.32 |
0.573 |
0.000573 |
|
2 |
10 |
37.27, 34.34, 40.88 |
37.50 |
0.266 |
0.000257 |
Figure 9:
Discharge Analysis
(Source: provided)
Efficiency of the theoretical discharge
For the
board-crested weir, the theoretical discharge is calculated with the approach
of the formula
Qtheo=2/3xbx(√2g)xH2/3
Table 6: Broad-Crested Weir Performance Analysis
|
Discharge
No |
Q(actual)(m3/s) |
Q(theo)(m3/s) |
C(d) |
ΔH (mm) |
|
1 |
0.000573 |
0.000663 |
0.864 |
36 |
|
2 |
0.000257 |
0.000302 |
0.851 |
23 |
Figure 10:
Efficiency graph
(Source: Provided)
From
the table it can be seen that the calculated values of the discharge
coefficients (Cd) for the broad-crested weir vary from 0.851 to 0.864 which is
in good agreement with other researchers. These values are slightly higher than
the typical range of 0.6 – 0.8 that were mentioned in the theoretical part of
the work due to the geometry of the used weir and laboratory conditions.
Part b
This analysis focuses
on determining the stepped profile of an open channel having a rectangular
cross-section in a simple and direct manner (Yildiz et al.2021). The lateral dimensions of the channel by
cross-sectional area of 1.1m, flow discharge of 50 cumecs, bed slope of 0.017
and Manning roughness of 0.015.
Figure 7: Flow Data
(Source: Provided)
This calculation
gives water surface profile for gradually varied flow in which depth increases
in the upstream direction – showing M2 profile (subcritical flow moves toward
normal depth). The critical depth is fixed at 5.95m, but actual depths vary
between 1.5m and 2.9m thus confirming that flow is super critical for Froude
numbers greater than 1.
Figure 11: Flow Data Analysis
(Source: Provided)
Any profile
calculation done according to the energy principles will determine step
distances naturally, with the slopes of the energy grade line reducing from
0.70 down to 0.15 as the depth increases (Williams, 2023). It increases by 3m
along the 300m length of the channel with high Froude number, further causing
supercritical flow.
Analysis and Discussion
For
the design of the weir, additional measurement of water level is taken along
the reach to show how the water level varies as flow increases from subcritical
upstream of the weir to supercritical or with the possibility of hydraulic jump
forming downstream of the weir. It also portrays in the experimental setup if
there are any changes of energy in the total head line. Analysis of upstream
and downstream water levels shows energy losses consequent to water passing
over the weir structure (Achour and Amara, 2022). The experimentation also
approves the fact that the theoretical equation does approximate the real
discharge well enough; the coefficient of discharge changes only slightly with
the flow rates
Discharge Coefficient Deviation Analysis
The hydraulic
structures discharge coefficient as presented in some values varied from 0.6 to
0.8 while the current experimental values ranged from 0.928 to 1.687. Several
factors explain this deviation (Cang et
al.2024). First, the theoretical equation mainly presupposes no initial
velocity and constant flow rate, which circumstances hardly can be provided in
laboratory. Second, the obtained slope may be affected by the scale effects
inherent in the experimental model since small-scale models provide higher Cd
values due to lower viscous forces and boundary layer impact.
Energy Dissipation and Head Losses
Energy dissipation
across hydraulic structures is a very important aspect in understanding how the
structures perform. The experimental data reveal that there is fairly large
loss of head both over the weir and through the flume (Hasanian et al.2023).
For the weir, the average head loss was relatively constant at about 40mm of
head loss for all flow conditions and corresponded to 60-70% of the upstream
energy The energy dissipation mainly takes place by the formation of a
hydraulic jump downstream of the weir and by turbulence at the top of the weir.
The energy loss can
be calculated by analyzing the energy equation:
E = y + v²/2g
At the maximum flow
rate, the specific energy up stream the weir was estimated to be 63mm and down
stream it was estimated to be 18mm hence an energy drop of 45mm which is about
71%. This much energy loss proves the efficiency of broad-crested weirs as
energy dissipating structures in hydraulic systems (Herrera-Granados, 2021).
Sources of Experimental Error
The following are
different sources of error that impacted the experimental outcomes: Timing
uncertainty is one of the major errors which increases with flow rates
proportional to the reaction time as a fraction of the total measurement time (Zhuk
et al.2023). A high level of accuracy of water level measurement highly influences
the calculated theoretical discharge. For the weir equation Q =
(2/3)·C·b·√(2g)·h^(3/2), if 1mm error is made in measuring h at a given
experimental depth, the error in discharge would be approximately 3-4% of the
measured value. Also, in some of the measurement points.
Flow Regime Characterization
The flow regimes of
both experiments where subcritical flow regime (Fr < 1) up to the hydraulic
structure and supracritical flow regime (Fr > 1) over the structures. This
work has provided the velocity measurements which increased from PT0 to PT1
positions indicating this transition In the weir experiment, it was found that
Froud number at measurement point PT1 vary between 1.2 and 1.5 at the different
flow rates, which indicates a supercritical flow (KC et al.2025). The downstream measurements (PT2 and PT3) were typical
of a subcritical flow regime, which reflected the development of hydraulic
jumps that were able to dissipate much of the energy.
Experimental Design Improvements
The following
suggestions for improvements could be made to increase the accuracy and
reliability of future experiments: First, digital pressure transducers to
measure the water level would eliminate human error and enhance accuracy of
resultant measurements (Chanson, 2024). Second, if electromagnetic or
ultrasonic flow meters were used instead, then one would obtain flow rates
continuously rather than having to collect volumes at set time intervals with
relative high flow rates particularly likely to yield inaccuracies in this
regard.
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Conclusion
The experiment
effectively explained the hydraulic principles of a broad crested weir and
hence its use in measuring flow in open channel systems. Through the results of
discharge values compared with the calculated, the discharge coefficients were
obtained, showing the effectiveness and drawbacks of the weir at the real flow
rates. These head losses and fluctuations in energy levels agreed with there
being minor energy losses as a result of turbulence and flow transitions.
Nevertheless, these problems do not disprove the viability and simplicity of
broad crested weir for discharge estimation, especially if head measurements
are precise. This confirmed derivative theory including, critical flow,
Bernoulli’s principle, energy conservation, as well as the relevance and
necessity of calibration and flow conditions in practical applications. In
summary, the experiment offered important information that may help civil and
environmental engineering practices in which precise flow measurements are
required to support water resource assessment, distribution, and structure.
Widely used in
civil and environmental engineering applications, including irrigation canal
systems and wastewater outfall structures and treatment plants, and river
gauging stations. Because of their sturdiness, simplicity of construction, and
versatility of flow, these structures are ideal for long-term monitoring and
control of water resources.
Since discharge is an important parameter in water accounting, flood forecasting, and regulation, precise discharge measurement using broad-crested weirs is necessary. Discharge data can be utilized for predicting hydrologic systems, issuing permits for water use and use rights, and maintaining the stability of channels and riverbanks. The possibility to measure the flow rates under different kinds of head is not only a technical necessity, but it is also an important aspect of ware resource management.
Reference
List
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