the weirs

1. 1
CHARACTERISTICS OF
SHARP WEIRS AND
THE HYDRAULIC JUMP
EXPERIMENTAL ANALYSIS OF THE ABOVE
PHENOMENA
BY MIMISA DICKENS
EN251-0305
2014
CCEE DEPARTMENT
JOMO KENYATTA UNIVERSITYOF AGRICULTURE ANDTECHNOLOGY
9/4/2014

2. 2
TABLE OF CONTENTS
EXPERIMENT ON V NOTCH
Abstract
Introduction
Materialsandapparatus
Procedure
Observations
Tabulateddata
Discussions
Graph work
EXPERIMENT ON BROAD CRESTED WEIR
Abstract
Introduction
Materials and apparatus
Procedure
Observations
Tabulated data
Discussions
Graph work
Explanation on graph work
EXPERIMENT ON HYDRAULIC JUMP
Abstract
Introduction
Materials and apparatus
Procedure
Observations
Tabulated data
Discussions
Graph work
Conclusions
Recommendations
Bibliography

3. 3
A seriesof experimentswere carriedoutinordertoanalyze the propertiesof sharpcrestedweirs.The
findingsof these experiments,tabulateddata,resultdiscussions,graphworkandconclusionshave been
includedtohelpilluminate the relevanceof certainphenomena.Theseexperimentshave been
discussedasbelow.
THE V-NOTCHEXPERIMENT
ABSTRACT
The resultsof an experiment carried out to investigate the relationshipbetween
the discharge and head above the notch are presented with much focus on the
rates of actual and theoreticflow. The experiment was carried out to allow the
observation of the properties of the v-notch in relation to discharge, and the
coefficient of discharge. The experiment was conducted under tight conditions
on a control volume at the point of discharge of water at the notch. The
properties of the flowing water; i.e. the temperature and density were put into
consideration properties of the V-notch were also determined and recorded.
These properties included width of channel,height of crest, half angle of notch,
and the crest level. The K value was also gotten from these properties. The data
collected in this experimentswere used in the calculation of; the K value of the
v-notch, actual discharge, theoretical discharge,coefficient of discharge for each
stage and the coefficient for each stage. To help relate certain values collected,
certain graphs were plotted to indicate the relationships. These graphs
included;
1. A graph of head (H) on the abscissa and the actual discharge on ordinate on
log-log graph paper and the following relationshipindicated. The mean value
of the coefficients of each stage and the mean value of the coefficients of
discharge were used after putting aside doubtful data.
2. A graph of theoretical discharge on abscissa and the actual discharge on
ordinate was also drawn on a section paper.
3. The coefficient of discharge on abscissa was plotted against H/Z on ordinate
on a section paper.
Herein discussed are the procedures, results, and theories behind the
experiments. Also indicated are the recommendations that have been put
across.

4. 4
INTRODUCTION
A weir is an overflow structure extending across a stream or channel and
normal to the direction of flow. They are usually categorized based on their
shape as either sharpcrested or broad crested.In this experiment,focus is laid
on a v-notch which is a sharp crested type of weir. It is used as a simple flow
measuring tool due to its mechanics of operation. The V-notches used in
measurement of discharge are designed and calibrated using standards that
have been laid to ensure minimum errors.The flow predicted from this weir is
inaccurate when the lower side of the stream wets the downstream chamber-
face. Standards may indicate the minimum as a fixed distance from the base of
the V also known as the crotch.
The theoretical discharge is related to the variables of this experiment as
follows;
𝑄 𝑡 =
8
15
√2𝑔. 𝐻
5
2.tan 𝜃 = 𝐾′ 𝐻
5
2
Where;
g = gravitational acceleration
H = head above notch
𝜃= half-angle of notch
𝐾′ =
8
15
√2𝑔. tan 𝜃
After the theoretical and actual discharges were determined, the coefficient of
discharge could be obtained according to the following relationship;
𝐶 𝑑 =
𝑄 𝑎
𝑄𝑡
Where;
𝑄 𝑎Represents the actual discharge obtained by the discharge measurement
device/ the gravimetric method
The head may be converted to the actual discharge;
𝑄 𝑎 = 𝐶 𝑑 𝑄 𝑡
8
15
𝐶 𝑑√2𝑔. 𝐻
5
2 = 𝐶 𝑑 𝐾′ 𝐻
5
2
Replacing
8
15
𝐶 𝑑√2𝑔 by K,
𝑄 𝑎 = K . 𝐻
5
2

5. 5
Since from the experiment 𝑄 𝑎 and H are measured, K is obtained from the following
equation;
K =
𝑄 𝑎
𝐻
5
2
.
When logarithmic scale paper is applied to 𝑄 𝑎 = K. 𝐻
5
2, K is determined based on an H-
Q graph. Applying the logarithmicoperation to this equation, the following is obtained;
Log 𝑄 𝑎 = log K +
5
2
log H.
From this relationship, we can conclude that whenthe experimental data are joined by
a straight line with a gradient of
5
2
, the actual discharge corresponding to H = 1m gives
the value of K
According to British Standard 3680 part 4A, the discharge equation for a v-notch with
the angle between 20° 𝑎𝑛𝑑 100° is as indicated below;
𝑄 𝑎 =
8
15
𝐶 𝐵√2𝑔.𝐻 𝐵
5
2.tan 𝜃
Where; 𝐶 𝐵= coefficient of discharge varying with the value of Z/B and H/Z
𝐻 𝐵 = head which enables for the effective viscosity and surface tension.
Using 𝐾ℎ for the effects,
𝐻 𝐵 = H + 𝐾ℎ
The value of 𝐾ℎ is a constant value of 0.00085m for a corresponding range of H/Z and
Z/B and is neglected in this experiment as it is very small.
PROCEDURE
The width of the approach channel and the height of the crest were measured using
the steel tape measure. The temperature of the water was then measured. The crest
level of the V-notch was then measured using a hook gauge after the channel was
filled up to the crest level with water The operation of the steady water supply system
was started and a small discharge set withthe gate valve after which the water level
was measured withthe hook gauge after the flow became steady. The discharge was
measured using the bucket, stop watch and the weighing balance. The discharge was
increased a little for several times ensuring that the discharge is not too high to hinder
water collection by the bucket. Proceduresfour and five were repeated and all data
tabulated as will be indicated herein.

6. 6
OBSERVATIONS AND RESULTS
This was the viewed cross section of the v-notch weir. The height H measured using
the hook gauge and recorded was taken as the height from the crest to the liquid
surface.
crest
It was observed that when the flow became steady, an aligned streamof water flowed
out of the notch with a constantly placed Nappe. However, it was also observed that
some head was lost when water flowed along the wall of the notch lowering the level of
expected efficiency.
Water trickling down the wall of the device
The head loss due to that amount of water was takento be minimal and was therefore
not used in the computation of the resultsdue to the complexity of acquiring the exact
quantities of loss involved.
The weir was observed as below in a side view. The nappe increased with increasing
range from the device and with increase in discharge. It also increased the ventilation.
This aspect can be applied in aeration of water during water treatment process in
treatment systems.
Turbulence occurring at the bottom of the collection

7. 7
The results that were obtained and recorded are as below;
Fundamental Data
Properties of water
Temperature 20°C
Density (ρ) 1000 kg/m3
Mass of bucket 0.65 kg
Properties of V-notch
Width of channel (B) 0.6 m
Height of crest (Z) 0.117 m
Half angle of notch (θ) 45°
K’ [=
8
15
√2𝑔 tan 𝜃] 2.362
Crest level (gauge) 0.224 m
Operation Data
Stage
Actual Discharge Point gauge
𝐇
𝐙
Theoretical
discharge
× 𝟏𝟎−𝟑
𝐦 𝟑
/𝐬
Cd K
Total
mass
kg
Mass
of
w ater
kg
Volume
× 𝟏𝟎−𝟑
𝐦 𝟑
Time
sec
Discharge
× 𝟏𝟎−𝟑
𝐦 𝟑
/𝐬
Mean
discharge
(𝑸 )
× 𝟏𝟎−𝟑
𝐦 𝟑
/𝐬
Reading
M
Head
(H)
m
1
7.1 6.45 6.45 5.28 1.222
1.632 0.154 0.070 0.598 3.062 0.533 1.2597.2 6.55 6.55 3.71 1.765
12.8 12.15 12.15 6.36 1.910
2
11.5 10.85 10.85 5.26 2.063
2.140 0.148 0.076 0.650 3.761 0.569 1.34410.6 9.95 9.95 4.72 2.108
9.8 9.15 9.15 4.07 2.248
3
9.9 9.25 9.25 3.82 2.421
2.430 0.144 0.080 0.684 4.276 0.568 1.34210.2 9.55 9.55 4.02 2.376
10.4 9.75 9.75 3.91 2.494
4
10.2 9.55 9.55 3.58 2.668
2.694 0.141 0.083 0.709 4.688 0.575 1.3579.4 8.75 8.75 3.28 2.668
10.7 10.05 10.05 3.66 2.746
5
9.4 8.75 8.75 2.99 2.926
3.014 0.138 0.086 0.735 5.123 0.588 1.3909.4 8.75 8.75 2.89 3.028
10.5 9.85 9.85 3.19 3.088
6
11.2 10.55 10.55 2.87 3.676
3.651 0.133 0.091 0.778 5.900 0.619 1.46212.0 11.35 11.35 3.13 3.626
- - - - -
Mean value 𝑪 𝒅𝒎=0.575 Km=1.358

8. 8
DISCUSSION AND CONCLUSIONS FROM RESULTS
From the resultsobtained and tabulated above, certainaspects have been derived. The
graphs hereinplotted have been used to explain concepts that the experiment was
expected to bring out.
LOG-LOG GRAPH OF H AGAINSTQa
Thisgraph shouldproduce a straightline.Howeverdue toerrorsinthe experiment,thisisnotthe case.
Howeverif the trendline isdrawn,itshouldproduce astraightline whose gradientshouldbe
arithmeticallyequal toCd*K
Where;Cd = coefficientof discharge of the v-notch
K = coefficientof the v-notch
In thiscase the gradientresultingfromthe line of bestfitis0.332 indicatingthatCd*K= 0.332.
The interceptof the Log H axisshouldindicate the logof the crestlevel of the v-notch.
For the relationshipbetweenQandH to be linear,the intercept,where H=0,needstobe takeninto
consideration.
y = 0.332x - 1.2259
-1.18
-1.16
-1.14
-1.12
-1.1
-1.08
-1.06
-1.04
-1.02
0 0.1 0.2 0.3 0.4 0.5 0.6
logH
logQa
Graph of log H againstlog Qa

9. 9
GRAPH OF Qt AGAINST Qa
The graph of Qt againstQa drawn above producesagradual curve due to erroneousdatacollected.It
was,however,expectedtoproduce astraightline whose gradientwastogive the coefficientof
discharge of the v-notch.
In thiscase,if a trendline isdrawnas a line of bestfit,itsgradientisobtainedas0.533. therefore the Cd
obtainedfromthisgraphis0.533.
y = 0.5339x + 2.5995
0
1
2
3
4
5
6
7
0 1 2 3 4 5 6 7
theoreticaldischarge,Qt
actual discharge,Qa
graph of Qt againstQa

10. 10
GRAPH OF H/Z AGAINST Cd
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6 0.61 0.62 0.63
H/Z
Cd
Graph of H/Z againstCd

11. 11
These graphshereindrawnhave beenusedtoindicate justhow possible itistorelate calculateddata
and experimenteddata.The differencesattainedare howeverminimalsince itishighlyexpectedthat
duringthe experiment,alotof data islost randomlyordue to observercarelessness.Itisalso
recommendedthatthe equipmentsbe repairedfromleakagessoasto reduce errorsindata collected.
It wouldalsobe expectedthatmore time shouldbe issuedforextensive studyonthese principles
before experimentingandreportingonthe same.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6 0.61 0.62 0.63
H/Z
Cd
Graph of H/Z against Cd with line of best fit

12. 12
THE BROAD-CRESTED WEIR EXPERIMENT
ABSTRACT
Discharge characteristics of a broad crested weir defined by a laboratory test
are described. Broad crested weirs may be classified as short, normal or long
depending on the water-surface profile over the weir. The discharge equation is
obtained by dimensional analysis, and the coefficient of discharge is related to
dimensionless ratios that describe the geometry of the channel and the relative
influence of the forces that determine the flow pattern.
There is no involvement of new experimental work. The broad crested weir used
comprises of a square edge on one side and a rounded edge on the other used
for the measurement of low flows. The weirs then broaden to a wide
rectangular section at higher flow depths. By positioning the flow appropriately,
the burble of flow that results from the rounding of the edge can be
investigated. The inflow and outflow processes on the broad crested weir are
also investigated. They are normally used as flow of water measuring device in
irrigation canals. The purpose of this paper is to present data that will be of
use in the design of hydraulic structures for flow control and measurement. A
series of steps were followed in this test to indicate the effects of width and step
height of broad crested weirs in a rectangular cross-sectional channel on the
values of the coefficient of discharge and the approaching coefficients of
velocity. The experiment was done severally for a range of different discharges.
The sill-referenced heads at the approach channel and at the tail channel were
measured in each experiment. The results obtained indicate a discontinuity
that occurs in head discharge ratings because of the sudden change of shape
of the section width which results into a break in slope when the flow enters
the other section.
INTRODUCTION
A weir is a simple device used for measuring discharge and control of flow in
open channels. The techniques that are used in making discharge measuring
equipment at gauging stations are very important. Portable instruments like
weirs, flumes, floats, and volumetric tanks are commonly used for this
purpose. Discharges are measured from very small channels like ditches to
very large river channels. Broad crested weirs operate under the theory that
critical flow conditions are crested above the weir. As such, the depth of water
above the weir is equivalent to the critical depth. Critical condition is created
when the relationship between the inertial and gravitational forces of flow is
equal to 1.0. This occurs when the velocity of flow equals the velocity of the

13. 13
wave (celerity), C =√ 𝑔𝑦. This relationship is referred to as Froude Number (Fr).
When flow is critical, Fr = 1.0
𝐹𝑟 =
𝑉
√ 𝑔𝑦
Where, y = depth of water. At critical point of flow, it becomes 𝑦𝑐
V= average flow velocity
G= gravitational force exerted on flowing liquid
Fr= Resulting Froude number
A lot of research has been carried out on weirs to determine their properties in
relation to flow of water. This study was also extended to include the
relationship between the discharges obtained from calculations and those
obtained from experimental data. Jan et al researched on the same and came
up with equations that described flow in simple broad crested weirs and in
compound broad crested weirs too. His equations indicated that the values
obtained from calculations and the measured ones are less than 3% for flows
over broad crested weirs under the experimental conditions. According to
Sarker and Rhodes (2004) works, rectangular broad crested weir experiments
were performed over laboratory scales and the results obtained compared with
numerical calculation results obtained using commercial software. From these,
it was found out that for a given flow rate, it was excellently possible to predict
the upstream flow depth and the flow profile over the broad crested weir that
was rapidly varied was reproduced quite well. It was however, not easy to
predict the downstream depth after the energy losses since the determination
of this energy is widely based on certain assumptions. The top of the broad
crested weir which is opposed to the direction of flow corresponds to a channel
inlet whereas the bottom corresponds to the overflow.
Traditionally, the weir discharge is determined from a single depth
measurement on the crest. This elementary method, however, is not
satisfactory when an accurate discharge determination is required. The flow
depth does not correspond to that obtained everywhere on the weir crest. The
location of the control, or critical depth, section, is not constant, but varies
with the discharge, weir geometry and crest roughness.

14. 14
The flow rate over the broad-crested weir can be represented by the following
equation;
In which case;
Q = actual volumetric flow rate ( 𝑚3
/𝑠)
𝐶 𝑑= coefficient of discharge
G = gravity
B = width of channel
H = total energy head of the flow upstream measured relative to the weir-
crested elevation
𝑦0 = depth of water upstream
𝑦𝑐 = critical depth of flow in the channel
ℎ1 = energy head upstream relative to the top of the broad-crested weir
𝐻 = ℎ1 +
𝑣0
2
2𝑔
In actual application of the broad-crested weir concept, it is more convenient to
use ℎ1 in the equation instead of H. the equation of discharge is then effected
by a coefficient of velocity as indicated below.

15. 15
According to French (1985), a proper operation of the broad crested weir is
achieved when flow conditions are restricted to an operation range of 0.08 <
ℎ1 < 0.33 where L is the length of the weir.
In the case of the experiment that was operated, a v-notch of known
dimensions and coefficient was used thus making the calculations easier. The
actual discharge was measured by the v-notch whereby;
𝑄 𝑎 = 𝐾𝑣 𝐻 𝑣
5
2
𝐾𝑣 =
8
15
𝐶 𝑑𝑣√2𝑔𝑡𝑎𝑛𝜃
Where, 𝐻 𝑣 = head above V-notch
𝐶 𝑑𝑣 = Coefficient of discharge of V-notch
𝜃 = Half-angle of v-notch
𝐾𝑣 = Coefficient of V-notch
The values of 𝐶 𝑑𝑣 and 𝐾𝑣 that are used in this experiment were obtained from
the v-notch experiment.
Normally, the total head relative to the crest level of the broad crested weir at
section one is given by;
𝐸 = 𝐻1 − 𝑍 +
𝑉1
2
2𝑔
= 𝐻1 − 𝑍 +
1
2𝑔
(
𝑄 𝑎
𝐵 𝐻1
)2
Where 𝐻1 = depth at section 1
𝑉1 = velocity of flow at section 1
Z = height of weir
B = width of weir
The specific energy at the weir is equal to the total head, E. there exists a
relationship between the specific energy and the depth at the control section
(critical depth, 𝐻𝑐 as indicated in the equation below:

16. 16
𝐸 =
3
2
𝐻𝑐
If the critical depth is measured, it becomes easy to calculate the specific
energy and the discharge of the weir. Determining the exact position of the
critical flow is, however, the difficult task. In order to determine the coefficient
of discharge in this experiment, it becomes necessary to adopt the upstream
depth and the approaching velocity in order to use the same in the following
calculation𝑄 𝑎/𝐵𝐻1.
After the actual discharge and the depth hsve been determined, it now becomes
possible to calculate the Froude number so as to help determine the states of
flow tht are involved. The following formulae are used;
Velocity of flow, V =
𝑄 𝑎
𝐵𝐻
Celerity, u = √ 𝑔𝐻
Froude number is given as a relationship between the velocity of flow and the
celerity.
𝐹𝑟 =
𝑉
𝑢
=
𝑄 𝑎
𝐵𝐻√ 𝑔𝐻
The values obtained from this relationship are used in classifying flow
according to the following criterion;
Fr > 1.0 supercritical flow
Fr = 1.0 critical flow
Fr < 1.0 supercritical flow
The control section therefore is located at the point where the critical flow
occurs, i.e. where Fr = 1.0
Critical flow is normally assumed to occur at the weir crest.
MATERIALS USED
1. A steady water supply system
2. A round-nose broad-crested weir with rubber packings
3. An adjustable slope rectangular open channel with point gauges
4. A v-notch with a hook gauge

17. 17
5. A steel tape measure
6. A thermometer
PROCEDURE
After the dimensions of the broad crested weir and the distances from section
2A to 2F were measured, the slope of the channel was set as zero. The
temperature of the water was then measured after which the crest level of the
broad crested weir and the channel bed level were measured using the point
gauges. The crest level of the v-notch was measured using the hook-notch,
then water was filled up to the crest level. The operation of the steady water
supply system was started and a small discharge set. The head above the v-
notch was measured after the flow became steady.
The depth of flow in the upstream where the weir does not exert influence on
the water surface was measured. The change of state of flow by the broad
crested weir was observed and the control flow section identified by letting a
drop of water fall on the flow surface. The discharge was then increased a little
and the procedure skipped back to the stage of measuring the head on the v-
notch until the last one. At one flow rate, the depth at sections 2A to 2F were
measured, recorded and used to calculate the discharge over the weir.
Observations Made
for this experiment, photographs and diagrams were collected and included in
this report to support the theoretical and analytical discussions of the
tabulated data. The layout and change in states of flow were also indicated as
shown by the images herein included. The flow was observed to fluctuate over
the weir as shown below.

18. 18
The flow depth was observed to reduce suddenly fall as the water flew over the
weir indicating a change in the state of flow. These changes observed can be
attributed to the analysis of the graph work that is also included in this report.
Results Obtained
***FUNDAMENTAL DATA***
Properties of water Temperature 19 °C
Density (ρ) 1000 kg/m3
Dimensions of broad
crested weir
Width (B) 0.3m
Length(L) 0.3m
Height (z) 0.15m
1-0.006L/B 0.994m
Crest level (point gauge) 0.696m
Property of channel Bed level (point gauge) 0.546m
Properties of v-notch Half angle of V-notch 45°
Coefficient of discharge
(Cdv)
0.567
Coefficient (KV) 1.358
Crest level(hook gauge) 0.216m
*****OPERATION DATA*****
V-notch

19. 19
Sta
ge
Readi
ng
M
Hea
d
(HV)
Disch
arge
(Qa)
×10-
3m3/s
Readi
ng
m
Dept
h
(H1)
m
H1-
Z
M
L/(
H1-
Z)
Veloc
ity of
flow(v
1)
m/s
Veloci
ty
head(
V12/2
g)
m
×10-4
Specif
ic
energy
(E)
m
×10-2
Theor
etical
discha
rge
(Qt)
×10-
3m3/s
Cd Cdt
1 0.132 0.0
84
2.778 0.729 0.18
3
0.0
33
9.0
91
0.030
9
0.485
8
3.304
85
3.064 0.9
06
7
0.9
54
2 0.100 0.1
16
6.223 0.738 0.18
7
0.0
37
8.1
08
0.069 2.438 3.724
3
3.666 0.9
58
3 0.128 0.0
88
3.12 0.733 0.18
7
0.0
37
8.1
08
0.034 0.612
7
3.706
1
3.639 0.8
57
0.9
58
4 0.127 0.0
89
3.21 0.735 0.18
9
0.0
39
7.6
92
0.035
7
0.648
6
3.906
5
3.938 0.8
15
0.9
60
5 0.124 0.0
92
3.49 0.737 0.19
1
0.0
41
7.3
17
0.038
8
0.766
7
4.107
7
4.246 0.8
22
0.9
61
6 0.120 0.0
96
3.878 0.739 0.19
3
0.0
43
6.9
77
0.043
1
0.946
7
4.309
4
4.563 0.8
49
8
0.9
63
7 0.115 0.1
01
4.403 0.743 0.19
7
0.0
47
6.3
83
0.048
9
1.22 4.712
2
5.216
8
0.8
44
0
0.9
66
8 0.112 0.1
04
4.737 0.746 0.2 0.0
5
6.0
0
0.052
6
1.413 5.014
1
5.726 0.8
27
2
0.9
61
9 0.110 0.1
06
4.968 0.746 0.2 0.0
5
6.0
0
0.055
2
1.554 5.015
5
5.729 0.8
67
2
0.9
61
10 0.100 0.1
16
6.224 0.755 0.20
9
0.0
59
5.0
85
0.069
2
2.439 5.924
4
7.354 0.8
46
0.9
71
TABLE 6.2 DATA SHEET

20. 20
Selected stage 10
Actual discharge Qa m3/s 6.224*10-3
Crest level of weir (m) 0.696
Width of the weir (B)
0.3
OPERATION DATA
Section Distance
from
section
2A
Water
level
(point
gauge)
m
Depth
(H)
M
Velocity
of flow(v)
m/s
Propagation
Velocity(u)
m/s
Froude
number(Fr)
2A 0.00 0.748 0.052 0.3990 0.7141 0.5587
2B 0.05 0.74 0.044 0.4715 0.6569 0.7178
2C 0.10 0.734 0.038 0.546 0.6104 0.8945
2D 0.15 0.731 0.035 0.5928 0.5858 1.0119
2E 0.20 0.729 0.033 0.6287 0.5689 1.1051
2F 0.25 0.721 0.025 0.8297 0.4951 1.6758

21. 21
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.2 0.4 0.6 0.8 1
LogE
Log Qa
Y-Values
y = 0.4216x + 0.374
R² = 0.4574
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.2 0.4 0.6 0.8 1
LogE
log Qa
graph of log specific energy against
log of Qa with trend line
Y-Values
Linear (Y-Values)

22. 22
y = 6.289x + 0.1679
R² = 0.9909
0.18
0.185
0.19
0.195
0.2
0.205
0.21
0.215
0 0.002 0.004 0.006 0.008
H1(m)
actual discharge,Qa
depth H1 againstactual dischargeQa
Depth H1
Linear (Depth H1)
y = 6.289x + 0.1679
0.18
0.185
0.19
0.195
0.2
0.205
0.21
0.215
0 0.002 0.004 0.006 0.008
H1(m)
actual discharge,Qa
depth H1 againstactual dischargeQa with
trendline
Depth H1
Linear (Depth H1)

23. 23
y = 0.2461x - 0.0157
R² = 0.3543
0.18
0.185
0.19
0.195
0.2
0.205
0.21
0.215
0.82 0.84 0.86 0.88 0.9
H1
Cd
Graph of H1 againstCd
Depth H1
Linear (Depth H1)
y = 0.2461x - 0.0157
0.18
0.185
0.19
0.195
0.2
0.205
0.21
0.215
0.82 0.84 0.86 0.88 0.9
H1
Cd
Graph of H1 againstCd with trendline
Depth H1
Linear (Depth H1)

24. THE HYDRAULIC JUMPEXPERIMENT
DETERMINATION OF THE PROPERTIES AND APPLICATIONS OF THE HYDRAULIC
JUMP
ABSTRACT
The resultsof an experimental investigation of the phenomenon of the hydraulic jump
are presented,with focus on the dependence on the flow rates and the level of
opening on the sluice gate. The experiment was carried out so as to open up some
information about the hydraulic jump. It was centered on observing its physical
appearance and understanding the relationshipbetween the depth and the specific
energy under a condition of constant discharge. During the formationof the hydraulic
jump, there is an unknown amount of energy that is lost. To determine the possible
value of this energy,there is need to apply the Momentum equation since the energy
equation cannot be applied at this point. A control volume is used by enclosing the
jump as will be indicated herein and also discussed using the continuity equation.
Data is collected for this purpose. The data collected in this experiment include the
fundamental and operation data. The temperature and density properties of the
water,the dimensions of the channel and the propertiesof the v-notch are measured
out as the fundamental data. At varying volumetricrates of flow, the operational data
is collected. This data include the head, discharge and water surface levelsat different
stages on the V-notch. The water surface levels at two different levelson the
rectangular channel are also measured out at the three different stages using the
same discharge.
While the valuesof the fluid depth after and before the jump and Froude number
inside the jump strongly depend on variations in flow rate and levelsof openings on
the sluice gate,this dependence does not seem to be strong for the Froude number
outside the jump. The collection of these data will be highly instrumental in the
determination of energies in the system using the knowledge of momentum and the
momentum equation and conservation of mass. Hereinillustrated and discussed is
the whole process that led to the determination of the required energies and their
possible applications in the field of engineering.
INTRODUCTION
A classical jump (hydraulicjump in a rectangular section) is a phenomenon that
involves the water surface rising,surface rollersforming, intense mixing occurring, air
being entrained and energy being dissipated at the transitionwhenever flow changes
from supercritical to subcritical.
This experiment was purposed to observe the hydraulic jumpphenomenon and to
compare measured flow depths with theoretical results based on the application of the
momentum principle and continuity. In the laboratory flume, the flow is regulated
from the upstream end by a sluice gate to developa shallow and rapid supercritical

25. 25
flow. Gradually, a hydraulic jumpis formed at the transition point where the
downstream subcritical and the upstream supercritical flows coincide. It occurs
analogously to the shock wave phenomenon in aerodynamics where a supersonic
flow meets a subsonic flow and a shock front develops at the transition between
the two flow regimes. When observed on a control volume, its properties and
capabilitiescan be observed and analyzed. An observation of the same may be covered
by the following illustration.
The channel is taken to be having a uniform width, b.
Using the above illustrated diagram, the continuity equationmay be expressed as;
Q = 𝑏𝑣1ℎ1 = 𝑏𝑣2ℎ2-----------------------------------------------------------------------------(i)
Whereby Q represents the discharge, v representsthe velocities at the different
sections. ’h’ values indicate the heights at section just before and exactly after the
jump. The momentum equationtaking into consideration the hydrostatic forces and
the momentum fluxesignoring the frictional forces at the bottom and side surface of
the channel is;
1
2
𝜌𝑔𝑏ℎ1
2
=
1
2
𝜌𝑔𝑏ℎ2
2
= 𝜌𝑄(𝑣1 − 𝑣2)------------------------------------------------------------(ii)
The flowing water is homogeneous thus the density is taken to be constant together
with the gravitational force acting on it. Taking a momentum function to be equal to;
𝑀 =
𝑣2ℎ
2𝑔
+
ℎ2
2
----------------------------------------------------------------------------------(iii)
Then using equation (i), it is correct to suggest that equation (ii) implies that

26. 26
𝑀1 = 𝑀2-----------------------------------------------------------------------------------------(iv)
The relationshipbetweenthe water depths before and after the jump may be
expressed from equation (i) and (ii) as;
ℎ1
ℎ2
=
1
2
(√1 + 8𝐹𝑟2
2
− 1) or;
ℎ2
ℎ1
=
1
2
(√1 + 8𝐹𝑟1
2
− 1)
Where 𝐹𝑟1 =
𝑣1
√ 𝑔ℎ1
and 𝐹𝑟2 =
𝑣2
√ 𝑔ℎ2
;
For a hydraulic jump, the upstream flow is supercritical and Fr1>1.
On the other hand, the Froude number Fr2 of the downstream subcritical flow needs
to satisfy
Fr2=𝑉2 𝑔ℎ2<1
We can further expressthe principle of conservation of mass in this open channel
section as
ℎ1 +
𝑣1
2
2𝑔
= ℎ2 +
𝑣2
2
2𝑔
+ ℎ 𝑙
And show that the “head loss” ℎ 𝑙for hydraulic jumpis calculated as;
ℎ 𝑙 =
(ℎ2ℎ1)3
4ℎ1ℎ2
Therefore the energy loss at a hydraulic jump becomes a simple function of the relative
depths of flow in question. This leads to an increased ease of hydraulic jump function
application. This does not, however, eliminate the need to access the significance of
the result as far as precision is concerned. Severe hydraulic jumps may lead to very
large energy losses and the dissipation of this energy may be used relevantly in
different fieldsof engineering.
MATERIALS AND METHODS
APPARATUS
For the purpose of this experiment, the following apparatus were needed and therefore
provided for the said purpose. The availability and effectivenessof these apparatus did
much in contributing into the final observations made since great losseswould lead to
gross errorsthat would be difficult to adjust. The equipments used include:
1. An adjustable-slope rectangular open channel with point gauges.
2. A steady water supply system.
3. A v-notch with a hook gauge.
4. A sluice gate withrubber packings.
5. An adjustable-height suppressed weir.

27. 27
6. A steel tape measure.
7. A thermometer.
METHOD
For collection of values that are close to an accurate, it was expected that the
procedures were followed keenly witha high degree of attention so as to ensure
accuracy of collected data. Failure to follow the right procedure or a tendency to skip
certain steps may lead to gross errors that are not desirable in this case. Be low are the
steps that were followed during the experiment.
PROCEDURE
After the equipment was set-upas illustrated by the following diagram,the steps were
followed as follows.
The sluice gate was put on the open channel with rubber packings in the space
between the gate and the channel bed after which the channel bed was set to be
horizontal so that the slope will be zero. The width of the channel was thenmeasured
with the steel tape measure and the channel bed levels at sections one and two were
also measured using the point gauges. The temperature of the water was measured
after the crest level of the v-notch that was pouring water into the channel was
measured.
It was then that the operation of the steady water supply system was started with the
opening on the sluice gate left as 0.009m. The head above the v-notch was measured
and the water surface levelsat sectionsone and two also measured using the point
gauges. The change in flow was observed. The opening height of the sluice gate was
increased by 0,002m two more timesand other hydraulicjumps created by adjusting

28. 28
the height of the suppressed weir. The sixth Procedure was repeated twice
simultaneously after procedure seven to observe values for statesB and C. The
discharge was increased for stagestwo and three and corresponding valuesfor states
A, B and C recorded as the experiment proceeded.
OBSERVATIONS MADE AND RESULTS COLLECTED
During the experiment,certain observationswere made that were relevant to the
expected results.As the discharge was set and water allowed to flow, the conditions of
flow after the sluice gate kept changing until a constant condition became dominant.
This occurred when the flow became steady. The flow became steady whenthe height
of liquid upstream of the sluice gate became a constant and no further changeswere
observed on the height. The steady flow was first observed at the input section when
the flow through the v-notch ceased to change and the height above the crest became
a constant.
As the discharge rate was increased gradually and/or the opening on the gate
increased,the type of jump and its characteristics also changed similarly due to an
change in the relationshipbetweenthe velocity of flow and the celerity. This change is
illustrated in the diagrambelow.
It was observed that the turbulence at the point of the jump was more violent with
smaller gate openings. It took approximately sevenminutes for the jump to properly

29. 29
form after whichdata was taken and recorded at each stage as indicated in the tables
below.
RESULTS TABULATION
TITLE: EXPERIMENT DATE: 28TH MARCH 2014
EXPERIMENTER: NO. :
***FUNDAMENTAL DATA***
Properties of water Temperature
22 ℃
Density
( 𝜌 ) 1000 kg/m3
Dimensions of
channel
Width
( B ) 0.30 m
Channel Bed
Level
Section
1 0.4750 m
Section
2 0.4750 m
Properties of V-
Notch
Half angle of notch
( 𝜃 )
45 °
Coefficient of Discharge
( CdV ) 0.575
Coefficient
( KV ) 1.36
Crest Level
0.2180 m
***OPERATION DATA***
Stage State
V-Notch Reading of point
gauge
Depth
Reading
m
Head
( HV )
M
Discharge
( Q )
x 10-
3m3/s
Section
1
m
Section
2
m
Section
1
( H1 )
m
Section
2
( H2 )
M
1
A
0.1304 0.0876 3.089
0.489 0.526 0.014 0.051
B 0.482 0.528 0.007 0.053
C 0.480 0.536 0.005 0.061
A 0.482 0.516 0.007 0.041

30. 30
2 B 0.1395 0.0785 2.348 0.481 0.521 0.006 0.046
C 0.480 0.530 0.005 0.055
***CALCULATION***
Stage Stat
e
Velocity Velocity
Head
Specific
Energy
Froude
Number
Actu
al
(
𝑯 𝟐
𝑯 𝟏
)
Theo
retic
al
(
𝑯 𝟐
𝑯 𝟏
)
Actu
al
head
loss
( ∆E )
m
Theoret
ical
Head
loss
( hj )
m
Secti
on 1
( V1 )
m/s
Secti
on 2
( V2 )
m/s
Secti
on 1
(
𝑽 𝟐
𝟏
𝟐𝒈
)
m
Secti
on 2
(
𝑽 𝟐
𝟏
𝟐𝒈
)
x10-3
m
Secti
on 1
( E1 )
M
Secti
on 2
( E2 )
m
Secti
on 1
( Fr1 )
Secti
on 2
( Fr2 )
1
A 0.735 0.202 0.028 2.080 0.042 0.053 1.983 0.286 3.643 2.349 -
0.011
0.018
B 1.471 0.194 0.110 1.918 0.117 0.055 5.613 0.269 7.571 7.454 0.062 0.066
C 2.059 0.169 0.216 1.456 0.221 0.062 9.297 0.218 12.20
0
12.65
7
0.159 0.144
2
A 1.118 0.191 0.064 1.860 0.071 0.043 4.266 0.301 5.857 5.554 0.028 0.034
B 1.304 0.170 0.087 1.473 0.093 0.047 5.375 0.253 7.667 7.118 0.046 0.058
C 1.565 0.142 0.125 1.028 0.130 0.056 7.066 0.193 11.00
0
9.505 0.074 0.114
These results were recorded without any erasure whatsoever. They have been used in
the determination of the values that were used in the plotting of the graphs herein
included.

31. 31
At section 1 it is expected that as the depth of water increases, the specific energyof
the flow reduces gradually. It is expected that there should be alternate depths at
which the specificenergies are the same. This is however not the case as the value s
y = -0.0483x + 0.0148
R² = 0.8457
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0 0.05 0.1 0.15 0.2 0.25
specificenergy
depth
specific energy against depth in section 1
stage 1
s.1 depth
Linear (s.1 depth)
y = -0.0332x + 0.0093
R² = 0.9789
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
specificenergy
depth
graph of specific energy against depth at
section 1 stage 2
s.1 depth2
Linear (s.1 depth2)

32. 32
collected in the first stage were not sufficient enough to produce the expected graph
therefore the relationshipwas not indicated as expected.
y = 1.1194x - 0.0084
R² = 0.9995
0.05
0.052
0.054
0.056
0.058
0.06
0.062
0.052 0.054 0.056 0.058 0.06 0.062 0.064
specificenergy
depth
graph of specific energy against depth at
section2 stage 1
s2 depth1
Linear (s2 depth1)
y = 1.0639x - 0.0044
R² = 0.997
0
0.01
0.02
0.03
0.04
0.05
0.06
0 0.01 0.02 0.03 0.04 0.05 0.06
specificenergy
depth
graph of specific energy against depth at section2
stage 2
s2 se22
Linear (s2 se22)

33. 33
These graphs derived from depths of flow and specific energy at section indicate that
the depth increases as time passeslinearlywith the specific energy indicating that the
two variables are linearly related. The variablesare directlyproportional.
Under the considerationsthat have been asked for in the laboratory practical manual,
the following series of equations have been derived to help explain the phenomena;
Q = A1V1 =A2V2
Bh1V1 =Bh2V2
Therefore,V2=
h1V1
h2
(V2)2
=(
h1V1
h2
)2
= 𝑉1
2
(
h1
h2
)2
Change of pressure forces
ΔFp = ϱgA1
ℎ1
2
- ϱgA2
ℎ2
2
= ϱg(
𝐵ℎ1
2
2
-
𝐵ℎ2
2
2
)
= 𝜚g
𝐵
2
(ℎ1
2
- ℎ2
2
)
= ϱg
𝐵
2
(h1+h2)(h1-h2)
Change inthe momentum
ΔFm = ϱBh1 𝑉1
2
-ϱBh2 𝑉2
2
= ϱB(h1 𝑉1
2
-h2 𝑉2
2
)
Therefore,
ΔFm = ϱB [(h1 𝑉1
2
-h2 𝑉1
2
(
h1
h2
)2
]
=ϱB𝑉1
2 h1
h2
(h1-h2))
From the Newton’ssecondlaw of motion;
-ΔFm = ΔFp
-ϱB𝑉1
2 h1
h2
(h1-h2))=ϱg
𝐵
2
(h1+h2)(h1-h2)
𝑉1
2
=
𝑔
2
(h1+h2)
ℎ2
ℎ1
…eqn(a)
Q=AV
Q=B2
h1[
𝑔
2
(h1+h2)
ℎ2
ℎ1
]
But q=
𝑄
𝐵
,
Therefore,q2
=ℎ1
2 𝑔
2
(h1+h2)
ℎ2
ℎ1
=gh1h2(
(ℎ1+ℎ2
2
)…eqn(b)
From eqn(1);
0=h1h2+h2
2
-
2h1v12
g
basingthe above on the quadraticequation,
x=
−𝑏+_(√𝑏2−4𝑎𝑐
2𝑎
thena=1 ;b=h1;c=−
2h1v12
g
h2=
−ℎ1+_(√ℎ12+4(ℎ12v12/𝑔
2

34. 34
2h2=-h1+_√ℎ12 + 8
𝑣12ℎ1
𝑔
2h2=-h1+_ℎ1√1 + 8
𝑣12ℎ1
𝑔
h2=h1/2[√1 + 8
𝑣12ℎ1
𝑔
-1]
butFr=
𝑣
√ 𝑔ℎ
therefore
ℎ2
ℎ1
=
1
2
[√1 + 8𝐹𝑟12 − 1]…eqn10.5
ℎ1
ℎ2
=
1
2
[√1 + 8𝐹𝑟22 − 1]..eqn10.6
Energychange is givenby
ΔE=(
𝑣12−𝑣22
2𝑔
)-(h2-h1)
Substitutingforvaluesof V1 andv2
gives
ΔE=
(ℎ2−ℎ1)3
4ℎ1ℎ2
…eqn10.7
CONCLUSION
These experiments carried out under controlled conditionswere expected to explain
the phenomena of flow through weirs and the characteristics of the resultants.These
relationships have been brought out as such though there accuracy may be in a lot of
question.
The errors herein obtained may be as a result of negligence and fault of equipment
being used. Negligence, on the part of the observer, led to gross errors that were
indicated in the broad crested weir experiment. Fault of equipment, e.g.leakages, led
to random errors that were evenly distributed in the data collected as brought out in
the v-notch and Hydraulic jumpexperiments.
Recommendations
It is recommended that the equipment in the laboratory should be checked and
maintained regularly for the purpose of producing data that are closest to the
expected. The researchersshould also be given enough time and chance to study wide
and experiment repeatedly on these phenomena so as to acquaint themselvesproperly
with the expected proceduresin this study.
There should also be sufficient support and supervision by the technicians so as to
ensure the procedures are adhered to and to helpminimize gross errors.

35. 35
BIBLIOGRAPHY
1. DischargerelationsforRectangularBroadCrestedWeirs
Farzin Salmasi, Sanaz Poorescandar. Ali Hosseinzadeh Dalir, DavoodFarsadi Zadeh
Tabris University
2. EquipmentforEngineeringEducation
G.U.N.T.Geratebau G.M.B.H, Baisbuttel
Germany
3. HydraulicJumps
Sara Connoly, May 4, 2001
The college of Wooster.
4. Numerical Studyof a TurbulentHydraulicJump
Qun Zhao, Shubhra K. Misra, Ib A. Svendsen and James T. Kirby.
Engineering Mechanics conference
University of Delaware, Newark,DE
5. DischargeCharacteristicsofBroad-CrestedWeirs
H. J. Tracy
United States Department of the Interior
6. HydrologyandHydraulicEngineering
Dept of Civil Engineering, School of Engineering
City College of New York
7. Open Channel Hydraulics
Vent T. E. Chow, 1959, Singapore, McGraw-Hill
8. HydraulicsinCivil andEnvironmental Engineering
Andrew Chadwick and John Morfett, 1993
Edmunds Bury Press, Bury ST Edmunds, Suffolk,Great Britain
9. EssentialsofEngineeringHydraulics
Jonas M. K. Dake, 1972
London, Chapman and Hall Ltd
10. TheHydraulicsPractical Manual
Jomo Kenyatta University of Agriculture and Technology
Kenya.
11. Lecture Noteson Hydraulics
Dr. Kazungu Maitaria
Department of Civil, Construction and Environmental Engineering
Jomo Kenyatta University of Agriculture and Technology