ZN258719
Contents INTRODUCTION...........................................................................................................4 Research Methodology......................................................................................... 4 !!arat"s............................................................................................................. 4 #road crested $e%r..................................................................................................... 5 %&....................................................................................................................... 5 !!arat"s'............................................................................................................ 5 (roced"re............................................................................................................. ) Read%*gs a*d Calc"lat%o*s................................................................................... ) *alys%s................................................................................................................ 7 Calc"lat%o*s.......................................................................................................... 7 +ra!h%cal ðod................................................................................................. 8 #road crested $e%r co&!ar%so*............................................................................ 8 D%sc"ss%o*............................................................................................................ 9 ,har! Crested $e%r................................................................................................... 1I*trod"ct%o*........................................................................................................ 1%&..................................................................................................................... 1!!arat"s...........................................................................................................1(ROCDUR....................................................................................................... 11 O/ser0at%o*s...................................................................................................... 11 *alys%s.............................................................................................................. 11 #y calc"lat%o*s................................................................................................... 12 /.
+ra!h%cal ðod........................................................................................ 1
,har! crested $e%r Co&!ar%so*......................................................................... 1 D%sc"ss%o*.......................................................................................................... 15 Cr"&! $e%r............................................................................................................... 15 I*trod"ct%o*........................................................................................................ 15 %&..................................................................................................................... 15 !!arat"s...........................................................................................................15 (roced"re........................................................................................................... 1)
Page 1
ZN258719 O/ser0at%o*s...................................................................................................... 1) *alys%s.............................................................................................................. 17 a.
Calc"lat%o*s................................................................................................. 17
/.
+ra!h%cal ðod........................................................................................ 18
+ra!h or cr"&! $e%r......................................................................................... 18 Cr"&! $e%r co&!ar%so*..................................................................................... 19 D%sc"ss%o*.......................................................................................................... 2O0er shot $e%r.......................................................................................................... 2I*trod"ct%o*........................................................................................................ 2%&..................................................................................................................... 2!!arat"s'..........................................................................................................21 (roced"re........................................................................................................... 21 O/ser0at%o*s...................................................................................................... 22 *alys%s.............................................................................................................. 22 Calc"lat%o*s........................................................................................................22 /.
+ra!h%cal ðod........................................................................................ 2
O0er short $e%r co&!ar%so*...............................................................................2 D%sc"ss%o*.......................................................................................................... 24 Co*cl"s%o*.......................................................................................................... 24 23 To deter&%*e the coec%e*t o d%scharge or a e*t"r% 6"&e.............................. 24 I*trod"ct%o*........................................................................................................ 24 %&.................................................................................................................... 24 . .24 The aim of this experiment is to determine the coefficient of discharge for a venturi flume. !!arat"s...........................................................................................................25 ...............25 The apparatus used in this experiment are; Hydraulic work bench, venturi flume. (roced"re........................................................................................................... 25 O/ser0at%o*........................................................................................................ 2) *alys%s.............................................................................................................. 2) a. Calc"lat%o*s.................................................................................................... 27 +ra!h or 0e*t"re 6"&e..................................................................................... 1 DI,CU,ION......................................................................................................... 2
Page 2
ZN258719 To co&!are a*d d%sc"ss the hydra"l%c "&! a*d sl"%ce gate.................................... 2 I*trod"ct%o*........................................................................................................ 2 O/ser0at%o*........................................................................................................ *alys%s.............................................................................................................. Calc"lat%o*s........................................................................................................ /3 D%scharge !er "*%t $%dth :
¿ Q /¿ $%dth o the 6"&e................................5
Cr%t%cal De!th..................................................................................................... 5 Cr%t%cal e*ergy.................................................................................................... 7 +ra!hs................................................................................................................ 7 /.
#elo$ %s the gra!h o $ater de!th aga%*st e*ergy l%*e................................8
D%sc"ss%o*.......................................................................................................... 9 Co*cl"s%o*.......................................................................................................... 4;ealth a*d ,aety..............................................................................................4+NR< CONC>RC,............................................................................................................. 42
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ZN258719
INTRODUCTION The aim of the laboratory session is to gain an understanding on weirs, Hydraulic jump, head loss and the venturi flume, and to record and analyse laboratory results.A weir is a wall across a river aimed to alter its flow characteristics. eirs are commonly used to alter the flow of rivers to prevent flooding, measure discharge, and help render rivers navigable. !y report is based on the different types of techni"ues being used in the lab to determine or to understand the concept of weirs, hydraulic jump, head loss and venturi flume and how it is applied in laboratory exercises and in real life challenges. The experiments were carried out help explain the weirs, hydraulic jump, head loss, and venture flume. The different tests performed at the laboratory helped to learn the health and safety issues involved. The experiment was carried out in open channel laboratory with the supervision of !#!. H$!A%ATH&. The following experiments were carried out' (. )road crested weir *. +harp crested weir . -rump weir . /ver shot weir 0. %enturi flume 1. Hydraulic jump Research Methodology
&n this section, a full detail of the laboratory procedure is stated as well as the apparatus used for the experiment. Apparatus )elow are the apparatus that were used for the experiment • • • • •
Teaching flume Hydraulics work bench )road crested weir +harp crested weir -rump weir Page 4
ZN258719 • • •
/ver shot weir %enturi flume +luice gate
)elow is the teaching flume and hydraulics work bench
2igure taken in open channel laboratory
road crested !e"r &ntroduction A broad crested weir is an open channel flow measurement device which combines hydraulic characteristics of both weirs and flumes. A broad3crested weir is a flat3crested structure, with a long crest compared to the flow thickness. hen the crest is 4broad4, the streamlines become parallel to the crest invert and the pressure distribution above the crest is hydrostatic. &t can be calibrated for submerged flow conditions A"#
The aim of the broad crested weir is to determine the coefficient of discharge for weirs. Apparatus$
The apparatus used in this experiment are; Hydraulic work bench, weir. Page %
ZN258719
2igure(. +hows broad crested weir Procedure
•
The width of the broad crested weir was measure e placed the weir in the hydraulic bench at the weir holding position The channel slant was 56 before we could we started the experiment. e then Turned on the pump and opened the flow control valve which was then used
•
to control the flow rate. At each flow rate, the height of the water at the upper stream was measured and
• • •
recorded. This was repeated for five different flow rates. •
e then measured the height of water above the crest
•
7astly we closed the control valve and Turned off the pump and allowed water level to drop.
Read"ngs and Calculat"ons
&n this segment, the calculations are carried out on the collected data to get results which will be used to draw conclusions on the experiment that was carried out. )elow are the readings that were obtained from the laboratory on the broad crested weir. Table (' 8un no.
8eadings for broad crested weir 3
m /s Q¿ 9
):m9
H:m9
Page &
ZN258719
(
−3 0.67 × 10
5.5<
5.51
*
−3 1 × 10
5.5<
5.5
−3 1.33× 10
5.5<
5.50
−3 1.5 × 10
5.5<
5.500
0
−3 1.67 × 10
5.5<
5.50=
Where,
>= rate of water flow -d? coefficient of discharge )? channel width? 5.5< H? height of water level above crest -alculation of coefficient of discharge knows as -d, by making it the subject of the formula
Analys"s The analysis here is basically to determine the coefficient of discharge for the broad crested
weir.
Calculat"ons
To calculate coefficient of discharge
3 2
Q =1.705 C d B H
/
Cd
we use the formula' Q=1.705 C d B H
Q C d= 1.705 B H 3 /2 Page '
3 /2
ZN258719
C d (1 ) =
C ( )=
1.705 × 0.079 × 0.00683
= 0.67
−4 9.2 × 10
−3 1 × 10
−3 1 × 10
= 1.24 × 10− =
Average C d=
+
0.728 0.804
−3
× 10
1.705 × 0.079 × 0.00923
2 d
−3 0.67× 10
=0.728
0.804 3
+ 0.881+ 0.863+ 0.888 5
=0.833
The table below shows the calculated coefficient of discharge for each change in pressure. Table 3.2 Calculated coefficient of discharge Run no.
3
m /s Q¿ )
H(m)
H
3 2
∁d
( m)
(
−3 0.67 × 10
5.5<
5.51
−3 6.83 × 10
5.*=
*
−3 1 × 10
5.5<
5.5
−3 9.23 × 10
5.=5
−3 1.33× 10
5.5<
5.50
−3 11.2× 10
5.==(
−3 1.5 × 10
5.5<
5.500
−3 12.9× 10
5.=1
0
−3 1.67 × 10
5.5<
5.50=
−3 13.97 × 10
5.===
Average
Page (
¿
5.=
ZN258719
)raph"cal #ethod
)elow is the graph of height of water level above crest above flow rate. @raph was plotted on each weir H against >, and the shape of the graph is a linear :straight9 line graph. This therefore means that height of water level H increases with an increase in water flow rate.
!ater le*el +,- .s !ater /o! rate +0-.-7 -.-) -.-5 -.-4 ,+#-
$ater le0el aga%st $ater 6o$ rate
-.- -.-2 -.-1 ------0+#s-
-alculation for coefficient of discharge -d by using graphical method here >? 5.55( H? 5.5
Q -d ?
1.705 B H
3/ 2
−3 1 × 10
-d ?
1.705 × 0.079× 0.00923
? 5.= Page
ZN258719
road crested !e"r co#par"son
weir )roadcrestedweir
Averageofcoefficientof discharge :-d9 5.=
@raphical coefficient :-d9 5.=
D"scuss"on
2rom the analysis carried out on the data collected in the laboratory, both the coefficient of discharge for graphical and theoretical average of coefficient of discharge were calculated using the same formula for coefficient of discharge which is given by > ? (.50) H
3/ 2
-d .
The coefficient of discharge for graphical method was found to be 5.= while by calculation the coefficient of discharge is 5.=. The results on theoretical average of coefficient of discharge and that of graphical method were almost the same meaning the experiment was a success although where minor errors that occurred during the experiment that might have affected the outcome of the results.
harp Crested !e"r Introduct"on
A weir is an overflow structure extending across a stream or a channel and normal to the direction of the flow. They are normally categoried by their shape as either sharp3crested or broad3crested. This laboratory experiment focuses on sharp3crested weirs only. Page 1
ZN258719
A"#
The aim of the sharp crested weir is to determine the coefficient of discharge >.
Apparatus
The apparatus that were used are teaching flume, Hydraulics work bench, and sharp
•
crested weir.
PROC5DUR5
•
The width of the broad crested weir was measure e placed the weir in the hydraulic bench at the weir holding position The channel slant was 56 before we could we started the experiment. e then Turned on the pump and opened the flow control valve which was then used
•
to control the flow rate. At each flow rate, the height of the water at the upper stream was measured and
• • •
recorded. This was repeated for five different flow rates. •
•
e then measured the height of water above the crest 7astly we closed the control valve and Turned off the pump and allowed water level to drop.
O6ser*at"ons )elow are the readings that were obtained from the laboratory on the sharp crested weir
Table 8eadings for sharp crested weir. 3
8un no.
m /s Q¿ 9
(
0.67 × 10
):m9
H:m9
5.5<
5.5*<
−3
Page 11
ZN258719
*
−3 0.83 × 10
5.5<
5.5
−3 1 × 10
5.5<
5.50
−3 1.17 × 10
5.5<
5.5<
0
−3 1.33× 10
5.5<
5.5
2ormula'
Q = 2 C d B √ 2 g H 3/ 2 3
Where,
>= rate of water flow -d? coefficient of discharge )? channel width? 5.5< H? height of water level above crest
Analys"s The analysis is to determine the coefficient of discharge for the sharp crested weir.
The coefficient of discharge was determined through calculation and by graphical method.
y calculat"ons
To calculate coefficient of discharge -d we use the formula. here, -d is the coefficient of discharge
Page 12
ZN258719 2
Q = C d B √ 2 g H 3/ 2 3
C d=
C d (1 ) =
C d (2 ) =
3Q 2 B √2 g H
3 /2
−3 3 × 0.67 × 10
2 × 0.079 × √ 2 × 9.81 × 0.00494
−3 3 × 0.83 × 10
2 × 0.079 × √ 2 × 9.81 × 0.006
Average C d=
+
+
0.581 0.593 0.655
=
=
−3 2.01 × 10 −3 3.46 × 10
−3 2.49× 10 −3 4.199 × 10
+ 0.651+ 0.639
5
=0.581
=0.593
=0.624
Table .-alculated coefficient of discharge 3
m /s Q¿ 9
):m9
(
−3 0.67 × 10
5.5<
*
−3 0.83 × 10
−3 1 × 10
−3 1.17 × 10
0
−3 1.33× 10
8un no.
H:m9
H
3 2
∁d
( m)
5.5*<
−3 4.94 × 10
5.0=
5.5<
5.5
−3 5.99× 10
5.0<
5.5<
5.50
−3 6.55 × 10
5.10
5.5<
5.5<
−3 7.70 × 10
5.10
5.5<
5.5
−3 8.92× 10
5.1
¿ Average Page 13
5.1*
ZN258719
67
)raph"cal # ethod )elow is the graph of height of water level above crest above flow rate
The graph was piloted H against >, and the graph is straight :linear9 graph in shape.
!ater le*el +,- aga"nst !ater /o! rate +0-.-5 -.-4 -.- ,+#-
$ater le0el aga%*st $ater 6o$ rate
-.-2 -.-1 --------0+#1s-
Figure 4:
Grah of height of !ater le"el abo"e crest abo"e flo! rate.
2rom the graph, when; H is 5.50m, > ?5.55(mBs
C d=
C d=
3Q 2 B √2 g H
−3 3 × 1 × 10 3 /2
2 × 0.079 × √ 2 × 9.81 × 0.035
3 /2
=
−3 3 × 10 −3 4.583 × 10
=0.655
Page 14
ZN258719
harp crested !e"r Co#par"son
eir +harpcrestedweir
Averageofcoefficientof discharge :-d9 5.1*
@raphical coefficient of discharge :-d9 5.100
D"scuss"on
2rom the analysis carried out on the data collected in the laboratory, both the coefficient of discharge for graphical and theoretical average of coefficient of discharge were calculated using the same formula. The coefficient of discharge for graphical method was found to be 5.100 while by calculation the coefficient of discharge is 5.1*. 2rom the results we can tell that the experiment was a success although minor errors occurred during the experiment that might have affected the outcome of the results has can be seen from the different answers of coefficient of discharge.
Cru#p !e"r Introduct"on
A crump weir is commonly used to measure discharge in open flow channels. The cross3 section can be rectangular, trapeoidal and triangular and the slopes are made to specific angles. This type of weir is easy to construct and is used as an alternative to a rectangular weir when water head is limited.
A"#
The aim of this experiment is to determine the coefficient of discharge for weirs.
Page 1%
ZN258719
-rump weir is an alternative structure to measure the flow rate in open channel. 2rom )ernoulliCs e"uation, a weir e"uation can be derived and apply it to determine the flow rate, > of flow over a
Apparatus
The apparatus that were used are teaching flume, Hydraulics work bench, and crump crested weir.
Procedure
•
The width of the broad crested weir was measure e placed the weir in the hydraulic bench at the weir holding position The channel slant was 56 before we could we started the experiment. e then Turned on the pump and opened the flow control valve which was then used
•
to control the flow rate. At each flow rate, the height of the water at the upper stream was measured and
• • •
recorded. This was repeated for five different flow rates. •
e then measured the height of water above the crest
•
7astly we closed the control valve and Turned off the pump and allowed water level to drop. Page 1&
ZN258719
O6ser*at"ons )elow are the readings that were obtained from the laboratory on the crump weir.
Table 0 8eadings for crump weir 3
8un no.
m /s Q¿ 9
):m9
H:m9
(
−3 0.67 × 10
5.5<
5.5
*
−3 0.83 × 10
5.5<
5.50
−3 1.17 × 10
5.5<
5.5
−3 1.5 × 10
5.5<
5.51
0
−3 1.67 × 10
5.5<
5.50
Where,
>= rate of water flow -d? coefficient of discharge )? channel width? 5.5< H? height of water level above crest
Analys"s The analysis here is basically to determine the coefficient of discharge for the crump weir
a7 Calculat"ons To calculate coefficient of discharge :-d9 we use the formula'
Q =1.705 C d B H 3 /2 Page 1'
ZN258719
C d=
Q 1.705 B H
C d (1 ) =
C d (2 ) =
3 /2
−3 0.67 × 10
1.705 × 0.079 × 0.0052
−3 0.83× 10
+
−3 0.67 × 10 −4 7 × 10
=0.957
−3
1.705 × 0.079 × 0.00655
Average C d=
=
+
= 0.83 × 10− =0.941 8.82 × 10
+
+
4
0.957 0.941 1.09 1.13 1.11 5
=1.05
The table below shows the calculated coefficient of discharge Table .* -alculated coefficient of discharge 3
∁d
m /s Q¿ 9
):m9
(
−3 0.67 × 10
5.5<
5.5
−3 5.2 × 10
5.<1
*
−3 0.83 × 10
5.5<
5.50
−3 6.55 × 10
5.<
−3 1.17 × 10
5.5<
5.5
−3 8 × 10
(.5<
−3 1.5 × 10
5.5<
5.51
−3 9.87 × 10
(.(
0
−3 1.67 × 10
5.5<
5.50
−3 11.18 × 10
(.((
8un no.
H:m9
H
3 2
( m)
Average ¿ 1.05 Page 1(
ZN258719
67
)raph"cal # ethod )elow is the graph of height of water level above crest above flow rate.
The graph was plotted on each weir H against >, and the shape of the graph is a linear :straight9 line graph.
)raph 8or cru#p !e"r
graph o8 !ater le*el +,- aga"nst /o! rate+0-.-) -.-5 -.-4 ,+#-
gra!h o $ater le0el aga%*st 6o$ rate
-.- -.-2 -.-1 ------0+#s-
-alculation for coefficient of discharge -d by using graphical method here >? 5.55(0 H? 5.51
Q -d ?
1.705 B H
3/ 2
Page 1
ZN258719 0.0015
-d ?
1.705 × 0.079× 0.00987
? (.(
Cru#p !e"r co#par"son
eir -rump weir
Averageofcoefficientof discharge :-d9 (.50
@raphical coefficient of discharge :-d9 (.(
D"scuss"on
2rom the analysis carried out on the data collected from the laboratory, it is seen that the crump weir has a coefficient of discharge of (.50 from the calculation carried out and (.( from the graph. This shows that the experiment was very accurate and successful with few errors. e can further notice from the readings obtained in the laboratory that an increase in the discharge results in an increase in the height of water level above crest.
O*er shot !e"r Introduct"on
/ver shot weir is an overflow weir. A"#
The aim of the experiment it to determine the coefficient of discharge Apparatus$
The apparatus used in this experiment are; teaching over shot weir, Page 2
ZN258719
Procedure
•
The width of the broad crested weir was measure e placed the weir in the hydraulic bench at the weir holding position The channel slant was 56 before we could we started the experiment. e then Turned on the pump and opened the flow control valve which was then used
•
to control the flow rate. At each flow rate, the height of the water at the upper stream was measured and
• • •
recorded. This was repeated for five different flow rates. •
e then measured the height of water above the crest
•
7astly we closed the control valve and Turned off the pump and allowed water level to drop.
O6ser*at"ons )elow are the readings that were obtained from the laboratory on the over shot weir
Table '
8eadings for over shot weir
8un no.
m3 / s Q¿ 9
):m9
H:m9
(
−3 0.67 × 10
5.5<
5.5
*
−3 0.83 × 10
5.5<
5.5
−3 1 × 10
5.5<
5.51
−3 1.33× 10
5.5<
5.5 Page 21
ZN258719 −3 1.67 × 10
0
5.5<
5.5=
Where,
> ? water flow rate -d ? coefficient of discharge ) ? -hannel width H ? height of water level above crest
Analys"s The analysis here is basically to determine the coefficient of discharge for over shot weir.
The coefficient of discharge was determined by calculation and through graphical method.
Calculat"ons
To calculate coefficient of discharge -d we use the formula'
2
Q = C d B √ 2 g H 3/ 2 3
C d=
3Q 2 B √2 g H
3 /2
−3 3 × 0.67 × 10
C ( Run 1 )= 2 × 0.079 × √ 2 × 9.81 × 0.0052 = d
−3 2.01 × 10 −3 3.64 × 10
Page 22
=0.552
ZN258719
C d ( Run 2 )=
−3 3 × 0.83 × 10
2 × 0.079 × √ 2 × 9.81 × 0.00627
+
+
0.552 0.567 0.628
Average C =
= 2.49
−3 4.39 × 10
+ 0.618+ 0.682
= 0.567
0.609
=
5
d
−3
× 10
The table below shows the calculated coefficient of discharge for each change in pressure. Table 3.2 Calculated coefficient of discharge
m3 / s Q¿ 9
):m9
(
−3 0.67 × 10
5.5<
*
−3 0.83 × 10
−3 1 × 10
8un no.
H:m9
1.33× 10 −3 1.67 × 10
3 2
∁d
( m)
5.5
−3 5.2 × 10
5.00*
5.5<
5.5
−3 6.27 × 10
5.01
5.5<
5.51
−3 6.83 × 10
5.1*=
−3
0
H
−3
5.5< 5.5<
5.5 5.5=
9.23 × 10 −3 10.52× 10
Average
67
)raph"cal # ethod )elow is the graph of height of water level above crest above flow rate.
Page 23
5.1(= 5.1=*
¿ 0.609
ZN258719
!ater le*el +,- .s !ater /o! rate+0-.-) -.-5 -.-4 ,+#-
$ater le0el aga%*st $ater 6o$ rate
-.- -.-2 -.-1 ------0+#s-
-alculation for coefficient of discharge -d by using graphical method here >? 5.55( and H? 5.51
C d=
C d=
3Q 2 B √2 g H
−3 3 × 1 × 10 3 /2
2 × 0.079 × √ 2 × 9.81 × 0.036
3 /2
=
−3 3 × 10 −3 4.78 × 10
= 0.628
O*er short !e"r co#par"son
eir -rump weir
Averageofcoefficientof discharge :-d9 5.15<
Page 24
@raphical coefficient of discharge :-d9 5.1*=
ZN258719
D"scuss"on 2rom the analysis carried out on the data collected from the laboratory, it is seen that the over
shot weir has a coefficient of discharge of 5.15< from the calculation carried out and 5.1*= from the graph. Therefore, the over shot weir has a coefficient of discharge of approximately 5.1(= 2rom the readings collected too, it is seen that an increase in the discharge results in an increase in the height of water level above crest.
Conclus"on 2rom the general experiment carried out, it is therefore concluded that the crump weir has the
highest coefficient of discharge, followed by broad crested weir, then the sharp crested weir and lastly, the over shot weir. This therefore shows that the shape of the weir can affect the discharge of the weir. &n practice, where high discharge is re"uired such as hydro3electric systems, weirs such as the crump weir can be introduced. The different types of weirs can be used differently, depending on the volume of water involves as well as the discharge of water needed.
2- To deter#"ne the coe9c"ent o8 d"scharge 8or a .entur" /u#e7 Introduct"on
A venturi flume is a critical3flow open flume with a limited flow which causes a drop in the hydraulic grade line, creating a critical depth. Page 2%
ZN258719
&t is used in flow measurement of very large flow rates, usually given in millions of cubic units. A venturi meter would normally measure in millimeters, whereas a venturi flume measures in meters. !easurement of discharge with venturi flumes demands two measurements, one upstream and one at the throat :narrowest cross3section9, if the flow passes in a subcritical state through the flume. &f the flumes are designed so as to pass the flow from sub critical to supercritical state while passing through the flume, a single measurement at the throat :which in this case becomes a critical section9 is sufficient for computation of discharge. To ensure the occurrence of critical depth at the throat, the flumes are usually designed in such way as to form a hydraulic jump on the downstream side of the structure. These flumes are called Dstanding wave flumesD
A"#:
The aim of this experiment is to determine the coefficient of discharge for a venturi flume.
Apparatus
The apparatus used in this experiment are; Hydraulic work bench, venturi flume.
2igure shows a venture flume
Procedure •
e placed the venturi flume in the hydraulic bench at the holding position Page 2&
ZN258719
•
The channel slant was 56 before we could we started the experiment. e then Turned on the pump and opened the flow control valve which was then used
•
to control the flow rate. At each flow rate, the height of the water at the upper stream was measured and
•
recorded. This was repeated for five different flow rates. •
•
e then measured the height of water above the crest 7astly we closed the control valve and Turned off the pump and allowed water level to drop.
O6ser*at"on
%enture flume: standing wave condition, E ¿ 5, b ¿ 5.5m, slope ¿ 56 8un no.
m3 / s Q¿ 9
h:m9
(
0.67 × 10
5.51
*
0.83 × 10
5.5
−3 1 × 10
5.5=
0
1.33× 10
5.5< 5.(5<
1.67 × 10
Cd = Formula:
Q 1.705 b
( E) 3
2
here, > ? -d x b x :h (39 *g :H3:h(39
&n critical flow, h( ? *BH Page 2'
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H ? :h(39 F :v(9* B *g %th ? >B A $ ? :h(39 F %th* B *g h(?5.10:h9
Analys"s The analysis here is basically to determine the coefficient of discharge for a venture flume.
a7 Calculat"ons To calculate h1 ¿ 0.65h
(9 hi ¿ 5.10:5.519
¿ 5.5(m
*9 hi ¿ 5.10:5.59
¿ 5.5=m
m
To calculate Area,
(9 Area
¿ ¿ 9 A =¿
¿ bhi ( m ) 2
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A ¿ 5.5:5.5(9 2 A ¿ 5.55(* m
2
*9 Area
¿ bhi ( m ) A ¿ 5.5:5.5=9 2 A ¿ 5.55( m
m/s To calculate velocity, v =¿ 9
(9 2
Q = AV
V=
Q A
(9 %elocity
¿ Q :mBs9 A −3
¿ 0.67 × 10
0.00123
¿ 5.00:mBs9
*9 %elocity
¿
Q A :mBs9 −3 0.83 × 10
¿
0.00144
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¿ 5.0=:mBs9
m To calculate !"er#y, E=¿
V2 To calculate $nergy :m9 we use the formula' E= hi+ 2 g
V2
(9 $ ¿ hi+ 2 g 2
¿ 0.041+
0.545
2 × 9.81
¿ 0.056 m
V2
*9 $ ¿ hi+ 2 g 2
$
¿
0.048
+
0.576
2 × 9.81
$ ¿ 0.018 m
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Cd =
To calculate coe$$icie"t o$ dischar#e %&d we use the $ormula:
1.705 b
( E) 3
2
Q
Cd = (9
Q
1.705 b
( E) 3
2
−3 0.67 × 10
-d -d
¿
(
1.705 × 0.056
)
3 2
¿ 0.99
Q
Cd = *9
1.705 b
( E) 3
2
−3 0.83 × 10
-d
-d
¿
(
1.705 × 0.018
)3 2
¿ 0.98
The table below shows the calculated coefficient of discharge for each change in pressure.
Table .* -alculated coefficient of discharge 8un no.
3
m /s Q¿ 9
h:m9
h(:m9
bh(:
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%:mBs9
$:m9
-d
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m
2
9
(
0.67 × 10
5.51
5.5(
5.55(*
5.00
5.501
5.<==
*
0.83 × 10
5.5
5.5=
5.55(
5.01
5.5(=
5.<=
−3 1 × 10
5.5=
5.500
5.55(1
5.1(
5.5
5.<
1.33× 10
5.5<
5.515
5.55(=(
5.0
5.5==
5.<<1
0
1.67 × 10
5.(5<
5.5(
5.55*(
5.=
5.(5*
(.55
Average
Cd =¿
5.<=
)raph 8or *enture /u#e
!ater depth +,- aga"nst !ater /o! rate +0-.12 -.1 -.-8 ,+#-
$ater de!th aga%*st $ater 6o$ rate
-.-) -.-4 -.-2 ------0+#s-
-alculation for coefficient of discharge -d by using graphical method here >? 5.555= H? 5.5 Page 32
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Q Q = 0.0008 =¿ v= = 5.0=1( A b h 1 0.03 × 0.0455 2
( V th)
E = h1 +
2g
E= 0.0455+
( 0.5861)
2
2 × 9.81
=0.06301 m
E
¿ ¿
1.705 b
Cd=
C d=
¿
Q
¿ 0.0008
(
1.705 × 0.03 × 0.06301
/
3 2
)
=0.9888
DICUION
2rom the table above we can see that both the coefficient of discharge for venture flume was both calculated graphical and experimental with the same formula that has been given from the experiment. 2rom the calculation we noted that they are some are human error during the experiment, the value of average coefficient of discharge was 5.<= and the graphical coefficient of discharge was 5.<===. The difference between the calculation method and graphical method is 5.55( which is very minimal or small, therefore & can conclude that the experiment was accurate.
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To co#pare and d"scuss the hydraul"c ;u#p and slu"ce gate
Introduct"on
Hydraulic jumps mostly occur naturally in open channels. A hydraulic jump goes from supercritical :high velocity9 to subcritical :low velocity9 regime. &n fact, occasionally it might be necessary to create a jump to consume the excessive energy.
O6ser*at"on )elow are the readings that were taken from the laboratory
Table ((' 8eadings for hydraulic jump #escription
8ate of
ater
#istanc
flow >:
depth
e along
y:m9
channel
m3 Bs
G:m9
9 pstream
1.67 × 1
5.(
5.11
sluice #ownstrea
1.67 × 1
5.5*
(.(
m sluice +tart of
1.67 × 1
5.5
(.1*
1.67 × 1
5.5=0
*.*
hydraulic jump $nd of hydraulic jump
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Analys"s Calculat"ons
&ross sectio"al Area = width o$ $lume ×
'epth o$ water %(
¿ 5.5< × :I9
(9 Area
¿ 5.5< × 5.(
¿ 7.9 × 10− m 3
2
¿ 5.5< × :I9 ¿ 5.5< × 5.5*
*9 Area
¿ 1.6 × 10− m 3
)elocity, ) ¿
2
$low rate *Area
¿ > : m Bs9 ¿ A : m 9 3
(9
%elocity
¿ 0.211 m
−3 1.67 × 10
2
/¿
−3 7.9 × 10
/s
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¿ > : m Bs9 ¿ A : m 9 3
*9
%elocity
−3 1.67 × 10
¿
2
/¿
−3 1.6 × 10
2
¿v /2 g
)elocity +ead %m
(9
velocity head ( m )= v
2
/2 g
2
¿ 0.211 / 2 × 9.81
=
*9
0.00227 m
velocity head ( m )= v
2
/2 g
2
¿ 1.04 / 2 × 9.81 0.0556
¿
!"er#y li"e
¿Y + V
m
2
2g
2
(9 $nergy line
$nergy line
¿ 0.1 +
0.211
2 × 9.81
¿ 5.(5*m
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¿
1.044 m
/s
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1.044 *9 $nergy line ¿ 0.02 + 2 × 9.81
¿ 5.501 m
$nergy line
V Froude um-er
¿ √ gY
(9 2roude Jumber
2roude Jumber
2roude Jumber
*9 2roude number
2roude number
2roude number
¿
V √ gY
¿
0.21
√9.81 × 0.1
¿ 5.*(
¿ V
√ gY
¿
1.044
√9.81 × 0.02
¿ *.0
The table on the next page shows the result for the calculations carried out on the hydraulic jump and sluice gate experiment. Page 3'
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Table #2:
#escription
Results for the h$draulic %um and sluice gauge.
8ate of
ate
#istanc
Area
%elocit
%elocity +pecifi
2roude
flow >:
r
e along
A:
yv
Head
c
Jumbe
:mBs9
:m9
$nergy
r 2r
depth channel
m3 Bs
m2 9
y:m9
G:m9
, $:m9
5.(
5.11
5.55
5.*((
5.55**
5.(5*
5.*(
9 pstream
1.67
1
×
sluice #ownstrea
1.67 × 1
5.5*
(.(
< 5.55(
(.5
5.5001
5.501
*.0
m sluice +tart of
1.67 × 1
5.5
(.1*
1 5.55*
5.1<1
5.5*
5.50
(.*=
5.*<
5.55(
5.5==*
5.*
hydraulic
jump $nd of
1.67 × 1
5.5=0
*.*
hydraulic
5.551
1
jump
6- D"scharge per un"t !"dth< =
"
¿ Q /¿ 5.5<
"
¿ 1.67 × 10− /¿ 5.5<
"
¿ 0.02
¿ Q /¿ !"dth o8 the /u#e
3
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( ) 2
q Cr"t"cal Depth ¿ g
( ) 2
-ritical #epth ¿
1/ 3
0.02
1 /3
9.81
-ritical #epth ¿ 5.5
3
¿ ×critical depth
Cr"t"cal energy
2
3
-ritical energy
¿ × 0.03 2
-ritical energy ¿ 0.045
Table(. 2roudeno 2r( 2r* 2r 2r
2roude 5.*( *.0 (.*= 5.*
Type subcritical supercritical supercritical subcritical
)raphs
a.
/n the next page is a graph of water depth and specific energy against distance along
hydraulic flume
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)raph o8 !ater depth and spec">c energy aga"st d"stance -.12 -.1 -.-8 !ater dep th and 3pec ">c energy
$ater de!th?@3
-.-)
s!ec%Ac e*ergy?&3
-.-4 -.-2 -.5 1 1.5 2 2.5 D"stance +#-
Figure &:
Grah of !at er de th and se cific energ$ aga inst dis tance along h$draulic
flume
67
elo! "s the graph o8 !ater depth aga"nst energy l"ne
)raph o8 !ater depth aga"nst energy l"ne -.12 -.1 -.-8 ?ater depth +@-
-.-)
*ergy l%*e ?&3
-.-4 -.-2 -
-.-2
-.-4
-.-)
-.-8
5nergy l"ne +#-
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-.1
-.12
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Figure #':
Grah of !ater deth against energ$ line abo"e.
D"scuss"on Hydraulic jump occurs whenever the flow of a li"uid changes from super critical flow to sub
critical flow. As seen on table (*, The 2roude number changed from *.0 :super critical flow9 to 5.* :subcritical flow9. #ue to the transition from the super critical flow to the sub critical flow, there is a loss of energy and this is given by the formula below E = E4 − E3= 0.102− 0.088=0.014 m
This therefore shows that during the hydraulic jump, there was a change in energy of 5.5(m. )elow is a formula to know how efficient the hydraulic jump was
E 2 ( 8 !r 12 + 1)3 /2 −4 !r 12+ 1 = 2 2 E1 8 !r 1 ( 2 + !r 1 )
E2 E
( 8 × 2.35 + 1 ) / −( 4 × 2.35 )+ 1 2
=
1
3 2 2
8 × 2.35
2
2
=
( 2 + 2.35 )
303.68
−23.09
(
)
44.18 7.5225
E 1 280.59 = = 0.84 E 2 332.34 E""iciency =0.84 × 100=84
2rom the calculations carried out above, it is seen that the efficiency of the hydraulic jump is =6 which is good. The length of the hydraulic jump is given by the formula below 3=¿ 2.2−1.62 =0.580 m #engtho" hydraulic $ump= % 4− % ¿
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This therefore shows that the length of the hydraulic jump which happen to be the horiontal distance between start of hydraulic jump and end of hydraulic jump is 5.0=m The height of the hydraulic jump is given by the formula below Height o" hydraulic $ump = y 4− y3 =0.085− 0.03=0.055 m
2rom the above calculation, it is seen that the height of the hydraulic jump is 5.500m )elow is the formula to find the theoretical 2roude of the hydraulic jump.
y 4 √ 1 + 8 !r 3 t2−1 = y3 2
2
2
y4 y3
= √ 1 + √ 8 !r t −1 2
3
( )= 0.085 0.03
2.828 !r 3 t
!r3 t = 2.004
Error =
!r3 t − !r 3 2.004 −2.35 × 100 = × 100=17.27 !r3 t 2.004
2rom the calculation done above, it is seen that there was an error of (.6. This could be looked into properly when taking other experiments. &t could have most probably resulted from the error of parallax when taking the readings, inaccurate measurement of the depth and length of the hydraulic jump.
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Conclus"on +luice gate is a useful tool in creating hydraulic jump in an open channel. Also from this
experiment, & have learnt that a hydraulic jump can be created when one side of the flow is closed which enables water flow to movie form of a wave thereby forming a hydraulic jump.
,ealth and a8ety
Health and +afety in the laboratory looks at the health measures that are carried out in the laboratory before and during the experiment session. The following were the preventive measures that were taken when performing the experiments in the laboratory (. 2irst and foremost, when we got into the laboratory, we made sure that we open ed all the windows for air circulation and ventilation. *. hen performing the experiments, we had to ensur e that the e"uipmentCs we were using were check before we could use them. . e made sure that after assembling and disassembling, the tools werenCt kept in the water flow way. . e made sure that the weirs, venturi flume and sluice gate were fitted at the right spot to prevent damaging the attachment spot 0. e took prop er care when swit ched the apparatus from the switch to prevent any electric shock. 1. e made sure the switch cabinet was protected against water incursion. . And lastly when leaving the laboratory, we closed all the windows and made sure everything was in place.
)5N5RA CONCUION #uring our course of study and experiments in the laboratory, we learnt about different types of weirs, venturi flume and hydraulic jump. e learnt how to calculate the coefficient of discharge for different types of weirs and venturi flume and lastly how to compare and discuss the hydraulic jump and sluice gate. This has been a good experience for me because will be able to apply this knowledge that & have ac"uired in my line of work. Page 43
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APP5NDIB
R55R5C5 •
Jotes and references from books in the library
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