1.0
INTRODUCTION
A hydraulic jump is a phenomenon in the science of hydraulics which is frequently observed in open channel flow such as rivers and spillways. When liquid at high velocity discharges into a zone of lower velocity, a rather abrupt rise occurs in the liquid surface. The rapidly flowing liquid is abruptly slowed and increases in height, converting some of the flow's initial inetic energy into an increase in potential energy, with some energy irreversibly lost through turbulence to heat. !n an open channel flow, this manifests as the fast flow rapidly slowing and piling up on top of itself similar to how a shoc wave forms. The phenomenon is dependent upon the initial fluid speed. !f the initial speed of the fluid is below the critical speed, then no jump is possible. "or initial flow speeds which are not significantly above the critical speed, the transition appears as an undulating wave. As the initial flow speed increases further, the transition becomes more abrupt, until at high enough speeds, the transition front will brea and curl bac upon itself. When this happens, the jump can be accompanied by violent turbulence, eddying, air entrainment, and surface undulations, or waves. There are two main manifestations of hydraulic jumps and historically different terminology has been used for each. #owever, the mechanisms behind them are similar because they are simply variations of each other seen from different frames of reference, and so the physics and analysis techniques can be used for both types.
$
2.0
OBJECTIVE
$.
To observe the hydraulic jump phenomenon and to compare measured flow depths
%.
with theoretical results. To investigate the characteristic a standing wave &the hydraulic jump produced
(. ). *.
when waters beneath an undershot weir. To observe the flow patterns obtained. To create hydraulic jump. To determine the characteristics of the hydraulic jump obtained in the lab.
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3.0
THEORY
When water flowing rapidly changes to slower tranquil flow, a hydraulics jump or standing wave is produced. This phenomenon can be seen when water is shooting under the weir with deeper water downstream. !t occurs when a depth less than critical changes to a depth which is greater than critical and must be accompanied by loss energy. An undular jump occurs when the change in depth is small. The surface of the water undulates in a series of oscillations, which gradually decay to a region of smooth tranquil flow. A direct jump occurs when the change in depth is great. The large amount of energy loss produces a zone of e+tremely turbulent water before it settles the smooth tranquil flow. y considering the forces acting within the fluid on either side of a hydraulic jump of unit width it can be shown that 2
∆ H = d a +
Where,
v a
2g
(
−
2
dh+
vh
2g
)
∆ H is the total head loss across jump &energy dissipated&m,
mean velocity before jump &ms, is the depth of flow before hydraulic jump &m, mean velocity after hydraulic jump &m and &m. ecause the woring section is short, the above equation,
db
(
vb
is the
is the depth of flow after hydraulic jump
d a= d 1
∆ H = ( d 3−d 1 ) ³ / 4 d 1 d 3
v a is the
and
d b= d 3 . Therefore, simplifying
4.0
APPARATUS
$. /elf0contained 1lass /ided Tilting "lume.
%. Adjustable 2ndershot Weir
(. 3ontrol 4anel
). !nstrument 3arrier
)
*. #oo and 4oint 1auge
5. 6eter 7uler
*
5.0
PROCEDURE
$. 8nsured the flume was level, with the downstream tilting overshot weir, 8 at the bottom of its travel. 6easured and recorded the actual breadth, b &m of the undershot weir. !nstalled the undershot weir towards the inlet end of the flume and ensured that it was securely clamped in position. %. Adjusted the undershot weir to position the sharp edge of the weir %9mm above the bed of the channel. !ncreased the height of the tilting overshot weir until the downstream level just started to rise. (. 1radually opened the flow control valve and adjusted the flow until an undular jump is created with small ripple decaying towards the discharge end of the woring section. :bserved and setched the flow pattern. ). !ncreased the height of water upstream of the undershot weir by increasing the flow rate and increased the height of the titling overshot weir to create a hydraulic jump in the centre of the woring section. :bserved and setched the flow pattern. *. 6easure and record the values ofd;$,d;(, d;g and q. 7epeat this for other flow rates q &upstream head and heights of the gate,d;g.
5
6.0
RESULT AND DATA ANALYSIS
Weir
Upstrea
Flow
Flow
Flow
Openin
m Flow
Depth
Depth
rate (
Depth,
Above
Below
m /s
Jump,
Jump,
d 1 (
d 3 (
) "#"%!
) "#"&&
dg
g, (
m
d0
)
(
m )
m
"#"$ "#"$ "#"$ "#"$ "#"$ "#"$
"#!"$ "#!!+
"#"%$
"#!$"
"#"%*
"#!*&
"#"%!
"#!&
"#"%%
"#!'*
To calculate
∆ H
Formula , ∆ H =
"#"%$
3
3
!
)
∆ H d1
d3 d1
m
"#"&& "#"& "#"+& "#"+' "#"'!
"#""'
"#""
"#%%%
"#*"*
%#+!
"#""
& "#""+
"#%%+
"#%'
" %#$!
"#""
* "#""'
" "#%%+
$ "#%!
$ %#*!+
"#"!"
" "#"!&
' "#%%+
' "#'&%
' $#"&
"#"!!
"#"!+
% "#%%+
* "#'+
$ $#"*&
"#"!%
"#"!'
"#%%+
% "#'$
& $#"'
"
"
!
"
-
( d −d )
∆H
3
1
4 d1 d 3
$. <# = &9.9** > 9.9%$? @ &)&9.9%$&9.9** = &9.9()? @ 9.99)5 = 9.99* %. <# = &9.9** > 9.9%(? @ &)&9.9%(&9.9** = &9.9(%? @ 9.99*$ = 9.995) (. <# = &9.9* > 9.9%)? @ &)&9.9%)&9.9* = &9.9()? @ 9.99*5 = 9.99B9
B
). <# = &9.95* > 9.9%$? @ &)&9.9%$&9.95* = 9.9$* *. <# = &9.95B > 9.9%%? @ &)&9.9%&9.95B = &9.9)*? @ 9.99*) = 9.9$5C 5. <# = &9.9B$ > 9.9%(? @ &)&9.9%(&9.9B$ = &9.9)? @ 9.995* = 9.9$B9
To calculate V1 Formula ,V 1=
Q d 0 ×b
$. v = 9.99B @ &9.$9(&9.(9* = 9.99B @ 9.9($) = 9.%%%C %. v = 9.99 @ &9.$$5&9.(9* = 9.99 @ 9.9(*) = 9.%%59 (. v = 9.99C @ &9.$(9&9.(9* = 9.99C @ 9.9(CB = 9.%%5B ). v = 9.9$9 @ &9.$)*&9.(9*
- "#"!" . "#"**% - "#%%+% &# v - "#"!! . ("#!&)("#$"&) - "#"!! . "#"*& - "#%%+ 5. v = 9.9$% @ &9.$B)&9.(9* = 9.%%59
To calculate ∆H/d₁: Formula=
∆ H d1
$. <#d = 9.99* @ 9.9%$ = 9.)9)
%. <#d = 9.995) @ 9.9%( = 9.%B( (. <#d = 9.99B9 @ 9.9%) = 9.%C$B ). <#d = 9.9$* @ 9.9%$ = 9.B*%) *. <#d = 9.9$5C @ 9.9%% = 9.B5% 5. <#d = 9.9$B9 @ 9.9%( = 9.B(C$
To calculate d₃/d₁:
Formula=
d3 d1
$. d/d = 9.9** @ 9.9%$ = %.5$C9 %. d/d = 9.9** @ 9.9%( = %.(C$( (. d/d = 9.9* @ 9.9%) = %.)$5B
). d/d = 9.95* @ 9.9%$ = (.9C*( *. d/d = 9.95B @ 9.9%% = (.9)** 5. d/d = 9.9B$ @ 9.9%( = (.9B9
To calculate d -
dc=
√[ ] 3
Q
2
gb
2
, d 1
C
0.305
¿ ¿ 2
0.007
( 9.81 ) ¿
= 0.038 m
¿ 3 d c =√ ¿ 0.305
¿ ¿ 2
0.008
( 9.81 ) ¿
= 0.041 m
¿ 3 d c = √ ¿ 0.305
¿ ¿ 0.009
2
( 9.81 ) ¿
= 0.045 m ¿ 3
d c =√ ¿ 0.305
¿ ¿ 2
0.010
( 9.81 ) ¿
= 0.048 m
¿ 3 d c =√ ¿ 0.305
¿ ¿ 2
0.011
( 9.81 ) ¿
= 0.051 m
¿ 3 d c = √ ¿ 0.305
¿ ¿ 0.012
2
( 9.81 ) ¿
= 0.054 m
¿ 3 d c =√ ¿
Hence,
dg = 0.03 : 0.021
$9
¿
0.038
¿ 0.055
dg = 0.03: 0.023
¿
0.041
¿
0.055
dg = 0.03: 0.024
¿
0.045
¿
0.058
¿ 0.048
¿ 0.065
dg = 0.03: 0.022
¿
0.051
¿
0.067
dg = 0.03: 0.023
¿
0.054
¿
0.071
dg = 0.03: 0.021
$$
!.0
DISCUSSION
y following the procedures, our group has to set up the weir opening starting with 9.9(9m and constant to the end of e+periment. The flow rate is increasing order. "or precautions, the flow rate used must not be more than 9.9$(mD(s because it can lead to overflow. We found out that there was an error in our e+periment. The result should be increasing or decreasing, but there is a constant data at one point. These are caused by two main factors that could influence our reading. The factors are-0 The instrument factor. The equipment was not in a good condition. The weir gate has lea, so there are water that flow through the hole of the lea, although we have taen precautions such as cover the hole with the clay, but the water still flow because the clay is not strong enough to hold the water. #uman factor. Where the readings taen are not consistent because there is more than one observer. 4aralla+ error could also occur. The mistae in booing will also contribute to the error. !f one of the values is wrong, it will affect all the calculation. To avoid all of these errors happen, precautions must have been taen in every single step of the procedure. We have verified that the force of the stream on the other side of the jump is the same and the specific energy curve predicts a loss equal to 0#dc. There is application where the loss energy in hydraulic jump would be desirable, which are in hydraulic structures, especially for energy dissipation below spillways and outlets. !t can provide for 590B9E energy dissipation of the energy in the basin itself, limiting the damage to structures and the stream bed. 8ven with such efficient energy dissipation, stilling basins must be carefully designed to avoid serious damage due to uplift, vibration, cavitation, and abrasion.
%$ ".0
CONCLUSION
!n conclusion, our e+periment did have achieved the intended objectives. We succeed in investigating the characteristic a standing wave &the hydraulic jump produces when waters beneath an undershot weir. When liquid at high velocity discharges into a zone of lower velocity, a rather abrupt rise occurs in the liquid surface. The rapidly flowing liquid is abruptly slowed and increases in height, converting some of the flow's initial inetic energy into an increase in potential energy, with some energy irreversibly lost through the turbulence to heat. The increase when the weir opening increase causing the velocity to increase. "or this e+periment, the important thing that we must follow is the flow rate used for the e+periment must be constant or we would not see the change in pattern of hydraulic jump caused by the changing of weir opening. "or the recommendation, students must now how to conduct the basic and manual operations of this equipment. esides, carefully consider the flow rate used in this e+periment. 8nsure the weir gate is in good condition. 2se the hoo and point gauge to measure the height of the water for each section.
#.0
RE$ERENCE
$. https-en.wiipedia.orgwii#ydraulic;jumpFcite;ref08nergy;loss;$C09 %. "low in :pen 3hannel lab sheet, "aculty of 3ivil G 8nvironmental 8ngineering, 2T#6
$(
