PA
PART A RT A : THE HYDRAULIC JUM: THE HYDRAULIC JUMPSPS
1.0
1.0 INTRODUCTIONINTRODUCTION
The concept of the hydraulic jump when the hydraulic drop that occurs at a The concept of the hydraulic jump when the hydraulic drop that occurs at a sudden drop in the bottom of a channel, and the free surface flow around obstructions like sudden drop in the bottom of a channel, and the free surface flow around obstructions like bridge piers. A hydraulic jump forms
bridge piers. A hydraulic jump forms when a when a supercritical flow changes supercritical flow changes into a subcriticalinto a subcritical fl
flowow. . ThThe e chchanange ge in in ththe e flflow ow reregigime me occoccururs s wiwith th a a susuddedden n ririse se in in wawateter r susurfrfacace.e. Considerable turbulence, energy loss and air entrainment are produced in the hydraulic Considerable turbulence, energy loss and air entrainment are produced in the hydraulic jump. A hydraulic
jump. A hydraulic is is used used for for mixing mixing chemicals chemicals in in water water supply supply systems, for systems, for dissipatingdissipating ene
energy rgy belbelow ow artartifiificiacial l chachannel contrnnel controlsols, , and and as as an an aeraaeratition on devidevice ce to to incincrearease se thethe dissolved oxygen in
dissolved oxygen in water.water.
In a hydraulic jump there occurs a sudden change in liuid depth from less! In a hydraulic jump there occurs a sudden change in liuid depth from less! tha
thancrincritictical al to to gregreateater!r!thathan!cn!critriticaical l deptdepth. h. The The velvelociocity ty of of the the flflow ow chachanges nges frofromm supercritical to subcritical as a result of the jump. This transition takes place over a supercritical to subcritical as a result of the jump. This transition takes place over a relatively short distance, usually less than " times the depth of flow after the jump, over relatively short distance, usually less than " times the depth of flow after the jump, over which the height
which the height of the liuid of the liuid increase rapidly, incurring a considerable loss of increase rapidly, incurring a considerable loss of energy. energy. AnAn example of a hydraulic jump can
example of a hydraulic jump can be observed when a be observed when a jet of water from a faucet strikes thejet of water from a faucet strikes the hori#ontal surface of the kitchen sink. The water flows rapidly outward and a circular hori#ontal surface of the kitchen sink. The water flows rapidly outward and a circular jump occurs.
jump occurs.
$e shall restrict the derivation of the basic euation of the hydraulic jump to $e shall restrict the derivation of the basic euation of the hydraulic jump to rectangular hori#ontal channels. %irst, we shall determine the downstream depth of the rectangular hori#ontal channels. %irst, we shall determine the downstream depth of the jump
jump by by using using the the momentum momentum and and continuity continuity euations euations for for one!dimensional one!dimensional flow. Thenflow. Then the energy loss due to the jump will be
the energy loss due to the jump will be evaluated, using the energy euation.evaluated, using the energy euation.
2.0
2.0 OBJECTIVEOBJECTIVE
To investigate the characteristic a standing wave &the hydraulic jump' produced when To investigate the characteristic a standing wave &the hydraulic jump' produced when waters beneath an undershot weir and
4.0 THEORY
$hen water flowing rapidly changes to slower tranuil flow, a hydraulic jump or standing wave is produced. This phenomenon can be seen where water shooting under a sluice gate mixes with deeper water downstream. It occurs when a depth less than critical changes to a depth which is greater than critical and must be accompanied by loss of 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 tranuil flow. A direct jump occurs when the change in depth is great. The large amount of energy loss produces a #one of extremely turbulent water before it settles to smooth tranuil flow.
(y considering the forces acting with the fluid on either side of a hydraulic jump of unit width it can be shown that )
∆* + da va 2 2g ! d a ¿ vb 2 2g '
$here -* is the total head loss across jump &energy dissipated' &m'. va is the mean velocity before jump &ms', da is the depth of flow before hydraulic jump &m'. v b is the mean velocity after hydraulic jump &m' and d b is the depth of flow after hhydraulic jump &m'. (ecause the working section is short, d a / d b and d b / d0.Therefore, simplifying the above euation,
5.0 EQUIPMENT
2' 3elf! contained 4lass 3ided Tilting %lume.
5' Adjustable 6ndershot $eir Tilting %lume.
0' Instrument Carrier.
%igure 0) Control 7anel
6.0 PROCEDURES
2. 9nsure the flume is level, with the downstream tilting overshot weir, E at the bottom of its travel. :easure and record the actual breadth b &m' of the undershot weir. Install the undershot weir towards the inlet end of the flume and ensure that it is securely clamped in position.
5. Adjust the undershot weir to position the sharp edge of the weir 5;mm above the bed of the channel. Increase the height of the tilting overshot weir until the downstream level just stars to rise.
0. 4radually open the flow control valve and adjust the flow until an undular jump is created with small ripple decaying towards the discharge end of the working section. <bserve and sketch the flow pattern.
8. Increase the height of water upstream of the undershot weir by increasing the flow rate and increase the height of the titling overshot weir to create a hydraulic jump in the centre of the working section. <bserve and sketch the flow pattern.
". :easure and record the values of d 1 , d 3 , d g , and q. repeat this for other flow rates q &upstream head' and heights of the gate d g
7.0 RESULT
2. Calculate v1 and plot dg against v1
5. Calculate∆* d1 and plot∆* d1 against d3 d1
0. Calculate dc and verify d1 = dc = d3
$eir breadth, b + ;.0;; m $eir opening, dg &m' 6pstream flow depth, do &m' %low >epth above jump, d2 &m' %low depth below jump, d0 &m' %low rate &m0s' -* ?2 ∆ H d1 d3 d1 ;.;52 ;.0"5; ;.;2;@ ;.;28 ;.;25 ;.2;5 2.B;8 B.@B .@ ;.;58 ;.05"5 ;.;28@ ;.;B20 ;.;25 ;.;8@ 2.@@ ".B" @.5" ;.;5 ;.5"8" ;.;2" ;.;B@B ;.;25 ;.;2 2.82 "."25 @.20 ;.;0; ;.588 ;.;2@8 ;.;BB" ;.;25 ;.;B 2.000 2.80 @.; ;.;00 ;.2B@8 ;.;2 ;.2;"5 ;.;25 ;.;2" 2.525 8.08 ".@; ;.;0@ ;.20" ;.;2B@ ;.22;; ;.;25 ;.;" 2.222 8.0 ".@2
8.0 DATA ANALYSIS
Calculation for opening weir, dg + ;.;52m
∆* + &;.;28 D ;.;2;@' 10 8&;.;2;@' &;.;28' + ;.2;5 Calculation for v1 , E + A? ? + EA A + dg x b + ;.;52 x ;.0;; + ;.;;@0 m 2 Therefore, ? + ;.;25 ;.;;@0 + 2.B;8 ms dc + 3
√
q2 g + E b + &;.;25 ;.0;;' + ;.;8 m 2 s Therefore, dc +√
3(
0.04)
2/g + ;.;"" m The weir opening,dg d2 = dc = d0 52 58 5 ;.;2;@ = ;.;"" = ;.;28 ;.;28@ = ;.;"" = ;.;B20 2.2" = ;.;"" = ;.;B@B
0; 00 0@ ;.;2@8 = ;.;"" = ;.;BB" ;.;2 = ;.;"" = ;.2;"5 ;.;2B@ = ;.;"" = ;.22;; 9.0 QUESTION
2. ?erify the force of the stream on either side of the jump is the same and that the specific energy curve predicts a loss eual to -* dc.
F before= F after
5. 3uggest application where the loss of energy in hydraulic jump would be desirable. *ow is the energy dissipatedF
The hydraulic jump flow process can be illustrated by use of the specific energy concept. Equation loss energy can be written in term of the specific energy
9 + do ?5 5g
!here d o and E are feet. "ecause of the head loss across the jump, the upstream #alues of E are different. $bout the graph, %1& to state %'& the fluid does not proceed along the specific energy cur#e and pass through the critical condition. The energy dissipates when
water flow at weir opening and the energy became ( because d ( and d 3 has are force from ad#erse. )ame li*e the equation,
F before= F after .
10.0 DISCUSSION
7ractical applications of hydraulic jump are)
2. To dissipate energy in water flowing over hydraulic structures as dams, weirs, and others
and prevent scouring downstream structures.
5. To raise water level on the downstream side for irrigation or other water distribution
purposes.
0. To increase weight on an apron and reduce uplift pressure under a structure by raising the
water depth on the apron.
8. To indicate special flow conditions such as the existence of supercritical flow or the
presence of a control section so that a gaging station maybe located. ". To mix chemicals used for water purification.
@. To aerate water for city water supplies.
. To remove air pockets from water supply lines and prevent air locking.
11.0 CONCLUSION
The conclusion from the experiment, we can investigate the characteristic a standing wave &the hydraulic jump' produced when waters beneath an undershot weir and to observe the flow patterns obtained. %rom the experiment, we can get the force at weir opening, G*. In the water channel, water flowing rapidly changes to slower tranuil flow a hydraulic jump or standing wave is produced. This phenomenon can be seen where water shooting under a sluice gate mixes with deeper water downstream. It occurs when a depth less than critical changes to a depth which are greater than critical and must be accompanied by loss of energy.
%rom the result, we get the inverse line from graph gd2 against v2 and curve line from graph - *d2against d0d2. (oth graphs are sloping downward. %inal result we can get the value of dc between d2 and d0. 3o the objective achieved and the experiments are success. Heason the experiment perform because almost drain are open channel. %rom the experiment, we know about water flowing.
12.0 REERENCES
i. ohn .9.A. 2B. Introduction to %luid :echanics, pp 00;!085. 7rentice *all, Inc.
ii. Chaudhry, :. *. 2BB0. <pen Channel %low, pp 0;5!8;. 7rentice!*all, Inc. iii. 3imon, A. J.2BB. *ydraulics, pp 50!025. 7rentice *all, Inc
iv. http)www.engineeringcivil.com &serve on 2B225;22'
PART B: THE FORCE ON A SLUICE GATE
1.0 INTRODUCTION
The 3luice gate is a device used to control the passage of water in an open channel. $hen properly calibrated it may also serve as a means of flow measurement. As the lower edge of the gate opening is flush with the floor of the channel, contraction of the bottom surface of the issuing stream is entirely suppressed. 3ide contraction will of
course depend on the extent to which the opening spans the width of the channel.
A variety of gate!type structure is available for flow rate control at the crest of an overflow spillway, or at the entrance of an irrigation canal or river from a lake. Three
Picture 1: Drowned outfow rom a sluice gate.
typical types are vertical gate, radial gate and drum gate. The flow under a gate is said to be free outflow when the fluid issues as a jet of supercritical flow with a free surface open to the atmosphere.
In certain situation, the depth downstream of the gate is controlled by some downstream obstacle and the jet of water issuing from under the gate is overlaid by a
mass of water that is
uite turbulent.
2.0 OBJECTIVE
To determine the relationship between upstream head and trust on a sluice gate &undershot
weir' for water flowing under the sluice gate.
!.0 LEARNIN" OUTCOMES
At the end of the course, students should be able to apply the knowledge and skill they
have learned to)
a' 6nderstand the basic terms and concept of a sluice gate.
4.0 THEORY
It can be shown that the resultant force on the gate is given by the euation )
F g + 1
2 pg d1 15 & d0 15 d1 15!2 ' D pg b d1 &2! d1 d0 '
The gate thrust for hydrostatic pressure distribution is given by the euation ) F H + K pg & d0 ! dg '15
where %g is the resultant gate thrust &L', %* is the resultant hydrostatic thrust &L', is volume flowrate &ms', M is density of fluid &kgm0', g is the gravitational constant &B.2ms5', b is breadth of gate &m', d
g is height of upstream opening &m', d; is upstream depth of flow &m' and d2 is downstream depth of flow &m'.
4.0 EQUIPMENTS
2. 3elf!contained 4lass 3ided Tilting %lume 5. Adjustable 6ndershot $eir
0. Instrument Carrier 8. *ook and 7oint 4auge
6.0 PROCEDURES
2. 9nsure the flume is level, with the downstream tilting overshot weir at the bottom of its travel its travel. The actual breadth b &m' of the undershot weir are measured and recorded.
5. The undershot weir adjusted to set its bottom edge 5;mm above the bed of the channel. 0. Introduce water into the flume until do + 5;;mm. with do at this position, the readings
for and d2 are taken. Haise the undershot weir in increments of 2;mm, maintaining
constant do by varying . At each level of the weir, record the values of dg, d2 and . 8. The procedure with a constant flow , allowing do to vary are repeated and the value of
do and d2 are recorded.
7.0 RESULT $eir breadth, b + 0;; m $eir opening, dg &m' 6pstream flow depth, do &m' >ownstream %low >epth, d2 &m' %low Hate q &m0s' 4ate Thrust %g &L' *ydrostatic Thrust, %* &L' %g %* dg do
;.;52 ;.0"0 ;.;2;; ;.;25 !0.2@ x2;@ @";.B@ !8"8.0 ;.;"" ;.;58 ;.050; ;.;28 ;.;25 !5.25 x 2;@ 80."2 !808."" ;..;8 ;.;5 ;.5@2 ;.;2"@ ;.;25 !2.B x 2;@ 5;.85 !58.B@ ;.2;0 ;.;0; ;.508 ;.;2@@ ;.;25 !;." x 2;@ 5;".0 !52B.55 ;.25 ;.;00 ;.2@ ;.;2" ;.;25 2."B x 2;@ 22.58 20"@2.B5 ;.2@ ;.;0@ ;.28; ;.;2B" ;.;25 2.8B x 2;@ B0.82 2"B"2.2 ;.5; 8.0 DATA ANALYSIS
Calculation for weir opening ;.;52m. 4ate Thrust, %g &L'
F g + 1 2 pg d1 15 & d0 15 d1 15!2 ' D pg b d1 &2! d1 d0 ' + !0.2@x 10 6 L
*ydrostatic Thrust, %* &L'
F H + K pg & d0 ! dg ' 15 + @";.B@ L
9.0 QUESTIONS
2. 7lot graph of the ratio %g %*against the ratio dg do. %+efer graph&
5. Comment of the graph obtained.
"ased on the graph, the pattern of the graph is linear line and an increased. !hen the #alue of d g d o are increased , the #alue of F g F - also increased.
0. Compared your calculated values for %g and %*and comment on any differences.
F g = /gd 1' 0 %d (' d 1' & 1 2 /g bd 1 0 1 %d 1 d ( &2, we get the #alue are in negati#e % #e& and when we calculated F -with F - = /g % d ( d g &' , we get the #alue in positi#e %4#e&. F g is resultant gate thrust %5& and F - is resultant hydrostatic thrust %5&. !e can conclude that before the water is flow to the sluice gate, the force are F -are in positi#e %4#e& because is follow the direction of the water flow. The force are happened after sluice gate are Fg in negati#e %#e& because the resultant force of the flow is opposite the
direction.
8. $hat is the effect of flow rate on the result obtainedF
From the result, the more flow rate will gi#e the less thrust for both of the gate and the hydrostatic. This is because of the decreasing pressure at both of them.
10.0 DISSCUSSION
%loodgates are adjustable gates used to control water flow in reservoir , river , stream, or levee systems. They may be designed to set spillway crest heights in dams, to adjust flow rates in sluices and canals, or they may be designed to stop water flow entirely as part of a levee or storm surge system.
3ince most of these devices operate by controlling the water surface elevation being stored or routed, they are also known as crest gates. In the case of flood bypass systems, floodgates sometimes are also used to lower the water levels in a main river or canal channels by allowing more water to flow into a flood bypass or detention basin when the main river or canal is approaching a flood stage.
11.0 CONCLUSION
The flow through a channel in which a gate partially obstructs the flow will be used for this measurement of total force. This obstruction is called a sluice gate &see %igure 2'. The flow is from left to right and enters at a velocity 6o. The fluid in the upstream section builds up against the gate to a level y; , and exits the upstream section under the gate of height b. The fluid attains a higher velocity 6 2 as it passes under the gate and a shallower free surface height y2 downstream.
Three assumptions will be made in this derivation of the euation for hori#ontal force on a sluice gate)
2' The viscous force at the bottom of the channel and the energy dissipation at the gate
are negligible.
5' The flow is steady and has a uniform velocity distribution at the inlet and outlet sections.
0' %low at upstream and downstream sections is uniform and the effect of the side! walls is negligible.
%igure 2. %low under a vertical
sluice gate.
12.0 REERENCES
2. ohn .9.A. 2B. Introduction to %luid :echanics, pp 00;!085. 7rentice *all, Inc. 5. Chaudhry, :. *. 2BB0. <pen Channel %low, pp 0;5!8;. 7rentice!*all, Inc.
