LABORATORY REPORT CVE 4307 OPEN CHANNEL HYDRAULICS Experiment 5: Investigating the Hydraulic Jump Bachelor of Civil Engineering (BCEGI)
Submission Date: 4 April 2016
OBJECTIVE
This experiment was carried out to investigate on the hydraulic jump created by the downstream of a sluice gate. Hence the following will be investigated: 1) Whether a hydraulic jump can occur or not. 2) Depths and velocity at the upstream and downstream. 3) Energy loss through the hydraulic jump.
INTRODUCTION Hydraulic jump is a phenomenon when a rapidly flowing stream rapidly becomes a slower flowing stream in a larger cross-sectional area. In other words, the flow is changed from super critical flow to subcritical flow and there is a depth increase for a hydraulic jump to exist. Hence the depth of flow in supercritical is less than the depth at sub critical flow (after hydraulic jump occurs) THEORY Hydraulic Jumps can be observed in rivers, spillways, outfalls of dams and irrigation works for example Undular jump, weak jump, oscillating jump, steady jump and strong or choppy jump are among the many classifications of jumps observed in open channels.
Hydraulic jump on a River Hydraulic jump on a spillway
Possible applications of a jump include; Dissipation of energy of water flowing over dams to prevent any erosion that might happen due to the high velocity of flow. Requirement of raising the levels in canals to enhance irrigation practices and hence reduce pumping heads. Reduce the uplift pressure under the foundations of hydraulic structures. (Abstract from : http://udel.edu)
The two equations that are used to describe the hydraulic jump are conservation of mass and conservation of linear momentum. Conservation of mass Continuity equation is obtained by considering the basic equation Q=VA. Since the flow rate is constant in section 1 and 2. Therefore,
Sluice gate and possible jump situation
The sluice gate act as a barrier that somewhat blocks the inflow of water in a rectangular channel, thus this blockage produces a subcritical flow upstream of the gate, the gap (height of sluice gate) enables water to travel downstream with a higher velocity thus the downstream flow is supercritical. When supercritical flow is attained, regulating the stop logs at exit will increase the water depth at the downstream end. This flow is subcritical. Hence the transition from supercritical to subcritical flow takes place through a hydraulic jump. Q1 Q2 V1 A1 V2 A2
( width b same)
V1h1 V2 h2
Conservation of linear momentum The equation is obtained by using Newton’s second law, which states that the net force acting on a body in any fixed direction is equal to the rate of increase of momentum of the body in that direction.
D12 D2 g 2 Q (v2 v1 ) 2 2 D2 1 8v 2 1 1 1 D1 2 gD1 D2 1 1 8F12 1 D1 2
Fx F1 F2 g
Note : Q is flow rate per unit width. Fr Here, we define
v1 gD1
and Fr is called the Froude Number.
When Fr = 1 it is critical flow Fr < 1 it is subcritical flow Fr > 1 it is supercritical flow Energy dissipation The energy will be loss in the hydraulic jump and the energy loss is
( D2 D1 )3 H 4 D1D2
Hydraulic jump diagram with corresponding specific energy diagram for given flow.
Location of the jump is one aspect that is needed to be determined since it is a requirement that the channel be designed in such a way that the jump is located at a particular place. The height of jump is expressed as the difference in height of D2 and D1 as shown in the above diagram. These depths are known as conjugate depths since they can be interchanged and determined with use of one formula as follows.
D2
D1 1 8 F12 1 2
Where Fr12 is at depth D1
Where Fr12 is at depth D1
D1 is depth before jump
y1 is depth before jump
D2 is depth after jump. Depth D1 can be alternatively used in place of D2 in the above formula and determined. The length of jump is taken generally as six (6) times the height of jump.
Fig.2 Fig 2. Shows the following region-specific characteristics (Kim, Choi, Park and Byeon. April 2015): Region 1: A supercritical flow region formed when water is discharged by the sluice gate. Region 2: Hydraulic jumps appear in this region in the discharged water flow of the sluice gate. Region 3: The discharged flow stabilizes after the hydraulic jumps. Region 4: The upstream domain. To rate the performance of a hydraulic we have to consider the Froude number before the jump occurs. Froude number is calculated using the formula in the theory part. Here is the classification of Froude number with respect to type of jump. FR NUMBER
JUMP DESCRIPTION
< 1.0
No jump since flow is already subcritical
1.0 to 1.7
An undular jump, with about 5% energy dissipation
1.7 to 2.5
A weak jump with 5% to 15% energy dissipation
2.5 to
Unstable, oscillating jump, with 15% to
FR NUMBER
JUMP DESCRIPTION
4.5
45% energy dissipation
4.5 to 9.0
Stable, steady jump with 45% to 70% energy dissipation
> 9.0
Rough, strong jump with 70% to 85% energy dissipation
Apparatus Gunt HM 160 Experimental flume
Schematic Diagram
PROCEDURE -
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The instrument was set up accordingly and the experiment was carried out by keeping the height upstream water depth as the control and discharge as variables. Sluice gate was set at the height of 30mm initially and pump was started initially the discharge amount was increased slowly.
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Wait until water level rises to 200mm (as a control) to allow a short interval of time between each adjustment of the pump to allow the water level to stabilize. Tail gate was adjusted to create a hydraulic jump in the centre of section. Then a supercritical flow can be seen throughout the entire length of the channel. Let it run for a few more minutes to ensure stability. Measure the heights yg, D1 and D2 by means of flow meter. Increase the height of sluice gate by 5mm for and discharge was varied to obtain initial water depth upstream of 200mm. Hence the discharge that gives upstream water depth of 200mm was noted as well as the height of yg, D1 and D2 was measured by means of flow meter. By increasing the height of sluice gate by 5mm the discharge was varied for 6 times to calculate the depths accordingly and readings were noted down.
DATA & RESULTS Table: 1
# 1 2 3 4 5 6
Yg (m) 0.030 0.035 0.040 0.045 0.050 0.055
Yo (m) 0.200 0.200 0.200 0.200 0.200 0.200
D1 (m) 0.0255 0.0300 0.0380 0.0450 0.0470 0.0550
D2 (m) 0.0810 0.0860 0.1000 0.1050 0.1070 0.1150
Note: Breadth of weir: 0.364 m Lj: is approximately 6 times height of the jump Y g Yo D 1 D 2 Q Hj Lj ∆ H
Height of gate opening Upstream flow depth Conjugate Depth D1 Conjugate Depth D2 Discharge Height of Jump Length of Jump Energy Loss at Jump
Q (m3/s) 0.012 0.014 0.016 0.018 0.019 0.021
Hj (m) 0.056 0.056 0.062 0.060 0.060 0.060
Lj (m) 0.333 0.336 0.372 0.360 0.360 0.360
∆H (m) 0.021 0.017 0.016 0.011 0.011 0.009
CALCULATIONS Table: 1 Taking the first reading from table 1; The energy will be loss in the hydraulic jump is calculated using this formula;
( D2 D1 ) 3 (0.0810 0.0255) 3 H 0.021m 4 D1 D2 4 0.0810 0.0255
Height of Jump = D2-D1 = 0.0255 - 0.0810 = 0.056m Length of jump = 6 x 0.056 = 0.333m All calculations for the remaining parts follow the same procedure as above.
Table: 2 # D1 (m)
D2 (m)
V1 (m/s)
V2 (m/s)
Fr1
Fr2
D2 (Theoreti cal)
Error % D2
Hj
Error % Hj
1
0.0255
0.081 0
1.29
0.41
2.58
0.46
0.0813
0.03
0.056
0.03
2
0.0300
0.086 0
1.28
0.45
2.36
0.49
0.0864
-0.04
0.056
0.04
0.0380
0.100 0
0.047
1.54
4
0.0450
0.105 0
1.07
0.46
1.62
0.45
0.0828
2.22
0.038
2.22
5
0.0470
0.107 0
1.11
0.49
1.64
0.48
0.0877
1.93
0.041
1.93
6
0.0550
0.115 0
1.05
0.50
1.43
0.47
0.0869
2.81
0.032
2.81
Average:
1.41
Avera ge:
-1.40
3
g
9.81 m/s2
1.16
0.44
1.89
0.44
0.0846
1.54
CALCULATION Table: 2 Taking the first reading from table 2; Velocity before the jump (v1) and velocity after the jump (v2) are calculated using this formula;
V1
Q 0.012 1.29m / s A1 (0.0255 0.364)
Q 0.012 0.41m / s A2 (0.0810 0.364)
V2
Froude number before and after the jump is calculated using the formula; Fr1
1.29 2.58 0.0255 0.364 9.81 0.364
Fr 2
0.41 0.46 0.081 0.364 9.81 0.364
Sequent depth D2 after the jump is calculated using the formula;
D2
D1 2
1 8F 1 0.0255 1 82.58 1 0.0813m 2 2 1
2
Height of jump is calculated using the formula
D1 1 8F Hj
2 1
0.0255 1 82.58
3D1
2
2 1
0.056m
30.0255
2
All calculations for the remaining parts follow the same procedure as above. Graphical Demonstration of Energy Loss against Depths
ΔH vs D1 0.025 0.020 0.015
ΔH /m 0.010 0.005 0.0200
0.0300
0.0400
D1 / m
0.0500
0.0600
ΔH vs D2 0.025 0.020 0.015
ΔH /m
0.010 0.005 0.0700
0.0800
0.0900
0.1000
0.1100
0.1200
D2 /m
DISCUSSION The upstream depth was kept constant throughout the experiment, height of the sluice gate was raised by 5mm for each readings. The discharge was varied to enable the upstream depth of 200mm. The basic requirement for hydraulic jump is there shall be a change in flow condition. Since the upstream flow in in subcritical flow, when the water passes under the sluice gate velocity increases and flow changes from subcritical to supercritical flow. Towards the downstream the water accumulates and flow changes to subcritical. Hence the hydraulic jump occurs when the flow changes from supercritical to subcritical in the downstream section. To check whether the flow is super or sub critical Froude number is calculated. As we can see in table 2 the calculated Froude number in the region of depth D1 is all above 1.0, thus confirming the flow is supercritical. The calculated Froude number after the jump where the depth is D2, is below 1.0, confirming the flow is subcritical. This is verification that Fr number is the parameter controlling the hydraulic jump. The Froude number before the jump ranges from 1.7 to 2.5, hence we can classify the jump as a weak jump with 5% to 15% energy dissipation Calculated value for D2 is compared with theoretical value of D2 calculated using the experimental value of D1 as shown in the calculations. As we can see the average error is about 1.41% which is less than 5%, hence acceptable. As well the height of jump is compared between experimental and theoretical values obtained by using the Froude number and formula mentioned above. The difference is about 1.4% < 5% hence acceptable.
As seen from the graphs, as D1 and D2 increase, the head loss decreases. This is due to the fact that the energy loss values are lesser for corresponding D1 and D2 values. Precautions were taken in keeping the upstream depth as constant throughout the experiment. When the discharge was varied it was allowed to settle the flow prior to taking measurements and readings. Depth reading were taken by ensuring the instruments was calibrated properly. Discrepancies were observed to be less for this experiment due to the fact that the all collected data shows predictable results. That is to say that Fr numbers were observed to be more than 1 for supercritical and less than 1 for subcritical conditions. The check for D1 with conjugate depth D2 yields results within acceptable range as the difference in experimental and theoretical values are very small. However it should be noted that minute changes in readings show significant changes being made to the graph. Hence it is crucial to ensure that accurate reading be taken for accurate analysis of results. Accuracy of the readings could have been improved if multiple readings for each flow rate were taken and an average determined. CONCLUSION The hydraulic jump has been investigated under controlled conditions in the laboratory for varying values of flow. Jumps occur when flow with higher velocities or subcritical conditions crosses the critical depth and end in a zone with subcritical conditions. This is confirmed with the Fr number determined as seen from the calculations. Fr number is the parameter controlling the hydraulic jump. The main aim of this experiment has been achieved where the analytical method of determining a hydraulic jump has been observed. The results of this experiment show a basic understanding of applications in theoretical and practical solutions. Hydraulic jumps, its locations and relevant data need to be determined for a given set of parameters in design stages for a hydraulic engineering application. Some designs require the application of a jump while others require a jump to be eliminated.
References: -
http://udel.edu/~inamdar/EGTE215/Jump_weirs.pdf https://en.wikipedia.org/wiki/Hydraulic_jumps_in_rectangular_channels Properties of Hydraulic Jump Down Stream Sluice Gate
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Hana A. Hayawi and Ahmed Y. Mohammed, 2010 Department of Water Resources, Engineering University of Mosul, Iraq Sluice gate flow and hydraulic jump analysis by Gilberto E. Urroz, September 2010 Hydraulic Jump and Energy Dissipation with Sluice Gate. Youngkyu Kim 1, Gyewoon Choi 2, Hyoseon Park 2 and Seongjoon Byeon, 2015
