Introduction On *date the *date the experiment of Sluice Gate and Hydraulic Jump was held at the Hydraulic lab of * your university name. name. The experiment was done in a group of *number of people involved of of *
* your university name students. name students. The experiment was guided and assisted ass isted by Sir/Madam your lecturer’s name until
we completed the experiment successfully.
Theory Hydraulic jump in open channels can be attributed to rapidly varied flow where a significant change in velocity occurs from super-critical flow to sub-critical flow. This fact may owe to the presence of some structures obstructing the movement of flow in open channels. Undershot weir or gate is the most impressive example for hydraulic jump formation formati on in canals where the flow undergoes high velocity under gates with upstream small depth and returns back to a higher downstream conjugate depth away from the gate with lower velocity. Froude number represents the clear impact of non-uniform flow velocity in open channels where super-critical flow is obtained at Froude number greater than 1, whereas sub-critical flow is indicated at Froude number less than 1. The main advantage of hydraulic jump occurrence in canals is energy dissipation downstream spillways where accumulation of water behind the gate is associated to the high flow velocity which abruptly declines downstream gate and thus avoiding bed erosion and scour.
For a constant flow in a rectangular open channels, the depth of flow immediately downstream part that allow for depth control within the flume represented represented by:
=
[ 1 + 1+8 1 +8 ] 2
Fr = Froude number of flow entering the jump. For a rectangular flume,
=
= =
Q = Flow rate (m 3/s) B = Channel width (m) V = Velocity (m/s)
The energy loss due to the jump in rectangular channel can be estimated by the following equation:
( ) = 4 The power loss due to the jump in a rectangular channel can be estimated by the following equation:
= EL = Energy Loss (m) Y1 = Depth before the jump (m) Y2 = Depth after the jump (m) PL = Power Loss (watt)
Objective
To visualize the phenomena of hydraulic jump in a sluice gate.
To compare the upstream and downstream depth of flows from experimental data to theoretical data.
To determine the energy losses and power losses through hydraulic jump.
To determine the equation for the length of the hydraulic jump.
Apparatus
Figure 1.0: Hydraulic Jump Apparatus 1. Hydraulic Jump Apparatus 2. Flow depth gauge
Procedure 1. Width Width of channel (flume) is measured. 2. Water storage tank of hydraulic bench is then filled up with clean and fresh water up to ¾ of tank capacity. 3. By pass valve then opened to 50% position. 4. Reservoir outlets are closed. 5. Pump is switched on. 6. The flow is slowly released into the reservoir until the water level is stable. 7. A stationary hydraulic jump is created in the flume by adjusting the sluice gate and downstream control gate. 8. Depth of flow Y1, Y2 and the length of jump, L is measure accordingly. 9. Steps 6 to 9 is repeated for another four different flow rates.
Data collection Results: g =9.81 m/s 2
Channel Width, B = 0.079 m Run No.
Q (L/min)
Q (m 3/s)
Y1 (m)
Y2 (m)
L (m)
1
30
5.00×10 -4
7.60×10-3
2.69×10-2
0.205
2
35
5.83×10 -4
6.90×10-3
2.27×10-2
0.185
3
40
6.67×10 -4
7.70×10-3
3.68×10-2
0.238
4
45
7.50×10 -4
7.40×10-3
4.27×10-2
0.365
5
50
8.33×10 -4
6.10×10-3
4.77×10-2
0.490
Run No.
Q (L/min)
Q (m 3/s)
Froude number, Fr
EL (m)
PL (watt)
1
30
5.00×10-4
3.05
8.79×10 -3
0.043
2
35
5.83×10-4
3.56
6.30×10 -3
0.036
3
40
6.67×10-4
4.07
2.17×10 -2
0.142
4
45
7.50×10-4
4.57
3.48×10 -2
0.256
5
50
8.33×10-4
5.08
6.19×10 -2
0.506
Type of Jump Oscillating Jump Oscillating Jump Oscillating Jump Steady Jump Steady Jump
2.69×10-2
Y2 (m) THEORY 2.92×10 -2
% OF ERROR 7.88
5.83×10-4
2.27×10-2
3.15×10 -2
27.94
40
6.67×10-4
3.68×10-2
4.06×10 -2
9.36
4
45
7.50×10-4
4.27×10-2
4.43×10 -2
3.61
5
50
8.33×10-4
4.77×10-2
4.09×10 -2
|16.63|
Run No.
Q (L/min)
Q (m 3/s)
Y2 (m) EXP
1
30
5.00×10-4
2
35
3
Run No.
Conjugate depth (Y 2 / Y1)
Jump length (L / Y2)
Jump height (Y2 - Y1 )
1
3.539
7.621
0.0193
2
3.290
8.150
0.0158
3
4.779
6.467
0.0291
4
5.770
8.548
0.0353
5
7.820
10.273
0.0416
Data analysis Sample Calculation: L/min to m3/s conversion:
× = 5.00×10-4 m3/s × Froude Number, Fr:
5.00×10− = = − )⁄ × √ 9.81 0.0 0. 0 7 9 × ( 7 . 6 0 × 1 0 9.81
= 3.05
Energy Loss, E L:
( ) (2.69 × 10− 7.60 × 10−) = = 4 4×7.60×10− × 2.69 × 10− = 8.79×10 -3 m
Power Loss, P L:
= = 1000 × 9.81 × 5.00 × 10− × 8.79 × 10− = 0.043 watt
Y2 (theory), m:
=
[1+ √ 1+8 1 +8
=
.× [1+ 1 + 8(3. 8(3.005)]
= 2.92×10-2 m
Percentage of Error (%):
(ℎ) ( ) 2.92×10− 2.69×10− × 100 = ×100 (ℎ) 2.92×10− = 7.88 %
Graph 1:
Graph of Conjugate depth (Y2 / Y1) vs Froude number (Fr) 9 8 ) 7 1 Y / 26 Y ( h t 5 p e d 4 e t a g u j 3 n o C 2
y = 2.1771x 2.1771x - 3.812 3.8125 5
1 0 0
1
2
3
4
5
6
Froude number (Fr)
Graph 2:
Graph of Jump length (L / Y2) vs Froude number (Fr) 12
10
y = 1.122x + 3.6499
) 2 Y 8 / L ( h t g 6 n e l p m 4 u J
2
0 0
1
2
3
Froude number (Fr)
4
5
6
Graph 3:
Graph of Length Length of jump, jump, L vs Jump height height (Y2 - Y1 ), m 0.6
0.5 y = 11.264x 11.264x - 0.021 0.0213 3
L 0.4 , p m u j f 0.3 o h t g n e L 0.2
0.1
0 0
0.005
0 .0 1
0.015
0.02
0.025
Jump height (Y2 - Y1 ), m
0.03
0.035
0 .0 4
0.045
Discussion The experiment results indicates clearly that hydraulic jump in open channel happens with the transition from supercritical to subcritical flow. In our experiment the magnitude of Froude number of flow entering the jump indicates oscillating jump for flow rates of 30, 35 and 40 L/min, whereas for flow of 45 and 50 L/min it indicates steady jump. Observation indicates large waves created by multiple irregular pulsation travelling further downstream in the channel for Froude number ranging from 2.5 to 4.5. As the Froude number increases from 4.5 the observations indicates the disappearance of large waves and stable and well balanced jump is produced. The observed hydraulic jump characteristics were consistent with theory and a proposed approximation for a theoretical jump equation were found to be in favor of with observed characteristics.
The results expected are slightly different with the theoretical value. Errors ranging from 0% - 20% is present in the total experiment, whereby it is acceptable percentage error scale. However, for the flow rate of 35 L/min, the percentage error is 27.94%. The large difference between experiment value and theoretical value of height of hydraulic jump has caused this error. This error is assumed to be caused by bad accuracy of the apparatus. Water pump and the flow pump pump with faults could have caused the error. Parallax error also could have been the cause whereby the measurement reader had some distance between the measuring scale and the indicator used to obtain a measurement.
Conclusion Hence, we can conclude that hydraulic jump is the condition where the rise of water level occurs in channels. This happens when supercritical flow (Fr > 1) changes to subcritical flow (Fr < 1) whereby the supercritical flow encounters a submerged objects such as dam or weir throwing the water upwards. Hydraulic jump advantages include energy dissipation in in dams and channels, scouring prevention in the downstream of a dam, reversing water flow and high water level on the downstream side. A disadvantage of hydraulic jump is the turbulence which may lead to channel erosion and degradation.
References 1. Les Hamil, Understanding of hydraulics 2011, 2011, third edition, (Pages 263-270)
2. https://www.researchgate.net/publication/236154641_Experimental_Study_of_Hydra ulic_Jump_Characteristics_in_Sloping_Prismatic_Channels
3. http://www.brighthubengineering.com/hydraulics-civil-engineering/55054-openchannel-flow-basics-hydraulic-jump-calculations/
