Full Report Flow In Open Channel 185116
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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 kinetic energy into an increase in potential energy, with some energy irreversibly lost through turbulence to heat. In an open channel flow, this manifests as the fast flow rapidly slowing and piling up on top of itself similar to how a shock wave forms. The phenomenon is dependent upon the initial fluid speed. If the initial speed of the fluid is below the critical speed, then no jump is possible. For 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 break and curl back 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. However, 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.
1
2.0
OBJECTIVE 1. To observe the hydraulic jump phenomenon and to compare measured flow depths 2.
with theoretical results. To investigate the characteristic a standing wave (the hydraulic jump) produced
3. 4. 5.
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.
2
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. It 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 extremely turbulent water before it settles the smooth tranquil flow. By considering the forces acting within the fluid on either side of a hydraulic jump of unit width it can be shown that : 2 2 v v ∆ H=d a + a − d h + h 2g 2g
(
Where, ∆ H
)
is the total head loss across jump (energy dissipated)(m), v a
is the
mean velocity before jump (m/s), 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 hydraulic jump (m). Because the working section is short, d a=d 1 and d b=d 3 . Therefore, simplifying the above equation, ∆ H= ( d 3−d 1 ) ³ /4 d 1 d 3
3
4.0
APPARATUS 1. Self-contained Glass Sided Tilting Flume.
2. Adjustable Undershot Weir
3. Control
4. Instrument Carrier
4
5. Hook and Point Gauge
6. Meter Ruler
5
5.0
PROCEDURE 1. Ensured the flume was level, with the downstream tilting overshot weir, E at the bottom of its travel. Measured and recorded the actual breadth, b (m) of the undershot weir. Installed the undershot weir towards the inlet end of the flume and ensured that it was securely clamped in position. 2. Adjusted the undershot weir to position the sharp edge of the weir 20mm above the bed of the channel. Increased the height of the tilting overshot weir until the downstream level just started to rise. 3. Gradually 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 working section. Observed and sketched the flow pattern. 4. Increased 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 working section. Observed and sketched the flow pattern. 5. Measure and record the values ofd_1,d_3, d_g and q. Repeat this for other flow rates q (upstream head) and heights of the gate,d_g.
6
6.0
RESULT AND DATA ANALYSIS
Weir
Upstrea
Flow
Flow
Flow
Openin
m Flow
Depth
Depth
rate (
Depth,
Above
Below
m3 /s
Jump,
Jump,
m )
d1
d3
0.03
0.103
m ) 0.021
m ) 0.055
0.03
0.116
0.023
0.03
0.130
0.03
0.145
g,
dg
( m )
0.03 0.03
d0
(
0.159
Formula , ∆ H =
V1
0.007
0.008
0.055
0.008
0.024
0.058
0.021
0.065
(
0.022
0.174
To calculate ∆ H
∆H
0.023
∆H d1
d3 d1
0.222
0.404
2.619
5 0.006
9 0.226
8 0.278
0 2.391
0.009
4 0.007
0 0.226
3 0.291
3 2.416
0.010
0 0.015
7 0.226
7 0.752
7 3.095
0.011
8 0.016
2 0.226
4 0.768
3 3.045
0.012
9 0.017
8 0.226
2 0.739
5 3.087
0
0
1
0
)
(
0.067 0.071
:
( d 3−d 1 )
3
4 d1 d 3
1. ∆H = (0.055 – 0.021)³ ÷ (4)(0.021)(0.055) = (0.034)³ ÷ 0.0046 = 0.0085 2. ∆H = (0.055 – 0.023)³ ÷ (4)(0.023)(0.055) = (0.032)³ ÷ 0.0051 = 0.0064 3. ∆H = (0.058 – 0.024)³ ÷ (4)(0.024)(0.058) = (0.034)³ ÷ 0.0056 = 0.0070 7
4. ∆H = (0.065 – 0.021)³ ÷ (4)(0.021)(0.065) = 0.0158 5. ∆H = (0.067 – 0.022)³ ÷ (4)(0.02)(0.067) = (0.045)³ ÷ 0.0054 = 0.0169 6. ∆H = (0.071 – 0.023)³ ÷ (4)(0.023)(0.071) = (0.048)³ ÷ 0.0065 = 0.0170
To calculate V1: Formula ,V 1=
Q d 0 ×b
1. v₁ = 0.007 ÷ (0.103)(0.305) = 0.007 ÷ 0.0314 = 0.2229 2. v₁ = 0.008 ÷ (0.116)(0.305) = 0.008 ÷ 0.0354 = 0.2260 3. v₁ = 0.009 ÷ (0.130)(0.305) = 0.009 ÷ 0.0397 = 0.2267 4. v₁ = 0.010 ÷ (0.145)(0.305) = 0.010 ÷ 0.0442 = 0.2262 5. v₁ = 0.011 ÷ (0.159)(0.305) = 0.011 ÷ 0.0485 = 0.2268 6. v₁ = 0.012 ÷ (0.174)(0.305) = 0.2260
To calculate ∆H/d₁: Formula=
∆H d1
1. ∆H/d₁ = 0.0085 ÷ 0.021 = 0.4048 8
2. ∆H/d₁ = 0.0064 ÷ 0.023 = 0.2783 3. ∆H/d₁ = 0.0070 ÷ 0.024 = 0.2917 4. ∆H/d₁ = 0.0158 ÷ 0.021 = 0.7524 5. ∆H/d₁ = 0.0169 ÷ 0.022 = 0.7682 6. ∆H/d₁ = 0.0170 ÷ 0.023 = 0.7391
To calculate d₃/d₁: Formula=
d3 d1
1. d₃/d₁ = 0.055 ÷ 0.021 = 2.6190 2. d₃/d₁ = 0.055 ÷ 0.023 = 2.3913 3. d₃/d₁ = 0.058 ÷ 0.024 = 2.4167 4. d₃/d₁ = 0.065 ÷ 0.021 = 3.0953 5. d₃/d₁ = 0.067 ÷ 0.022 = 3.0455 6. d₃/d₁ = 0.071 ÷ 0.023 = 3.0870
To calculate dc :
dc=
√[ 3
]
Q2 , d 1
0.305 ¿ ¿ 2 0.007 =0.038 m ( 9.81 ) ¿ ¿ d c =√3 ¿ 0.305 ¿ ¿ 2 0.008 =0.041m ( 9.81 ) ¿ ¿ d c = √3 ¿ 0.305 ¿ ¿ 0.0092 =0.045m ( 9.81 ) ¿ ¿ d c =√3 ¿ 0.305 ¿ ¿ 0.010 2 =0.048 m ( 9.81 ) ¿ ¿ d c =√3 ¿ 0.305 ¿ ¿ 2 0.011 =0.051m ( 9.81 ) ¿ ¿ d c = √3 ¿ 0.305 ¿ ¿ 2 0.012 =0.054 m ( 9.81 ) ¿ ¿ d c =√3 ¿
Hence,
dg = 0.03 : 0.021
10
¿
0.038
¿
0.055
dg = 0.03: 0.023
¿
0.041
¿
0.055
dg = 0.03: 0.024
¿
0.045
¿
0.058
dg = 0.03: 0.021
¿
0.048
¿
0.065
dg = 0.03: 0.022
¿
0.051
¿
0.067
dg = 0.03: 0.023
¿
0.054
¿
0.071
11
7.0
DISCUSSION By following the procedures, our group has to set up the weir opening starting with
0.030m and constant to the end of experiment. The flow rate is increasing order. For precautions, the flow rate used must not be more than 0.013m^3/s because it can lead to overflow. We found out that there was an error in our experiment. 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:The instrument factor. The equipment was not in a good condition. The weir gate has leak, so there are water that flow through the hole of the leak, although we have taken 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. Human factor. Where the readings taken are not consistent because there is more than one observer. Parallax error could also occur. The mistake in booking will also contribute to the error. If one of the values is wrong, it will affect all the calculation. To avoid all of these errors happen, precautions must have been taken 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 △H/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. It can provide for 60-70% energy dissipation of the energy in the basin itself, limiting the damage to structures and the stream bed. Even with such efficient energy dissipation, stilling basins must be carefully designed to avoid serious damage due to uplift, vibration, cavitation, and abrasion.
12
8.0
CONCLUSION In conclusion, our experiment 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 kinetic 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. For this experiment, the important thing that we must follow is the flow rate used for the experiment must be constant or we would not see the change in pattern of hydraulic jump caused by the changing of weir opening. For the recommendation, students must know how to conduct the basic and manual operations of this equipment. Besides, carefully consider the flow rate used in this experiment. Ensure the weir gate is in good condition. Use the hook and point gauge to measure the height of the water for each section.
9.0
REFERENCE 1. https://en.wikipedia.org/wiki/Hydraulic_jump#cite_ref-Energy_loss_19-0 2. Flow in Open Channel lab sheet, Faculty of Civil & Environmental Engineering, UTHM
13
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 kinetic energy into an increase in potential energy, with some energy irreversibly lost through turbulence to heat. In an open channel flow, this manifests as the fast flow rapidly slowing and piling up on top of itself similar to how a shock wave forms. The phenomenon is dependent upon the initial fluid speed. If the initial speed of the fluid is below the critical speed, then no jump is possible. For 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 break and curl back 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. However, 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.
1
2.0
OBJECTIVE 1. To observe the hydraulic jump phenomenon and to compare measured flow depths 2.
with theoretical results. To investigate the characteristic a standing wave (the hydraulic jump) produced
3. 4. 5.
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.
2
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. It 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 extremely turbulent water before it settles the smooth tranquil flow. By considering the forces acting within the fluid on either side of a hydraulic jump of unit width it can be shown that : 2 2 v v ∆ H=d a + a − d h + h 2g 2g
(
Where, ∆ H
)
is the total head loss across jump (energy dissipated)(m), v a
is the
mean velocity before jump (m/s), 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 hydraulic jump (m). Because the working section is short, d a=d 1 and d b=d 3 . Therefore, simplifying the above equation, ∆ H= ( d 3−d 1 ) ³ /4 d 1 d 3
3
4.0
APPARATUS 1. Self-contained Glass Sided Tilting Flume.
2. Adjustable Undershot Weir
3. Control
4. Instrument Carrier
4
5. Hook and Point Gauge
6. Meter Ruler
5
5.0
PROCEDURE 1. Ensured the flume was level, with the downstream tilting overshot weir, E at the bottom of its travel. Measured and recorded the actual breadth, b (m) of the undershot weir. Installed the undershot weir towards the inlet end of the flume and ensured that it was securely clamped in position. 2. Adjusted the undershot weir to position the sharp edge of the weir 20mm above the bed of the channel. Increased the height of the tilting overshot weir until the downstream level just started to rise. 3. Gradually 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 working section. Observed and sketched the flow pattern. 4. Increased 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 working section. Observed and sketched the flow pattern. 5. Measure and record the values ofd_1,d_3, d_g and q. Repeat this for other flow rates q (upstream head) and heights of the gate,d_g.
6
6.0
RESULT AND DATA ANALYSIS
Weir
Upstrea
Flow
Flow
Flow
Openin
m Flow
Depth
Depth
rate (
Depth,
Above
Below
m3 /s
Jump,
Jump,
m )
d1
d3
0.03
0.103
m ) 0.021
m ) 0.055
0.03
0.116
0.023
0.03
0.130
0.03
0.145
g,
dg
( m )
0.03 0.03
d0
(
0.159
Formula , ∆ H =
V1
0.007
0.008
0.055
0.008
0.024
0.058
0.021
0.065
(
0.022
0.174
To calculate ∆ H
∆H
0.023
∆H d1
d3 d1
0.222
0.404
2.619
5 0.006
9 0.226
8 0.278
0 2.391
0.009
4 0.007
0 0.226
3 0.291
3 2.416
0.010
0 0.015
7 0.226
7 0.752
7 3.095
0.011
8 0.016
2 0.226
4 0.768
3 3.045
0.012
9 0.017
8 0.226
2 0.739
5 3.087
0
0
1
0
)
(
0.067 0.071
:
( d 3−d 1 )
3
4 d1 d 3
1. ∆H = (0.055 – 0.021)³ ÷ (4)(0.021)(0.055) = (0.034)³ ÷ 0.0046 = 0.0085 2. ∆H = (0.055 – 0.023)³ ÷ (4)(0.023)(0.055) = (0.032)³ ÷ 0.0051 = 0.0064 3. ∆H = (0.058 – 0.024)³ ÷ (4)(0.024)(0.058) = (0.034)³ ÷ 0.0056 = 0.0070 7
4. ∆H = (0.065 – 0.021)³ ÷ (4)(0.021)(0.065) = 0.0158 5. ∆H = (0.067 – 0.022)³ ÷ (4)(0.02)(0.067) = (0.045)³ ÷ 0.0054 = 0.0169 6. ∆H = (0.071 – 0.023)³ ÷ (4)(0.023)(0.071) = (0.048)³ ÷ 0.0065 = 0.0170
To calculate V1: Formula ,V 1=
Q d 0 ×b
1. v₁ = 0.007 ÷ (0.103)(0.305) = 0.007 ÷ 0.0314 = 0.2229 2. v₁ = 0.008 ÷ (0.116)(0.305) = 0.008 ÷ 0.0354 = 0.2260 3. v₁ = 0.009 ÷ (0.130)(0.305) = 0.009 ÷ 0.0397 = 0.2267 4. v₁ = 0.010 ÷ (0.145)(0.305) = 0.010 ÷ 0.0442 = 0.2262 5. v₁ = 0.011 ÷ (0.159)(0.305) = 0.011 ÷ 0.0485 = 0.2268 6. v₁ = 0.012 ÷ (0.174)(0.305) = 0.2260
To calculate ∆H/d₁: Formula=
∆H d1
1. ∆H/d₁ = 0.0085 ÷ 0.021 = 0.4048 8
2. ∆H/d₁ = 0.0064 ÷ 0.023 = 0.2783 3. ∆H/d₁ = 0.0070 ÷ 0.024 = 0.2917 4. ∆H/d₁ = 0.0158 ÷ 0.021 = 0.7524 5. ∆H/d₁ = 0.0169 ÷ 0.022 = 0.7682 6. ∆H/d₁ = 0.0170 ÷ 0.023 = 0.7391
To calculate d₃/d₁: Formula=
d3 d1
1. d₃/d₁ = 0.055 ÷ 0.021 = 2.6190 2. d₃/d₁ = 0.055 ÷ 0.023 = 2.3913 3. d₃/d₁ = 0.058 ÷ 0.024 = 2.4167 4. d₃/d₁ = 0.065 ÷ 0.021 = 3.0953 5. d₃/d₁ = 0.067 ÷ 0.022 = 3.0455 6. d₃/d₁ = 0.071 ÷ 0.023 = 3.0870
To calculate dc :
dc=
√[ 3
]
Q2 , d 1
0.305 ¿ ¿ 2 0.007 =0.038 m ( 9.81 ) ¿ ¿ d c =√3 ¿ 0.305 ¿ ¿ 2 0.008 =0.041m ( 9.81 ) ¿ ¿ d c = √3 ¿ 0.305 ¿ ¿ 0.0092 =0.045m ( 9.81 ) ¿ ¿ d c =√3 ¿ 0.305 ¿ ¿ 0.010 2 =0.048 m ( 9.81 ) ¿ ¿ d c =√3 ¿ 0.305 ¿ ¿ 2 0.011 =0.051m ( 9.81 ) ¿ ¿ d c = √3 ¿ 0.305 ¿ ¿ 2 0.012 =0.054 m ( 9.81 ) ¿ ¿ d c =√3 ¿
Hence,
dg = 0.03 : 0.021
10
¿
0.038
¿
0.055
dg = 0.03: 0.023
¿
0.041
¿
0.055
dg = 0.03: 0.024
¿
0.045
¿
0.058
dg = 0.03: 0.021
¿
0.048
¿
0.065
dg = 0.03: 0.022
¿
0.051
¿
0.067
dg = 0.03: 0.023
¿
0.054
¿
0.071
11
7.0
DISCUSSION By following the procedures, our group has to set up the weir opening starting with
0.030m and constant to the end of experiment. The flow rate is increasing order. For precautions, the flow rate used must not be more than 0.013m^3/s because it can lead to overflow. We found out that there was an error in our experiment. 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:The instrument factor. The equipment was not in a good condition. The weir gate has leak, so there are water that flow through the hole of the leak, although we have taken 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. Human factor. Where the readings taken are not consistent because there is more than one observer. Parallax error could also occur. The mistake in booking will also contribute to the error. If one of the values is wrong, it will affect all the calculation. To avoid all of these errors happen, precautions must have been taken 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 △H/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. It can provide for 60-70% energy dissipation of the energy in the basin itself, limiting the damage to structures and the stream bed. Even with such efficient energy dissipation, stilling basins must be carefully designed to avoid serious damage due to uplift, vibration, cavitation, and abrasion.
12
8.0
CONCLUSION In conclusion, our experiment 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 kinetic 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. For this experiment, the important thing that we must follow is the flow rate used for the experiment must be constant or we would not see the change in pattern of hydraulic jump caused by the changing of weir opening. For the recommendation, students must know how to conduct the basic and manual operations of this equipment. Besides, carefully consider the flow rate used in this experiment. Ensure the weir gate is in good condition. Use the hook and point gauge to measure the height of the water for each section.
9.0
REFERENCE 1. https://en.wikipedia.org/wiki/Hydraulic_jump#cite_ref-Energy_loss_19-0 2. Flow in Open Channel lab sheet, Faculty of Civil & Environmental Engineering, UTHM
13
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