FYP Presentation v2.0

FYP Presentation: Hydraulic
Jump in Aerated Flows
presented by
Dy, Raelene Ina Bianchi Mendez
FYP Student, Environmental Engineering Year 4
School of Civil and Environmental Engineering
10 May 2016

Contents
1. Introduction
2. Project Objective
3. Literature Review
4. Proof of Hydraulic Jump in UDRS
5. Methodology
6. Results
7. Conclusion
8. Future Work/Recommendations
9. References

1. Introduction
• Singapore is constantly looking for
ways to augment its water supply.
• A sizeable amount of rainfall ends
up in the sea due to a lack of
reservoir space on land (Kotwani,
2015).
• PUB looking into the design and
development of an Underground
Drainage and Reservoir System
(UDRS) to store excess rainwater.
• This FYP is part of study on effects
of transporting water in conduits
on the pipes themselves at least
150m below the surface.
Source: National Water Agency PUB looks underground
for Water Storage Solutions, Straits Times, June 2015

2. Project Objective
• To observe and describe the behavior of the flow and
the resulting hydraulic jump inside a closed conduit
– Focus on velocity and pressure
• To compare behavior of classical hydraulic jump to
that of closed conduit jump with respect to Belangér
equation
𝑦2
𝑦1
=
1
2
𝑥 1 + 8 𝑥 𝐹1
2
− 1

3. Literature Review: Uniform Flow
• In uniform flow, all flow parameters
are independent of both space and
time;
• A flow in a given channel must satisfy
the following conditions to be
considered as uniform flow:
– Bottom slope So be constant,
– Wall roughness must be uniformly
distributed,
– Discharge remains constant both in time
and space,
– Cross-section of channel must be prismatic
– Channel axis is straight
– Air pressure above surface is constant,
– Homogenous fluid
– Governing parameters must be
independent of time
V =
1
n
∗ Sf
1
2 ∗ R
2
3
Q =
1
n
∗ Sf
1
2 ∗ R
2
3 ∗ A

3. Literature Review: Froude Number
• The Froude number Fr is a governing
characteristic for free surface flows
• F<1: subcritical flow; composed of a large
static pressure portion y and a relatively small
dynamic portion
𝑣2
2𝑔
.
• F=1: critical flow; state at which the water has
maximum specific energy E;
– Has its own set of flow characteristics and
formulas that arise from the special
conditions and flow structure at critical flow,
such as a wavy or undulating water profile.
– At So = critical slope Sc, critical flow arises.
• F > 1.0: supercritical flow; have large dynamic
portion
𝑣2
2𝑔
in comparison to their static pressure
portion y.
𝐹 =
𝑣
𝑔𝑦
• Where F is the
dimensionless Froude
number
• v is the flow velocity,
• g is the gravitational
constant, and
• y is the depth of the flow

3. Literature Review: Hydraulic Jump
• A natural flow phenomenon observed in open channel water bodies such
as rivers and streams, or downstream of hydraulic structures, e.g. sluice
gates and spillways.
• Literal ‘jump’ from supercritical (Fr>1.0) to subcritical (Fr<1.0) flow
accompanied by strong turbulent mixing and air bubbles
• Through the hydraulic jump, excess mechanical energy is turned into heat,
serving as an energy dissipater Significant energy loss takes place in
the occurrence of the hydraulic jump (Hager, 1992).
Sources: Wikipedia Images

3. Literature Review: Classical Conduit
Jump
• Hydraulic jump in a rectangular cross section
(Rajatratnam, 1967)
– Received significant attention in the last sixty years
due to the simplicity of the requisite channel
geometry, and its importance in stilling basin design
• Characteristics of interest
– The ratio of sequent depths, i.e. the heights of the
flow upstream and downstream of the jump
• Jump roller: set of large-scale turbulent eddies that form
at the surface of a jump.; roller length Lr or distance from
the jump toe to the stagnation point (or where the jump
starts to stabilize) at the free surface of the flow is
described by:
𝑦2
𝑦1
=
1
2
𝑥 1 + 8 𝑥 𝐹1
2
− 1
𝐿 𝑟
𝑦2
= 4.3
Source: Wikipedia Images

3. Literature Review: Closed Conduit
Jump
• Free surface flow should take place in
sewers by principle:
– But flow inside pipes may become pressurized
due to submergence at the downstream end,
large flow rates or conduit damage.
– Figure c: As the jump builds to its sequent
subcritical depth it is choked by the ‘ceiling’ of
the conduit.
• Closed Conduit Jump: Sequent
depth hits ceiling or exceeds depth
of conduit, leading to pressurized
condition
• In current literature, there has not been
as much focus on the conditions and
equations that describe hydraulic jump
behavior in a closed conduit compared
to the classical hydraulic jump.
Source: Wastewater Hydraulics, Will Hager, 2010

• Assumes that P1 = P2 = 0 atm because they are both open to
the atmosphere at the surface of their respective reservoirs;
pressure due to air considered negligible.
• v1 = 0 m/s as it is the velocity in the surface reservoir.
• L = 400m; 𝜃 = 60o; ∆z = z1 –z2 = L * sin 𝜃 = 200m (Zhao et al,
1995)

P1/g + V1
2/2g + z1 = P2/g + V2
2/2g + z2 + hT + hL
z1 = z2 + hT + hL
0.0000
10.0000
20.0000
30.0000
40.0000
50.0000
60.0000
70.0000
0 0.5 1 1.5
Velocityvp,m/s
Turbine harnessing of energy head from
∆z , 𝛼30 deg 70 deg 10 deg
Where hT = turbine head, and hL
= head loss due to friction = 𝑓
𝐿
𝐷
𝑣2
2𝑔
∆z = hT + hL
However, hL may not be negligible. On the
other hand, hT is dependent on the
turbine’s ability to harness energy head
(represented by 𝛼) from ∆z
∴ hT = 𝛼∆z
hL = ∆z – hT
Replacing hL with the head loss due to
friction equation, 𝑓
𝐿
𝐷
∗
𝑣 𝑝
2
2𝑔
= ∆z * (1 - 𝛼)
where vp is velocity inside pipe or conduit
Vp =
∆z(1 − 𝛼)
𝑓
𝐿
𝐷 𝑥 2 𝑥 𝑔
; let K1 =
∆z
𝑓
𝐿
𝐷 𝑥 2 𝑥 𝑔
∴ Vp = 𝐾1 (1 − 𝛼)
Function of f, D, and L

5. Methodology: Set-up
• Experiments conducted at
the Hydraulics Lab, N1.1,
at Nanyang Technological
University.
• Glass flume: length 5m
by height15cm by base
20cm, with up- and
downstream reservoir.
• 1st Section covered up
• Next two flume sections of
the flume, had a larger
viewing area to observe
the flow.
• Last two sections had
reduced viewing area.

5. Methodology: Set-up
1 – Upstream gate lever 5 – Downstream sluice gate 9 – Flow rate meter (in m3/h)
2 – Upstream sluice gate
6 – Flume bed slope adjustment
lever
10 – Pressure transducers (12 in
total, but only 6 were used for the
experiments)
3 – Flume (15cm x 20 cm x 5m) 7 – Pump controls Entire flume covered with a duct as
a ceiling, to generate closed conduit
jumps.
4 – Downstream gate lever 8 – Circulation pipes from d/s to
u/s

5. Methodology: Pressure Sensors
• Keller Piezoresistive
Pressure Transducers,
Series 11
• Calibrated to read a range of
1.0 to 1.05 bars.
• Can also be adjusted to read
for temperature and voltage.
Source: Keller

5. Methodology: Sensor Calibration
Significance of sensor calibration:
• Ensure that pressure transducers were recording data accurately
• Obtain a governing linear equation for each of the six pressure
transducers to convert voltage (V) to water depth (cm).
• Use linear equation to adjust for atmospheric pressure, which
changes throughout the day.

3
5
7
9
11
13
15
17
1.200 1.400 1.600 1.800 2.000 2.200 2.400 2.600
WaterDepth(cm)
Voltage (V)
PT4 1141am
PT5
PT6
PT7
PT8
PT9
Pressure Transducer No. Slope, m Intercept, b
4 12.396 -12.317
5 11.282 -11.861
6 10.67 -10.984
7 11.376 -12.093
8 10.713 -9.9231
9 12.565 -13.729
The following slopes and
intercepts were obtained
for each transducer
based on the pressure
readings for 5cm, 10cm
and 15cm.
𝑦 𝑃𝑇4
= 12.396 𝑥 − 12.317
= 12.396 ∗ 1.407
− 12.317 = 5.13𝑐𝑚
Example:
Linear Equation:
y = mx +b

5. Methodology: Adjusting for
Atmospheric Pressure
• Atmospheric pressure changes rapidly within the course of one
day.
• Observed during preliminary tests to have significant effects on the
accuracy of the pressure readings.
• Reference for sensor adjustment: a single pressure transducer was
selected to record pressure readings at water heights of 5, 10 and
15cm at regular intervals during one set of experiments.
y = 12.396x - 12.317
R² = 0.9983
y = 11.797x - 12.104
R² = 0.9992
y = 11.799x - 10.222
R² = 0.9989
3
5
7
9
11
13
15
17
1.200 1.400 1.600 1.800 2.000 2.200 2.400
WaterDepth(cm)
Voltage (v)
PT4 11:41am
12:21PM
2:16PM

5. Methodology: Adjusting for
Atmospheric Pressure
PT4 11:41am (V) 12:21PM (V) Difference
Average of
differences
5 1.407 1.456 -0.050
-0.07310 1.781 1.860 -0.079
15 2.213 2.303 -0.091
PT4 12:21PM 12:21PM Adjusted New slope
5 1.456 1.383 11.797
10 1.860 1.787 New intercept
15 2.303 2.230 -11.24
y = 12.396x - 12.317
R² = 0.9983
y = 11.797x - 11.24
R² = 0.9992
y = 11.799x - 11.242
R² = 0.9989
3
5
7
9
11
13
15
17
1.200 1.400 1.600 1.800 2.000 2.200 2.400
WaterDepth(cm)
Voltage (V)
PT4 1141am
12:21PM
2:16PM

5. Methodology: Time Variation
• To determine minimum time of sampling for HJs
• Water depth recorded stabilized to a particular value after 2 to 3 minutes
• Decided on 3 minutes as sampling time at 1000Hz of sampling.
0
1
2
3
4
5
0 1 2 3 4 5 6
WaterDepth(cm)
Length of Sampling (minutes)
PT4
PT5
PT6
PT7

5. Methodology: Slope and Uniform
Flow

5. Methodology: Classical Hydraulic
Jump (HJ) and Closed Conduit Jump
(CCJ)
START

5. Methodology: Checking the
Classical Hydraulic Jump
• To confirm if generating classical hydraulic jump, compare experimental
sequent depth at Lr from roller length equation versus sequent depth from
Belangér equation
Jump Toe
location
(PT no.)
Water
Height (m)
Froude No.
Theoretical
Sequent
Depth
Roller
Length (m)
Experimental
Sequent
Depth
Location of
Experimental
Sequent
Depth from
Jump Toe
% error
HJ1: 4 0.023 3.165 0.092 0.396 0.079 8 (0.4m away) 14.5
HJ2: 4 0.03 2.677 0.100 0.453 0.089 8 (0.4m away) 10.9
HJ3: 4 0.031 3.240 0.127 0.548 0.099 9 (0.5m away) 22.6
HJ4: 4 0.035 2.992 0.132 0.566 0.108 9 (0.5m away) 17.8
𝐿 𝑟
𝑦2
= 4.3𝑦2
𝑦1
=
1
2
𝑥 1 + 8 𝑥 𝐹1
2
− 1

6. Results: Classical Hydraulic Jump
Jump Type
and Number
Flow Rate
(m3/h)
Froude
No.
Water
Depth at
PT4 (m)
Flow Rate
(m3/s)
HJ1 24.91 3.165 0.023 1.504
HJ2 31.38 2.677 0.03 1.453
HJ3 39.90 3.240 0.031 1.788
HJ4 44.20 2.992 0.035 1.754
HJ5 47.39 2.824 0.038 1.728
0.000
2.000
4.000
6.000
8.000
10.000
12.000
3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000
Waterdepth(cm)
Pressure Transducer No.
HJ2 HJ4 HJ1 HJ3
• Classical jump has d/s
sequent depth < 15cm
• Weak jumps: small rollers
on surface, downstream
water remains smooth
with fairly uniform velocity
and low energy dissipation
(Chow, 1973)

0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
3 4 5 6 7 8 9 10
Standarddeviation/Average
HJ1 HJ2 HJ3 HJ4
0.000
2.000
4.000
6.000
8.000
10.000
12.000
3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000
Waterdepth(cm)
HJ2 HJ4 HJ1 HJ3 • For all of the classical jumps,
standard deviation over
average (σ/μ) tapers down to
the 0 to 0.01 range
approaching PT9.
• Reflects ‘stagnation point’
behavior
– Where jump beings to
stabilize
– PT9 near true sequent
depth location

-1.00E-04
0.00E+00
1.00E-04
2.00E-04
3.00E-04
4.00E-04
5.00E-04
6.00E-04
7.00E-04
8.00E-04
3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000
Variance/Average
HJ1 HJ2 HJ3 HJ4
0.000
2.000
4.000
6.000
8.000
10.000
12.000
3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000
Waterdepth(cm)
HJ2 HJ4 HJ1 HJ3 • Same damping behavior
seen in the
variance/average graph.
• Peaks observed in HJs 2
and 3 may be due to large
fluctuations in the data from
noise or the effect of the
turbulent nature of the jump
roller as it dissipates
energy.
• Smaller range of
variance/average for all the
umps means that these
fluctuations in the recorded
values are relatively small.

6. Results: Closed Conduit Jump
0.000
2.000
4.000
6.000
8.000
10.000
12.000
14.000
3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000
Waterheight(cm)
HJ6 HJ5 HJ7
Jump Type and
Number
Flow Rate
(m3/h)
Froude No.
Water Depth
at PT4 (m)
Flow Rate
(m3/s)
Closed Conduit
Hydraulic Jump 1
or HJ5
47.39 2.824 0.038 1.728
Closed Conduit
Hydraulic Jump 2
or HJ6
48.44 4.132 0.030 2.243
Closed Conduit
Hydraulic Jump 3
or HJ7
43.17 13.189 0.030 2.462
• Closed conduit jumps
appear to display smoother
curves with less undulation.
• Dip at PT8 of HJ5: may be
due to excessive air
entrainment, noise in data
recording.

0.000
2.000
4.000
6.000
8.000
10.000
12.000
14.000
3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000
Waterheight(cm)
HJ6 HJ5 HJ7
Jump Type and
Number
Flow Rate
(m3/h)
Froude No.
Water Depth
at PT4 (m)
Flow Rate
(m3/s)
Closed Conduit
Hydraulic Jump 1
or HJ5
47.39 2.824 0.038 1.728
Closed Conduit
Hydraulic Jump 2
or HJ6
48.44 4.132 0.030 2.243
Closed Conduit
Hydraulic Jump 3
or HJ7
43.17 13.189 0.030 2.462
• HJ5, 6 Jump Type: weak
jump
• HJ7: Oscillating jump which
produces large wave of
irregular period, which,
commonly in canals, can
travel for meters doing
unlimited damage (Chow,
1973)

0.000
2.000
4.000
6.000
8.000
10.000
12.000
14.000
3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000
Waterheight(cm)
HJ6 HJ5 HJ7
Jump Toe
location (PT
no.)
Water Height
(m)
Froude No.
Theoretical
Sequent Depth
Roller Length
(m)
Experimental
Sequent Depth
Location of Experimental
Sequent Depth from Jump
Toe
% error
HJ5: 4 0.038 2.824 0.134 0.578 0.129 9 (0.5m away) 3.904
HJ6: 4 0.030 4.132 0.161 0.692 0.117 9 (0.5m away) 27.154
HJ7: 4 0.030 13.189 0.161 0.692 0.123 9 (0.5m away) 23.545
• Jumps hit flume ceiling at around PT9
• Froude numbers and sequent depths
generated from the assumed jump toe for
each jump by the the Belangér equation
(2-8) show large percentage error between
the theoretical values and the experimental
values.
• Possible that entirety of each
closed conduit jump is not
captured by the 6 pressure
transducers
• True horizontal location of the jump
toe lies beyond PT9

0.000
2.000
4.000
6.000
8.000
10.000
12.000
14.000
3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000
Waterheight(cm)
HJ6 HJ5 HJ7
0
0.002
0.004
0.006
0.008
0.01
0.012
3 4 5 6 7 8 9 10
Standarddeviation/Average
HJ6 HJ7 HJ8
• Standard deviation/average graph
shows a smaller range of values,
from 0 to 0.012 compared to the
classical hydraulic jump.
• Values being recorded by the
transducers lie within a range
closer to the mean.
• Same damping behavior as observed
in classical hydraulic jump when
nearing the sequent depth location
• When matched to their locations in the
CCJ, it can be seen that the closer
the transducer is to PT9, the lesser
the value of the standard
deviation/average
• Approach towards the sequent
depth and ‘stagnation point’,
which is a subcritical flow with
less turbulence compared to the
jump roller.

0.000
2.000
4.000
6.000
8.000
10.000
12.000
14.000
3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000
Waterheight(cm)
HJ6 HJ5 HJ7
0.00E+00
1.00E-03
2.00E-03
3.00E-03
4.00E-03
5.00E-03
6.00E-03
7.00E-03
8.00E-03
3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000
Variance/Average
Pressure Transducer No
HJ6 HJ7 HJ8
• PT4’s relatively larger values imply
that the jump toe changes location
quite often:
• Explains why spread of the data
is wider at this point versus PTs
7 to 9, which show less data
spread
• For CCJ, the the jump toe
adjusts itself to find its
corresponding subcritical depth
• May take longer to stabilize its
location due to the closed
conduit condition
• The jump toe would constantly move
back and forth during the experiments,
sometimes going further upstream
than PT4 and sometimes moving
further downstream than PT5.

7. Conclusion
• Objective: to observe and describe the
behavior of the flow and the resulting
hydraulic jump inside a closed conduit
• Several measures were taken to obtain
accurate and precise data.
– calibration of the pressure transducers at the start
of every experiment run,
– recalibration at regular intervals during the
experiments using a single transducer as basis for
the others.
• Before producing a closed conduit jump,
classical hydraulic jump first be generated
in the flume to ensure data accuracy.
– Verified against the Belangér equation.
𝑦2
𝑦1
=
1
2
𝑥 1 + 8 𝑥 𝐹1
2
− 1 Source: Wastewater Hydraulics, Willi H.
Hager, 2010

7. Conclusion
• Requirement for a jump to be considered as a closed conduit one:
– Water depth of15cm for this project
• Physical experiments did not return pressure readings for water depth
above 15cm
– Possible that the closed conduit hydraulic jumps observed in this study still follow the
Belangér equation
– No pressure transducers present in the section past Pressure Transducer 9, only an
incomplete picture of the closed conduit hydraulic jumps was obtained.
• Crucial that more descriptive set of data capturing the entirety of the
jump, and inclusive of some area before the jump toe and some area
after the sequent depth, be obtained to serve as basis for the behavior
of the closed conduit hydraulic jump.
Jump Toe location
(PT no.)
Water Height (m) Froude No.
Theoretical Sequent
Depth (m)
Roller Length (m)
Experimental Sequent
Depth (m)
HJ5: 4 0.038 2.824 0.134 0.578 0.129
HJ6: 4 0.030 4.132 0.161 0.692 0.117
HJ7: 4 0.030 13.189 0.161 0.692 0.123

• Only three water depths measured for calibration (5cm,
10cm, and 15cm):
– Issue: Limited the range of values that could be converted from
the raw data (volts) to water depth (cm).
– Recommendation: More water depths below 5cm, e.g. 1cm,
2cm and 3cm should be added to the calibration procedure to
obtain more descriptive linear equation for conversion and
adjustment of pressure data.
3
5
7
9
11
13
15
17
1.200 1.400 1.600 1.800 2.000 2.200 2.400 2.600
WaterDepth(cm)
Voltage (V)
PT4 1141am
PT5
PT6
PT7
PT8
PT9

• Calibration was time
consuming due to limitations
of container:
– Issue 1: Can only calibrate
one transducer at a time
– Issue 2: Transducer was
sensitive to small errors in the
measurement of the water into
the container, which made
obtaining a linear graph
challenging.
– Recommendation: Replace
current container with
container that has the capacity
to handle all of the transducers
at once be used in calibration.

• Only six pressure transducers used for
data collection, due to limits of
calibration and time:
– Issue 1: CCJ water profile described by the
six pressure transducers was not a
complete hydraulic jump.
– Issue 2: Exact location and water depth at
the sequent depth could not be recorded;
located beyond the range of the pressure
transducers.
– Recommendation: More transducers be
added before and after the jump to better
capture pressure readings about the water
profile, average values, and statistical
spread of the data.

THANK YOU FOR LISTENING!
Question and Answer Section

8. References
Chanson, H. (2004). Environmental hydraulics of open channel flows. Amsterdam:
Elsevier Butterworth-Heinemann.
Chow, V. T. (1973). Open-channel hydraulics. Singapore: McGraw-Hill.
Hager, W. H. (2010). Wastewater hydraulics: Theory and practice. Berlin: Springer.
Kotwani, M. (2015 June 16). PUB launches study on underground water reservoir
and drainage system. Retrieved from
http://www.channelnewsasia.com/news/singapore/pub-launches-study-
on/1918276.html.
Zhao, J., Zhou, Y., Sun, J., Low, B., & Choa, V. (1995). Engineering geology of the
Bukit Timah Granite for cavern construction in Singapore. Quarterly Journal of
Engineering Geology and Hydrogeology, 28, 153-162.

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