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. Introduction2. Project Objective3. Literature Review4. Proof of Hydraulic Jump in UDRS5. Methodology6. Results7. Conclusion8. Future Work/Recommendations9. 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

𝑦2𝑦1

=12𝑥 (√1+8 𝑥 𝐹 1

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=1n∗S f

12∗R

23

Q=1n∗S f

12∗R

23∗ 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 .

• 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 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:

𝑦2𝑦1

=12𝑥 (√1+8 𝑥 𝐹 1

2−1 )

𝐿𝑟

𝑦 2=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

4. Proof of Hydraulic Jump in UDRS

• 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; = 60o; ∆z = z1 –z2 = L * sin = 200m (Zhao et al, 1995)

4. Proof of Hydraulic Jump in UDRS

P1/g + V12/2g + z1 = P2/g + V2

2/2g + z2 + hT + hL

z1 = z2 + hT + hL

0 0.2 0.4 0.6 0.8 1 1.20.0000

10.000020.000030.000040.000050.000060.000070.0000

30 deg 70 deg 10 deg

Turbine harnessing of energy head from ∆z , 𝛼

Velo

city

vp,

m/s

Where hT = turbine head, and hL = head loss due to

friction =

∆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 ) from ∆z

hT = ∆z

hL = ∆z – hT

Replacing hL with the head loss due to friction equation, = ∆z * (1 - )

where vp is velocity inside pipe or conduit

Vp = ; let K1 =

Vp =

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 gate6 – 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 CalibrationSignificance 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.

5. Methodology: Sensor Calibration

5. Methodology: Sensor Calibration

1.200 1.400 1.600 1.800 2.000 2.200 2.400 2.6003

5

7

9

11

13

15

17PT4 1141amPT5PT6PT7PT8PT9

Voltage (V)

Wat

er D

epth

(cm

)

Pressure Transducer No.

Slope, m Intercept, b

4 12.396 -12.3175 11.282 -11.8616 10.67 -10.9847 11.376 -12.0938 10.713 -9.92319 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 𝑃𝑇 4=12.396 𝑥−12.317=12.396∗1.407−12.317=5.13𝑐𝑚Example:

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.

1.200 1.400 1.600 1.800 2.000 2.200 2.4003

5

7

9

11

13

15

17

f(x) = 11.7988445878784 x − 10.2219239355443R² = 0.998937011014161

f(x) = 11.7974846229959 x − 12.1040051673578R² = 0.999224820892746

f(x) = 12.3958842708498 x − 12.3170707325145R² = 0.998307636151605

PT4 11:41am

Linear (PT4 11:41am)

12:21PM

Linear (12:21PM)

2:16PM

Linear (2:16PM)

Voltage (v)

Wat

er D

epth

(cm

)

5. Methodology: Adjusting for Atmospheric Pressure

PT4 11:41am (V) 12:21PM (V) DifferenceAverage of differences

5 1.407 1.456 -0.050

-0.07310 1.781 1.860 -0.07915 2.213 2.303 -0.091

PT4 12:21PM12:21PM Adjusted

New slope

5 1.456 1.383 11.79710 1.860 1.787 New intercept15 2.303 2.230 -11.24

1.200 1.400 1.600 1.800 2.000 2.200 2.4003

5

7

9

11

13

15

17

f(x) = 11.7988445878784 x − 11.2421835728849R² = 0.998937011014161f(x) = 11.7974846229959 x − 11.2397351446957R² = 0.999224820892746

f(x) = 12.3958842708498 x − 12.3170707325145R² = 0.998307636151605

PT4 1141am

Linear (PT4 1141am)

12:21PM

Linear (12:21PM)

2:16PM

Linear (2:16PM)

Voltage (V)

Wat

er D

epth

(cm

)

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 60

1

2

3

4

5

PT4PT5PT6PT7

Length of Sampling (minutes)

Wat

er D

epth

(cm

)

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

𝐿𝑟

𝑦 2=4.3𝑦2

𝑦1=12𝑥 (√1+8 𝑥 𝐹 1

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 1.504HJ2 31.38 2.677 0.03 1.453HJ3 39.90 3.240 0.031 1.788HJ4 44.20 2.992 0.035 1.754HJ5 47.39 2.824 0.038 1.728

3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.0000.0002.0004.0006.0008.000

10.00012.000

HJ2 HJ4 HJ1 HJ3


Wat

er d

epth

(cm

)

• 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)


3 4 5 6 7 8 9 100

0.0050.01

0.0150.02

0.0250.03

0.0350.04

0.045HJ1 HJ2 HJ3 HJ4


Stan

dard

dev

iatio

n /

Aver

age

3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.0000.0002.0004.0006.0008.000

10.00012.000

HJ2 HJ4 HJ1 HJ3


Wat

er d

epth

(cm

)

• 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


3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.0000.00E+001.00E-042.00E-043.00E-044.00E-045.00E-046.00E-047.00E-048.00E-04

HJ1 HJ2 HJ3 HJ4


Varia

nce/

Aver

age

3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.0000.0002.0004.0006.0008.000

10.00012.000

HJ2 HJ4 HJ1 HJ3


Wat

er d

epth

(cm

)

• 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

3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.0000.0002.0004.0006.0008.000

10.00012.00014.000

HJ6 HJ5 HJ7


Wat

er h

eigh

t (cm

)

Jump Type and Number

Flow Rate (m3/h)

Froude No.


Flow Rate (m3/s)

Closed Conduit Hydraulic Jump 1 or HJ5

47.39 2.824 0.038 1.728


48.44 4.132 0.030 2.243


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.


3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.0000.0002.0004.0006.0008.000

10.00012.00014.000

HJ6 HJ5 HJ7


Wat

er h

eigh

t (cm

)

Jump Type and Number

Flow Rate (m3/h)

Froude No.


Flow Rate (m3/s)


47.39 2.824 0.038 1.728


48.44 4.132 0.030 2.243


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)


3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.0000.0002.0004.0006.0008.000

10.00012.00014.000

HJ6 HJ5 HJ7


Wat

er h

eigh

t (cm

)

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) 3.904HJ6: 4 0.030 4.132 0.161 0.692 0.117 9 (0.5m away) 27.154HJ7: 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


3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.0000.0002.0004.0006.0008.000

10.00012.00014.000

HJ6 HJ5 HJ7


Wat

er h

eigh

t (cm

)

3 4 5 6 7 8 9 100

0.0020.0040.0060.008

0.010.012

HJ6 HJ7 HJ8


Stan

dard

dev

iatio

n/Av

-er

age

• 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.


3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.0000.0002.0004.0006.0008.000

10.00012.00014.000

HJ6 HJ5 HJ7


Wat

er h

eigh

t (cm

)

3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.0000.00E+001.00E-032.00E-033.00E-034.00E-035.00E-036.00E-037.00E-038.00E-03

HJ6 HJ7 HJ8

Pressure Transducer No

Varia

nce/

Aver

age

• 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.

𝑦2𝑦1

=12𝑥 (√1+8 𝑥 𝐹 1

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 0.129HJ6: 4 0.030 4.132 0.161 0.692 0.117HJ7: 4 0.030 13.189 0.161 0.692 0.123

8. Future Work/Recommendations

• 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.

1.200 1.400 1.600 1.800 2.000 2.200 2.400 2.6003

5

7

9

11

13

15

17PT4 1141amPT5PT6PT7PT8PT9

Voltage (V)

Wat

er D

epth

(cm

)

8. Future Work/Recommendations• 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.

8. Future Work/Recommendations• 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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