Hydraulic Jump Data

7/28/2019 Hydraulic Jump Data

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Results:

Datum height= 0.16662m

Width of flume, b= 0.105m

Depth of flow data

TrialNo.

Height of flowdownstream/

Height of flowupstream/

Start ofhydraulic

jump, L1/ m

End ofhydraulic

jump, L2/ m

Length ofhydraulic

jump, L/ m=L2-L1

1 8.03 7.44 0.48 0.55 0.07

2 10.62 7.26 0.42 0.555 0.135

3 11.70 7.31 0.39 0.55 0.16

4 12.30 7.34 0.388 0.637 0.249

Rate of flow data

Volume of water measured= 300L = 0.3m3

Trial No. Volume of water/ L Time, t/ s Average time, t/s

Actual dischargerate, Qa/ m

3/s

1 300 57.86 57.86 0.005185

2 300 38.28 38.59 0.00777438.56

38.92

3 300 32.78 32.59 0.009205

32.4932.49

4 300 29.72 29.73 0.010091

29.7029.76

Treatment of results

Trial No.H1, Heightof flowupstream/m

Depth of flowupstream,d1/m(H1-Datum)

H2, height offlowdownstream/m

Depth of flowdownstream,d2/ m(H2-Datum)

Actualdischargerate,Qa/m

3/s

Dischargeper unitwidth, q/m3/s/m

Criticaldepth, d

1 0.188976 0.022356 0.203962 0.037342 0.005185 0.04938 0.0622 0.184404 0.017784 0.269748 0.103128 0.007774 0.074038 0.082

3 0.185674 0.019054 0.29718 0.13056 0.009205 0.087667 0.092

4 0.186436 0.019816 0.31242 0.1458 0.010091 0.096105 0.098


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Trial No. Velocityupstream, v1/m/s

Velocitydownstream,v2/ m/s

FroudeNumberupstream, Fr 1

FroudeNumberdownstream,Fr2

Critical velocity,vc/ m/s

1 2.205012 1.320102 4.708465 2.181093 0.78537

2 4.127841 0.711829 9.882657 0.707706 0.898895

3 4.600959 0.671467 10.64194 0.593314 0.950972

4 4.849857 0.659155 10.99984 0.551155 0.980554

Trial No. SpecificEnergyupstream,E1/ m

SpecificEnergydownstream,E2/ m

Specific Energyat critical depth,Ec/ m

Energy loss,

E/m=

1 0.27017 0.126163 0.094204 0.001008

2 0.88624 0.128954 0.122849 0.0847333 1.097995 0.15354 0.13828 0.139328

4 1.21865 0.167945 0.147016 0.173027

TrialNo. Force

upstream, F1/ N=()

Momentumupstream,M1/kgm/s=

(M+F)1

Force

downstream,F2/N=()

Momentumdownstrea

m, M2/kgm/s=

(M+F)2Force atcriticaldepth,Fc/N

Momentum atcriticaldepth,Mc/kgm/s (M+F)

1 0.256633 11.41819 11.6748 0.716009 6.83587 7.55188 2.025275 4.05987 6.089

2 0.162399 32.2678 32.4302 5.461056 5.56445 11.0255 3.444139 6.96707 10.43 0.186421 42.22477 42.4112 8.752734 6.16231 14.9150 4.363719 8.727438 13.094 0.20163 48.79309 48.9947 10.91537 6.631576 17.5470 4.932541 9.865081 14.79

Classification of hydraulic jump for each of the trial no.

TrialNo.

Froude numberupstream, Fr1

The classification of jumps foreach trial no.

Loss of energy in %((E/E1)x100)

1 4.708465 Steady jump 0.373054

2 9.882657 Strong jump 9.5609823 10.64194 Strong jump 12.68931

4 10.99984 Strong jump 14.19822


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0

0.05

0.1

0.15

0.2

0.25

0.3

0 2 4 6 8 10 12 14

Length

ofhydraulicjump,

L/m

Froude number upstream, Fr1

Length of hydraulic jump, L vs Froude number upstream, Fr1


4/12

0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10 12 14

Lossofenergy(%)

Froude number upstream, Fr1

Loss of energy (%) vs Froude number upstream


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0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 2 4 6 8 10 12

Energydissipation,

E

Froude Number Upstream, Fr1

Energy dissipation vs Froude Number upstream for the 4 trials


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0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 0.2 0.4 0.6 0.8 1 1.2 1.4

De

pthofflow,

d/m

Specific Eneegy, E

Depth, d vs Specific Energy, E

Trial No.1

Trial No.2

Trial No.3

Trial No.4


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0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 10 20 30 40 50 60

Depthofflow,

d/m

(M+F)

Depth,d vs (M+F)

Trial No.1

Trial No.3

Trial No.4

Trial No.2


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Procedure:

1) The flow rate was adjusted and the tailgate elevation set so that a stable acceptable

hydraulic jump occurs midway through the channel.

2) Using a stopwatch, the time taken for the needle on the gauge of the hydraulic jump

machine to make three revolutions was recorded for each trial of the experiment. Eachrevolution of the gauge represents 100 litres of water. This data is used to calculate the

discharge, Q.

3) The depth of flow in front, behind the hydraulic jump was measured.

4) Using a meter rule, the length of the hydraulic jump was measured.

5) The steps were repeated for the other three discharge values.


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Discussion:

The graph of Energy dissipation, E vs Froude number upstream, Fr1 shows an

exponential relationship between the two. The trend is that as Froude number upstream

increases, energy loss increases but at a non linear rate. Each consecutive trial number for the

experiment the flow rate was set to a higher value than it was before. The theory suggests thatboth the Froude number and specific energy are functions of velocity of the stream hence the

rate of discharge, Q as can be seen in there equations Fr and Specific E. And Q. Therefore,

increased velocities caused both the Froude number and the specific energy to increase. With

an increase in Froude number upstream, there was more energy dissipated as the hydraulic

jumps got more energetic, that is, an increase in specific energy upstream. From the graph this

is clearly illustrated. The graph also shows that the energy loss, E of the hydraulic jump is a

very low value for the first trial of the experiment with and approximate value of 0.001m. The

energy dissipation in percentage (%) is 0.373%. This small energy loss corresponds to an

upstream Froude number of approximately 4.7. The rate of flow for the first trial, that is, the

velocity of the stream was relatively low compared to the other trials. From this trend it can be

stated based on the graph that as the Froude number upstream falls below 4.7, the energy

dissipation tends to 0 (a negligible value). This is where the experimental results do not coincide

with the theoretical values. The classification of the hydraulic jump for this first run is a steady

jump. The other three jumps are classified as strong. For a steady hydraulic jump, the energy

dissipation theoretically supposed to range between 45-70%. The highest energy dissipation

that was computed was for the 4th trial with a value of only 14.9%.

The graph shows that the hydraulic jump is a very effective dissipater of energy as

the Froude number upstream is high. This can be a very effective means of reducing unwanted

energy in streams. If water from a steep spillway is fed into a channel, severe scouring of the

bed may occur if rapid flow is allowed to continue. Hence, an application of hydraulic jumps is to

dissipate much of the surplus energy and allow the stream to be safely discharge as tranquil

flow. Energy can be dissipated as sound or heat and therefore, after the hydraulic jump, the

water downstream may have a temperature higher than the one upstream.

The length of the hydraulic jump is the horizontal distance between the front of the

jump and the point just downstream of the last roller. The graph of Length of hydraulic jump vs

Upstream Froude number showed that there was a linear increase of the jump length as the

upstream Froude number increased. Theoretically the increased velocity would cause the

Froude number to increase making the flow more critical. This would affect the distance the

water would travel since velocity is a function of displacement. This can be observed from the

graph hence the experimental data supports the theory. The length of the hydraulic jump isusually in the order of 5 times its height. For this graph, the second, third point and fourth point

showed great deviation from the line of best fit than the first point. This can be considered

erroneous. This can be due to various sources of errors such as parallax error, poor human

averaging of the measurement of the last roller of a hydraulic jump or good sense of where the

jump actually begins in the channel for a specified flow rate needed for the determination of the

length of the hydraulic jump. There is also increased difficulty in measuring the start and end of

the hydraulic jump for the other three trials due to the addition of the problem of increased

turbulence and eddies. Human error can play a significant role in this case.

For this experiment, the following assumptions must be made in order to reduce

other potential errors and misconceptions:


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1) The bed of the stream is horizontal so that the component of weight in the direction of

flow may be neglected in calculations.

2) The rectangular cross section is uniform, that is, the width hydraulic jump is constant.

3) The velocities of each of the cross section (upstream, downstream of the hydraulic jump)

are uniform and are used without significant error.

4) The depth is uniform across the width.

There were problems in obtaining the hydraulic jump at the centre of the channel

since slight adjustments of the flow rate would cause the jump to move to the end of the channel

but careful alterations of the conditions created hydraulic jumps which was generally produced

in the middle of the channel. The position at which the hydraulic jump occurs is dependent on if

the momentum relation is satisfied. The value of the depth downstream is determined by the

conditions downstream of the jump and the rapid flow continues until the depth upstream has

reached the value which fits the equation 10.25. The turbulence in a jump may be sufficient to

induce large quantities of air into the liquid and as a result the depth immediately after the jump

may be greater than that predicted by equation 10.25. The delta E equation tells that a hydraulic

jump is possible only from rapid to tranquil flow and not vice versa. Factors that affect the

stability of the jumps are flow rate, friction at the boundaries of the channel and position of the

sluice gate.

Hydraulic jumps are applied to dissipate energy in water flowing over dams, weirs

and other hydraulic structures and prevent scouring downstream from the structure. To recover

and raise the water level on the downstream side of a measuring flume and maintain high water

level in the side of a measuring flume thus maintaining high water level in a channel for irrigation

and other water distribution methods. To increase discharge of a sluice gate by holding back

tailwater since the effective head will be reduced if the tailwater is allowed to drown the jump. To

indicate special flow conditions, such as the existence of supercritical flow or the presence of a

control section on that a gaging station may be located. To mix two chemicals together or to mix

chemicals for water purification. to aerate water for city supplies and to remove air pockets from

water that goes into supply lines thus preventing air locking.

Some other sources of errors include parallax error when reading flow gauge and vernier

scale, the flow may not have been fully stabilized when the reading were taken, inserting the

depth gauge into the channel may have affected the position of the hydraulic jump, reaction time

error when obtaining time for flow, it was assumed that the density of the water was 997kg/m^3

although the water wasnt pure since it was brown indicating that it contained other substances

which may cause errors in the experiment such as different values of momentum and energyreadings, additional energy losses due to friction.

Conclusion:

Within the limits of the experimental errors it was found that the experimental approach

to the h.j. phenomenon was not without errors and difficulties, inclusive of stabilizing the jump

ina fixed fume length, the method of obtaining the jump parameters and not being able to

account for the add. Energy losses, however was comparable to theoritical calcs. It was obs.

That the depth decrease upstream and the froude number increased and more energy was

dissipated.


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12/12

References:

1) Borthwick, M., Chadwich, A., Morfett, J. 2004. Hydraulics in Civil and Environmental Engineering.

Taylor & Francis.

2) Massey, Bernard. 2006. Mechanics of Fluids. Taylor & Francis.

3) Sholichin, Mohammad,and Shatirah Akib.2010.Development of drop number performance for

estimate hydraulic jump on vertical and sloped drop structure. International Journal of the

Physical Sciences Vol. 5(11), pp. 1678-1687. Accessed November 2,2012.

http://www.academicjournals.org/ijps/pdf/pdf2010/18%20Sept/Sholichin%20and%20Akib.pdf

4) Technological University Ministry of Science and Technology (MOST).(date unavailable).The

hydraulic pump. Nay Pyi Taw State: Myanmar, Technological University Ministry of Science and

Technology (MOST).

Accessed November 2,2012. http://www.most.gov.mm/techuni/media/CE_04016_chap8.pdf

Hydraulic Jump Data

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