THE UNIVERSITY OF THE WEST INDIES,ST. AUGUSTINE.DEPARTMENT OF CIVIL & ENVIRONMENTAL ENGINEERING

Kirk Woo Chong809003758Group: J

Table of Contents

OBJECTIVES...................................................................................................................3

INTRODUCTION..............................................................................................................3

PROCEDURE..................................................................................................................3

Equipment....................................................................................................................3

Method..........................................................................................................................4

THEORY..........................................................................................................................4

RESULTS.........................................................................................................................5

SAMPLE CALCULATIONS..............................................................................................9

DISCUSSION AND ANALYSIS OF RESULTS..............................................................11

GRAPH 1 - ΔE vs Upstream Froude Number Analysis..............................................11

GRAPH 2 - Jump Length vs Upstream Froude Number Analysis..............................11

Hydraulic Jump Classification and Stability................................................................11

Practical Applications of Hydraulic Jumps..................................................................12

Errors & Precautions..................................................................................................13

CONCLUSION...............................................................................................................13

REFERENCES...............................................................................................................13

OBJECTIVES

I. Experience taking experimental measurements and appreciate the inherent error

in comparison to theoretical calculations.

II. Observe that energy dissipation is a function of the upstream and downstream

depths and hence Froude numbers.

III. Demonstrate that hydraulic jumps are difficult to stabilize in a fixed flume length.

IV. Qualitatively understand and observe translations in the location of a hydraulic

jump.

INTRODUCTION

For a positive wave travelling upstream in a horizontal channel the wave may be

stationary relative to the bed of the channel, in which case the wave velocity, c may be

zero. This stationary surge wave, through which the depth of flow increases, is known

as a hydraulic jump (Massey, 2006).

Essentially, the experiment involves simulating a hydraulic jump in a hydraulic

channel by adjusting the flow rate, a sluice gate and a weir so that a shallow and rapid

supercritical flow develops upstream as well as subcritical flow due to the back up of

flow. A hydraulic jump would then form at the transition where measurements can thus

be taken.

PROCEDURE

Equipment

o Hydraulic Channel

o Depth Gauge

o Flowmeter

o Stopwatch

Method

1. The flow rate and tailgate elevation was set so that a stable hydraulic jump

occurred about midway through the channel.

2. The time taken for two revolutions on the flowmeter was noted, and an average

of two readings was taken.

3. The depth of flow in front of and behind the hydraulic jump as well as the

corresponding length of the jump was measured.

4. All relevant dimensions of the flume equipment were measured.

5. Steps 1 to 4 were then repeated for three other discharge values.

THEORY

The hydraulic jump itself is caused by a sudden dissipation of energy as a result of a

change from supercritical to subcritical or from very fast to slow flow. Hence for the

upstream flow the Froude number is greater than 1 and for the downstream flow the

Froude number is less than 1. This would occur when the depth of the liquid is less

than the critical depth before the jump and greater than critical depth after it. This

phenomenon may be observed when the liquid passes through a flood gate or entering

a channel through a spillway.

As a result of the jump, there is significant turbulence and eddy formation

causing the mechanical energy in the system to be reduced. Hence, there is a

decrease in both the specific energy and total energy after the jump. Because of this,

hydraulic jumps are used in the reduction of unwanted energy to reduce scour of

channels.

FIGURE 1

RESULTS

Jump Number

Upstream Depth, Du / m

Downstream Depth, Dd / m

Jump Length / m

Volume, V / m3

Time for 2

Revolutions, t / s

1 0.0492 0.1726 0.508 0.2 19.67

2 0.0514 0.1607 0.406 0.2 20.67

3 0.0492 0.1401 0.330 0.2 23.08

4 0.0504 0.1111 0.178 0.2 29.38

TABLE 1 showing the data obtained from the experiment

Jump NumberDischarge, Q /

m3s-1

Specific Discharge, q / m2s-1 Critical Depth, Dc / m

1 0.0102 0.1004 0.1009

2 0.0097 0.0955 0.0976

3 0.0087 0.0856 0.0907

4 0.0068 0.0669 0.0770

TABLE 2 showing calculated values for depth and discharges

Jump No.

Upstream Cross

Sectional Area / m2

Downstream Cross

Sectional Area / m2

Upstream Velocity,

vu /

ms-1

Downstream Velocity, vd /

ms-1

Critical Velocity, vc / ms-1

Upstream Kinetic

Energy / J

Downstream Kinetic

Energy / J

1 0.0050 0.0175 2.040 0.5829 0.9950 0.2121 0.0173

2 0.0052 0.0163 1.865 0.5951 0.9782 0.1773 0.0181

3 0.0050 0.0142 1.740 0.6127 0.9441 0.1543 0.0191

4 0.0051 0.0113 1.333 0.6018 0.8692 0.0906 0.0185

TABLE 3 showing velocity and energy data

Jump Number

Specific Energy

Upstream, Esu / J

Specific Energy

Downstream, Esd / J

Critical Specific Energy,

Ec / J

Energy Loss, ΔE / J

Froude Number

Upstream

Froude Number

Downstream

1 0.2613 0.1899 0.1514 0.0553 2.936 0.4480

2 0.2287 0.1780 0.1464 0.0395 2.626 0.4740

3 0.2035 0.1592 0.1395 0.0272 2.505 0.5226

4 0.1410 0.1296 0.1155 0.0100 1.896 0.5764

TABLE 4 showing energy and energy loss as well as the Froude numbers

Jump

Force Upstream, Fu / kgms-2

Force Downstream,

Fd / kgms-2

Critical Force,

Fc / kgms-2

Upstream Momentum, Mu / kgms-2

Downstream Momentum, Md / kgms-2

Critical Momentum, Mc / kgms-2

Fu + Mu /

kgms-

2

Fd + Md /

kgms-

2

Fc + Mc /

kgms-

2

1 1.207 14.82 5.074 20.81 5.946 10.05 22.02 20.77 15.12

2 1.311 12.85 4.747 18.09 5.772 9.489 19.40 18.62 14.24

3 1.207 9.827 4.100 15.14 5.330 8.214 16.35 15.16 12.31

4 1.261 6.158 2.955 9.064 4.092 5.911 10.33 10.25 8.866

TABLE 5 showing the forces and momentum

Jump Number

Upstream Froude Number

Energy Loss, ΔE /

JSpecific Energy

Upstream, Esu / J

Energy Dissipation /

% Classification

1 2.936 0.0553 0.2613 21.16

Oscillating Jump

2 2.626 0.0395 0.2287 17.27

Oscillating Jump

3 2.505 0.0272 0.2035 13.37 Weak Jump

4 1.896 0.0100 0.1410 7.09 Weak Jump

TABLE 6 showing the Hydraulic Jump Classification

1 1.5 2 2.5 3 3.5 40

0.01

0.02

0.03

0.04

0.05

0.06

ΔE vs Upstream Froude Number

Upstream Froude Number

ΔE /

J

GRAPH 1

0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.280

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

(E-y) Depth of flow vs Energy

Jump 1

Jump 2

Jump 3

Jump 4

Energy, E / J

Dept

h, D

/ ,

1.2 1.6 2 2.4 2.8 3.20

0.1

0.2

0.3

0.4

0.5

0.6

Jump Length vs Upstream Froude Number

Upstream Froude Number

Jum

p le

ngth

, x /

m

GRAPH 2

SAMPLE CALCULATIONS

All values obtained were in inches, therefore they were multiplied by 0.0254 to convert it

to meters.

Depth of water = measured height of water – measured height of channel

for eg. Jump 1 = 0.212 m – 0.1670 m = 0.0492 m

Volume, V = 100 L per revolution; 2 revolutions would be equal to 200 L

= 0.2 m3

Discharge, Q = Vt

= 0.2 / 19.67 = 0.0102 m3s-1

8 10 12 14 16 18 20 22 240

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

((F + M)-y) Depth of flow vs (F + M)

Jump 1

Jump 2

Jump 3

Jump 4

(F + M) / kgms-2

Dept

h, D

/ m

GRAPH 4

Specific discharge, q = Qb

= 0.0102 / 0.1016 = 0.1004 m2s-1

Critical depth, Dc = 3√ q2g = 3√ 0.100429.81 = 0.1009 m

Cross sectional area, A = width of channel x depth of flow

= 0.1016 x 0.0492 = 0.005 m2

Velocity, v = QA

= 0.0102 / 0.005 = 2.04 ms-1

Critical velocity, vc = Q

b xDc =

0.01020.1016 x0.1009

= 0.9950 ms-1

Kinetic energy, ke = v2

2g =

2.042x 9.81

= 0.2121 J

Specific Energy, E = D + V2

2g = 0.0492 +

4.16219.62

= 0.2613 J

Energy Loss, Δ E = ¿¿¿¿ = (0.1726 – 0.0492)3 / (4 x 0.0492 x 0.1726) = 0.0553 J

Froude Number = v

√gD = 2.04 / √(9.81 x 0.0492) = 2.936

Force, F = ρgbD2 / 2 = 1000 x 9.81 x 0.1016 x 0.10092 / 2 = 5.074 N

Momentum, M = ρQv = 1000 x 0.0102 x 2.04 = 20.81 kgms-2

Measured height of channel = 0.1670 m

Measured width of channel = 0.1016 m

DISCUSSION AND ANALYSIS OF RESULTS

GRAPH 1 - Δ E vs Upstream Froude Number Analysis

The graph plotted from the experimental data showed that as the upstream

Froude number increased, so did the energy loss associated with the system. Theory

suggests that both the Froude number and specific energy are a function of the velocity

in the system as seen in the equations Fr = v

√gh and E = h+ v2

2g. Increased velocities

caused both the Froude number and specific energy to increase. Also, since the Froude

number increased, there was more energy dissipated as the jumps got more energetic

(both total and specific energy). Hence the experimental data held true to the theory.

GRAPH 2 - Jump Length vs Upstream Froude Number Analysis

This graph 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 influence the

distance the liquid would travel since velocity is also a function of the displacement.

Again, the theory and experimental data is supportive of each other.

For both graphs, the second point showed a greater deviation to the line of best

fit than the others, and thus may be considered erroneous since it does not fit the

recognized trend of the results. This may have been due to the method of

measurement for the experiment which relies greatly on human averaging and good

sense, leaving a greater allowance for human error.

Hydraulic Jump Classification and Stability

Name F1 Energy Dissipitation

Undular jump 1.0 – 1.7 < 5%

Weak jump 1.7 – 2.5 5 – 15%

Oscillating jump 2.5 – 4.5 15 – 45%

Steady jump 4.5 – 9.0 45 – 70%

Strong jump > 9.0 70 – 85%

TABLE 6 showing the characteristics of hydraulic jump (USBR 1995) [1]

Table 6 shows the criteria to which the results of the hydraulic jump were

classified. Jumps 1 and 2 clearly fitted the characteristics of an oscillating jump in both

upstream Froude number and energy dissipation. Jump 4 was easily classified as a

weak jump however jump 3 there was some debate since the upstream Froude number

was 2.505 (oscillating jump) but the energy dissipation 13.37% fitted a weak jump.

Since the upstream Froude number was marginally close to a weak jump and the

energy dissipation was well within weak jump criteria, it was classified as a weak jump.

There were difficulties in obtaining a stable hydraulic jump in the centre of the

channel since slight variations in the flow rate would have a delayed effect on the

position of the jump and obtaining the right conditions for the jump were tricky. Factors

affecting the stability of the jump included the flow rate, position of the sluice gate as

well as the friction due to the hydraulic channel.

Practical Applications of Hydraulic Jumps

As a measure to reduce scour downstream of weirs, dams and other hydraulic

structures by dissipating the energy.

To mix chemicals used for water purification.

To aerate water for city water supplies.

To remove air pockets from water supply lines.

To maintain high water levels in channels for irrigation purposes.

FIGURE 2

One such example is at St. Anthony Falls on the Mississippi River where the hydraulic

jump is used to prevent scour on the channel bed.

Errors & Precautions

In determining the actual positions of the beginning and end of the jump as well

as the length of the jump there was no specific methodology used except “good

judgement”. This may have contributed to human errors.

Error due to parallax in reading the vernier scale and flow guage.

The flow may not have been fully stabilized when the readings were taken.

Inserting of the depth gauge into the flow may have caused the jump to shift

along the channel.

Reaction time error in obtaining the time for flow rate.

It was assumed that the density was for pure water however it should be noted

the water in the experiment was brown indicating it may have contained other

substances and impurities which may have caused erroneous momentum and

energy values.

There were addition energy losses (however minor) due to friction.

CONCLUSION

Within the limits of experimental error, it was found that the experimental

approach to the hydraulic jump phenomenon was not without errors and difficulties,

inclusive of stabilizing the jump in a fixed flume length, the method of obtaining the jump

parameters and not being able to account for additional energy losses, however was

comparable to theoretical calculations. It was also observed that as the depth

decreased upstream, the Froude number increased and more energy was dissipated.

REFERENCES

Borthwick, M., Chadwick, A., Morfett, J. 2004. Hydraulics in Civil and

Environmental Engineering. Taylor & Francis.

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