Hydraulic Jump-jeremy

8/18/2019 Hydraulic Jump-jeremy

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INTRODUCTION

The hydraulic jump is a natural phenomenon that occurs in open

channels, which are either natural or manmade. A hydraulic jump is

formed when water at supercritical ow is discharged into a zone of

water with subcritical ow, creating a rather abrupt rise in the water

surface accompanied by violent turbulence, eddying and surface

undulations. It occurs in canals below a regulating sluice, at the toe of

a spillway or anywhere along the channel where the slope suddenly

changes from steep to at.

This occurrence of a hydraulic jump results in a signi cant loss of energy in the jump, so that the total energy and speci c energy after

the jump are less than before the jump. The hydraulic jump s ability to

dissipate energy is a characteristic that is particularly useful in

hydraulic engineering. This property of hydraulic jump it has been used

in many practical applications in hydraulic structures such as

dissipation of high energy of water near the toe of spillways to prevent

scouring of the channel bottom, mi!ing of chemicals in water supplysystems and where aeration of water is re"uired.

OBJECTIVES

To observe the relation between energy dissipation and the upstream

and downstream depths as well as #roude s number

Appreciating the inherent error in the comparison of the theoretical

and e!perimental values obtained.

$bserve and understand the changes in the position of the occurrence

of the hydraulic jump


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%nderstand the di&culty in stabilizing a hydraulic jump in a !ed umelength

THEORY

The hydraulic jump, is a rapid transition from supercritical ow tosubcritical ow. The transition is generally a turbulent process with a

signi cant energy loss. The loss of energy due to the hydraulic jump

means that energy conservation principles no longer apply.

'onse"uently, the speci c energy diagram cannot be referred to in the

solution of hydraulic jump problems. Instead, the principles of

conservation of momentum are applied.

The principle of the conservation of momentum, as applied to the jump, simply means that the momentum remains constant throughout

the jump, that is, momentum before the jump (momentum after the

jump. #or a rectangular channel, li)e that used in the e!periment, this

balance of momentum is given by the following e"uation, )nown as the

*omentum #unction+

F 1 + M 1 = F 2 + M 2 −−−−−−−−−−−−−−− equ (1 )

Where:

# ( #orce per unit width due to hydrostatic pressure ( ρg y2

2

* ( *omentum u! per unit width ( ρqv

Where: ρ ( density of the uid

" ( ow rate per unit width - b/

v ( ow velocity

y ( depth of ow

0"u 1 then becomes+


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H L= ∆ E = E1 − E2 =( y2 − y1 )3

4 y 2 y1

where,01 ( upstream energy, m/03( downstream energy, m/

90 ( energy loss, m/

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COLLECTED DATA Jum

pNo.

UpstreamDepth D u

!m"

Do#$streamDepth D %

!m"

Jump&e$'th

!m"Vo&ume

!m ( "T)me *or +

Re,o&ut)o$s t - t t a,'

1 =.=>?=3 =.11@ ? =.@>BB =.>@.@@

@.3C @.>B

3 =.=>?BC =.1D@?1 =.@33D =.>>B.D

C>B.D

> >B.D@

D =.= = =.1>BD3 =.B@3 =.>>D.B >D.@

C>D.B1

> =.= =3? =.1@B@> =.?@ 3 =.> >=.3 >=.? >=.D? Table 1 showing colected data for the hydraulic jump

DISCHAR/E AND CRITICAL DE0TH

JumpNo.

D)s1har'e 2

!m ( 3s"

Spe1)41D)s1har'e

5 !m 3s"

UpstreamDepth D u

!m"

Do#$stream

Depth D %!m"

Cr)t)1a&Depth D 1

!m"

1 =.==B=C =.=@B>@ =.=>?=3 =.11@ ? =.=BB>13 =.==C> =.=C=>> =.=>?BC =.1D@?1 =.=CB=D =.==?1 =.=CB1> =.= = =.1>BD3 =.=?1C3> =.==??= =.=?>D1 =.= =3? =.1@B@> =.=?@BC

Table 3 showing the various depths associated witht the hydraulic jump


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CROSS6SECTIONAL AREA AND VELOCITY

Jump

No.

Upstream

CrossSe1t)o$a&

AreaAu

!m "

Do#$stream Crossse1t)o$a&Area A%

!m "

D)s1har'e 2

!m(3s"

Upstream

Ve&o1)t7 Vu!m3s"

Do#$stream

Ve&o1)t7V% !m3s"

Cr)t)1a&

Ve&o1)t7 V1!m3s"

1 =.== 1 =.=133> =.==B=C 1.DB@1> =. BC@>=.CB1>

3 =.== 3D =.=1>DC =.==C> 1.@1 BD =. CB >=.?3>=

C

D =.== D1 =.=1 >B =.==?1 1.B3>=@ =. ?1 D

=.?>?=

C

> =.== 3C =.=1B@= =.==??= 1.CB 1? =. @3 @=.?B>>

= Table D showing crossEsectional area and velocity data for the hydraulic jump

S0ECI8IC ENER/Y AND 8ROUDE NU9BERS Jum

pNo. Spe1)41 E$er'7 !J"

E$er'7Loss E3

J 8rou%e Num;er

Upstream Esu

Cr)t)1a&

Depth Es1

Do#$stream Es%

Upstream 8ru

Do#$stream 8r%

Cr)t)1a&

Depth 8r1

1 =.1> >=.11@1

3 =.1DD@ =.=1D>? 1.?C>>1 =. >1=@ 1

3 =.1C3C>=.1D=

B =.1 > = =.=3>3@ 3.D13=1 =. =@?C 1

D =.3=3=>=.1DBB

D =.1@ 1 =.=D=>D 3.>>CD@ =.>?3= 1

> =.33? 1=.1> 1

C =.1CDBB =.=>B?3 3.@@?@? =.>DC@B 1 Table > showing 8peci c 0nergy and #roude numbers data for the hydraulic jump


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D 3.>>C> =.=D=>D =.3=3=> 1 .=@$scillating

3.@@?B =.=>B?3 =.33? 1 3=.CC$scillating


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E$er'7 Loss ,s. Upstream 8rou%e No.

Fraph D showing 0nergy ;oss vs. %pstream #roude 5umber

Le$'th o* Jump ,s. Upstream 8rou%e No.

Fraph > showing ;ength of


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The hydraulic jump is the transitioning between two types of

ow, supercritical ow to subcritical ow. These ows of supercritical

and subcritical are governed by the #roude numbers. $bserving graphof energy 4issipation, ∆ 0 Hs. upstream #roude 5o., #r it shows that

the relations between the two variables are illustrated by a linear line.

It can be stated that this indicates that as the upstream #roude number

increases or decreases, the energy loss in the jump also does the same. It

can also be stated that both the #roude s number and the dissipation of

energy are inversely related to the upstream depth. Therefore, since the

depth is a factor in both #roude s number and the dissipation of energy, we

can state that as the upstream depth decreases or increases, the %pstream

#roude s number inversely increases or decreases and so does the energy

loss. The graph obtained in the e!periment is thus validated. In the graph,

the four points either lie on the line of best t or they are closely distributed

evenly on either side of the line, therefore, it can be said that there are no

clearly erroneous values.

8ince the amount of energy dissipated is governed by the

velocity in the channel, it also a ects the length of the hydraulic jump.

These theoretical behaviors can be observed from the graph length of

hydraulic jump Hs. #roude s number which illustrates the relationship

between upstream #roude numbers as a function of the amount of

energy dissipation. As can be seen there e!ists a linear relationship

between the two variables. which indicates that as the upstream #roude

number increases or decrease, the length of the jump does the same.

Theoretically, the length of the jump is e!pected to be linearly related to the

#roude number since the #roude number is dependent on the ow velocity

and velocity is a measure of distance over time. Therefore, if the length of the

jump increases, the velocity is larger and therefore the #roude number

increases. Thus, the e!perimental results are validated by the theory.


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It is observed for graph of, length of hydraulic jump Hs. #roude s

number the D rd point seemed to be slightly erroneous. This error may be due

rstly, to human errors in measurement. Additionally, the length of a

hydraulic jump is often di&cult to measure both in the eld and laboratory

e!periments due to the sudden changes in turbulence along the surface, the

formation of eddies and rollers and the fact that it is hard to distinguish the

end of the jump as the water surface is rather leveled at this point.

A wea) jump is characterized by the formation of eddies and rollers on

the surface of the uid, and a small loss of energy. $scillating jumps are

considered destructive and are characterized by waves generated on the

surface that continue beyond the end of the jump. According to theory, an

upstream #roude s number ranging from >. to ? characterizes a steady orstable jump and a strong jump is greater than ?. In the e!periment, there was

di&culty in establishing a stable jump midway through the ume. the

hydraulic jump for this e!periment was generated by use of a sluice gate.

Therefore, factors that could have a ected the stability of a jump included

the height of the sluice gate as well as the ow rate. These two factors a ect

the velocity of ow, which directly a ects the #roude number, which is an

indicator of stability. The hydraulic jumps in this e!periment were classi ed as

wea) and oscillating jumps, ranging for ?.3BJ to 3=.CCJ energy dissipation.

The forces which are acting on a hydraulic jump are the

hydrostatic forces upstream and downstream and the momentum

which occurs before and after the jump. #or a stable hydraulic jump to

occur the upstream depth 4 1 / must be e"ual to the se"uent depth 4 /

and the force plus momentum upstream must be e"ual to the force

plus momentum downstream. If 4 7 4 then the downstream force and

moment will be greater than the upstream force and momentum andthe jump will move upstream. 8imilarly if 464 the reverse is true and

the jump will move downstream. This relationship can be seen on the

#G* graph


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A hydraulic jump can is applicable to this purpose because it is capable of

rapidly increasing the turbulence of ow in a channel which enables the

proper mi!ing of di erent chemical components. An industry that implements

such a use of the hydraulic jump is the wastewater industry such as in the

coagulation

:ydraulic jump in coagulation chamber

:igh velocity ow in stream beds often causes erosion which in turn leads tothe transport of sediment. A hydraulic jump in the stream can help reducethe velocity of the ow and thus reduce the process of erosion. In such cases,

the jump is created by placing structures such as a weir or sluice gate at thepoint where the turbulent ow enters the channel. An e!ample of such astructure is the weir located in Tama River, Tokyo, Japan .

an e!ample of E$er'7 %)ss)pat)o$ through the use of a hydraulic jump to is

a hydraulic jump stilling basin such as the Burrendong Dam spillway WellingtonNSW Australia . In such basins, horizontal and sloping aprons, which are


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structures that prevent erosion, are used to dissipate the energy of theincoming ow. The e ectiveness of the devices used in the spillway todissipate energy is dependent on the #roude number of the upstream ow.

Kurrendong 4am spillway 2ellington 582 Australia#igure > E2eir in Liverfront Mar), 2ashington

as a lot of the "uantities that had to be measured depended on the "uic) judgment of the observer and were therefor subjective which decreasesaccuracy


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#ig 1+ :ydraulic

Hydraulic Jump-jeremy

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