Mfh-04 Aliran Melalui Pelimpah

8/17/2019 Mfh-04 Aliran Melalui Pelimpah

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NOTCHES WEIRS


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DEFINITIONSA notch may defined as an opening provided in the side of atank (or vessel) such that the liquid surface in the tank isbelow the top edge of the opening. Notches made of metallicplates, and are provided in narrow channels (laboratory) tomeasure the rate of flow.

A weir is the name given to a concrete or massonry structurebuilt across a river or stream in order to raise the level of thewater on the upstream side and to allow the excess water toflow over its entire length to the downstream side. Weirs mayalso be used for measuring the rate of flow water in rivers or

streams.

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CLASSIFICATION OF NOTCHES

Based on the shape of the opening:Rectangular notchTriangular (V-notch)Trapezoidal notch

Parabolic notch, andStepped notch.

According to the effect of the sides onthe nappe emerging from notch:

Notch with and contractionNotch without end contraction or suppressednotch.

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CLASSIFICATION OF WEIRS (1/2)

Based on the shape of the opening of:Rectangular notch,Triangular notch, andTrapezoidal notch

Based on the shape of the crest:Sharp crested weirs,Narrow crested weirs,

Broad crested weirs, andOgee shaped weirs

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5/27

CLASSIFICATION OF WEIRS (2/2)

According to the effect of the sides on thenappe emerging from notch:

Notch with and contraction

Notch without end contraction or suppressednotch.

According to the discharge conditions:Freely discharging weirs, andSubmerged (or downed) weirs

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FLOW OVER A RECTANGULAR SHARP CRESTEDWEIR OR NOTCH

Consider a rectangular sharp crested weir asshown below: L crest length, and H is the heightof the water surface above the crest.

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Head above the crest, H

Height of the weir or notch, p

Nappe


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CLASSIFICATION OF THE SHARP CRESTEDWEIR

Sharp crested weir can be classified as follows:1. Based on the shape of the weir

1) Rectangular 2) Triangular 3) Trapezoidal

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rectangular triangular trapezoidal

2. Based on the elevation of tail water (down stream water):

1) Free flow weir, when the downstream water surface is below the crest of the weir.

2) Submerged weir, when the downstream water surface is above the crestof the weir.

Free flow weir submerged weir


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RECTANGULAR SHARP CRESTED WEIR

Rectangular sharp crested weir: crest width b, overflow hight H,discharge coefficient Cd, and velocity approach can be neglected.

g2V

0z00z22

21

gh2)zz(g2V 212

8

Consider to water segment of dh at the depth h from water surface .Bernoulli equation between point 1 and 2 is,

g2

V

g

pz

g2

V

g

pz

222

2

211

1 hdh

b

V1

1

H 2 v2

As V 1 ≈ 0, and both points are at atmospheric pressure, then the equationbecome:

or


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H

0

H

0d

H

0

21

21

h32

g2Cdbdhhb.g2CdqQ 23

H.g2bC32

Q d

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Segment area : dA = b.dh

The discharge through the segment is : dAVdq 2

dh.b.gh2dA.Vdq 2

By considering the discharge coefficient Cd, then the discharge is :

dh.b.h.g2Cdq 21

d

Integration of the equation produces:

RECTANGULAR SHARP CRESTED WEIR(continued)


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dAVdq 2 )g2

vh(g2dh.b.Cdq

2a

d

H

ad

H

dhg

vhbgC dqQ

0

2

0

21

)2

(.2

2

32a

2

32a

d g2

v

g2

vh.g2b.C

3

2Q

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When the velocity approache is considered , V a , the energy headat the upstream of the weir is:

g2v

h2a

Velocity through the segment of dh is then :

)g2

vh(g2V

2a

2 The discharge through the segment is :

Intergration of the equation produces :

RECTANGULAR SHARP CRESTED WEIR(continued)


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TRIANGULAR SHARP CRESTED WEIR

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Discharge through the triangular sharp crested weir: water depth abovecrest H, discharge coefficient C d, and overflow angle α.

dh2

tg)hH(2dh.bda

gh2v

Consider to segment dh at the water depth h from the water surface. Segmentarea is

Velocity through the segment is

The discharge through the segment is :

gh2.dh2

tg)hH(2Cgh2daCdq dd

Bb

αhdh

V1

1

H 2

v2

V2 /2g


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12

Integration the equation produces the discharge through thewhole weir:

H

0d

H

0

dhh)hH(g22

tgC2dqQ 21

H

0d dh)hHh(g22tgC2Q

23

21

H05232d32 2523 hHhg22tg.CQ )HH(g2

2tg.CQ 2

525

52

32

d32

25

Hg22

tg.C158Q d

TRIANGULAR SHARP CRESTED WEIR(continued)


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13

When the velocity approache is considered, the the equationbecome:

2/522/52

d g2v

g2vHg2

2tg.C

158Q

TRIANGULAR SHARP CRESTED WEIR(continued)


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TRAPEZOIDAL SHARP CRESTED WEIR

14

25

23

Hg22

tg.C158

Hg2bC32

Q 2d1d

where: C d1 = discharge coefficient of rectangular weir C d2 = discharge coefficient of triangular weir

As the trapezoidal is the combination of rectangular and triangular, sothe discharge through the trapezoidal weir is the summation of discharge through the rectangular weir and triangular weir.

b

hdh

V1

1

H 2

v2

V2 /2g


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BROAD CRESTED WEIR

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Weir is called wide crested weir when the crest width iswider than 0.66 of the overflow depth ( t > 0,66H) , and thepresent of the straight flow-lines (horizontal) on the top of the crest.

The pressure on the overflow above the wide crest ishydrostatic pressure. Application of Bernoulli equation on thepoints before and on the top of the weir crest can be used tofind out the flow velocity above the crest.

By measuring the water depth at the upstream, H, thedischarge over the weir can be determined.

When the water level at the downstream of the weir is abovethe crest, the weir is called imperfect weir or submergedweir.


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g2V

gp

zg2

Vg

pz

222

2

211

1

g2

Vh00H0

22

g2

V

hH

22

)hH(g2v

16

Aplication of Bernoulli equation on wide crested weir results:

hH

21

BROAD CRESTED WEIR (continued)

V. A.CQ d

21

)hHh(g2bC)hH(g2h.bCQ 32dd

or

Discharge of the weir is then:


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Maximum discharge is occurred when (Hh 2-h 3) is maxsimum. The value of (Hh 2-h 3) is maximum when the value of dQ/dh = 0

2132

2 )hHh(gbCdhd

dhdQ

d

17

02 2132 )hHh(

dhd

gbCdhdQ

d

0

2

3221

32

2

)hHh(

hHh

2 Hh – 3h 2 = 0 atau Hh 32



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Substitute the value of h into the equation of Q, produces :

18

213322322 )H()H(HgbCQ d

32743

2783

94 22 HgbCHHgbCQ dd

2

3

233

2 HgbCQ d

The discharge over the weir can be calculated by measuring the water lever at the upstream of the weir, H.



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EXAMPLE1. Air mengalir melalui ambang lebar dengan bentang 20 m. Perbedaan

tinggi air akibat ambang adalah 0,4 m. Hitung besarnya aliran maksimummelalui ambang dengan koefisien debit 0,8

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Perbedaan tinggi muka air, H - h = 0,4 m

Jadi, h = H – 0,4m

Aliran maksimum bila Hh 32

Maka, 4,0HH32 3H - 1,2 = 2H

H = 1,2 mDebit maksimum melalui pelimpah,

23

23

23840233 2 HgbC.HgbCQ dd

Untuk percepatan gravitasi g=9,81 m/det


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EXAMPLE

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2. Hitung besarnya debit melalui peluap terendam dengan panjang ambang, b

dan koefisien debit Cd23

bHC71,1Q d

det/m95,352,1.20.8,0.71,1Q 323

H1 H2

Debit aliran melalui peluap terendam adalah jumlah aliran setinggi luapanH1-H2 dengan aliran terendam setinggi H2

Q = Q1 + Q2

)HH(g2bHC)HH(g2bCQ 212d21d32 23


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RECTANGULAR CRESTED WEIR

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CIPOLETTI WEIR

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V-NOTCH WEIR

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TIPE AMBANG

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SLUICE GATE

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Figure 9. Free outflow followedby a shooting tailwater flow

Figure 10. Free outflow followed by anundulating hydraulic jump in thetailwater

figure 11. free outflow followed by aperfect hydraulic jump with surfaceroller in the tailwater


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LABYRINTH WEIR

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SPILLWAY

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Mfh-04 Aliran Melalui Pelimpah