8/17/2019 Mfh-04 Aliran Melalui Pelimpah
1/27
NOTCHES WEIRS
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
2/27
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.
2
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
3/27
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.
3
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
4/27
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
4
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
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
5
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
6/27
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.
6
Head above the crest, H
Height of the weir or notch, p
Nappe
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
7/27
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
7
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
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
8/27
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
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
9/27
H
0
H
0d
H
0
21
21
h32
g2Cdbdhhb.g2CdqQ 23
H.g2bC32
Q d
9
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)
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
10/27
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
10
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)
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
11/27
TRIANGULAR SHARP CRESTED WEIR
11
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
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
12/27
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)
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
13/27
13
When the velocity approache is considered, the the equationbecome:
2/522/52
d g2v
g2vHg2
2tg.C
158Q
TRIANGULAR SHARP CRESTED WEIR(continued)
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
14/27
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
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
15/27
BROAD CRESTED WEIR
15
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.
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
16/27
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:
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
17/27
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
BROAD CRESTED WEIR (continued)
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
18/27
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.
BROAD CRESTED WEIR (continued)
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
19/27
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
19
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
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
20/27
EXAMPLE
20
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
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
21/27
RECTANGULAR CRESTED WEIR
21
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
22/27
CIPOLETTI WEIR
22
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
23/27
V-NOTCH WEIR
23
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
24/27
TIPE AMBANG
24
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
25/27
SLUICE GATE
25
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
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
26/27
LABYRINTH WEIR
26
8/17/2019 Mfh-04 Aliran Melalui Pelimpah
27/27
SPILLWAY
27