BAB V ANALISIS DAN PERHITUNGAN A.
1.
Debit Banjir Rencana (Design Flood)
Huja ujan Ka Kawas wasan (D (DAS)
Pada Pada penentu penentuan an hujan hujan kawasa kawasan n diambi diambill data dari 2 stasiun stasiun pencata pencatatt hujan hujan terdekat lokasi yaitu, stasiun pencatat hujan pamarayan dan ciujung. Untuk mencari hujan kawasan digunakan metode Aljabar atau Aritmatika Aritmatika,, karena menggunakan 2 stasiun pencatat hujan.
Tabel 5.1 Perhitungan Hujan DAS Metode Aljabar
No.
Tahun
1 2 3 4 5 6 7 8 9 10 11 ∑
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
2.
Cadasari (mm) 0 60 42 60 80 52 20 0 30 41 21
Pamarayan (mm) 107 124 100 77 84 86 148 163 103 75 0
Hujan DAS (mm) 53.5 92 71 68.5 82 69 84 81.5 66.5 58 10.5 736.5
Anali nalisa sa Frek Freku uensi ensi
Analisis frekuensi dilakukan secara bertahap dan sesuai dengan urutan kerja yang telah ada karena hasil dari masing-masing perhitungan tergantung dan saling mempengaruh mempengaruhii terhadap hasil perhitungan perhitungan sebelumnya. Berikut adalah langkahlangkah analisis frekuensi setelah persiapan data dilakukan.
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29
Tabel 5.2 Perhitungan Analisa Frekuensi
No.
Tahu ahun
1 2 3 4 5 6 7 8 9 10 11 ∑
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
X X-Xbar (mm) 53.5 -13.45 92 25.045 71 4.0455 68.5 1.5455 82 15.045 69 2.0455 84 17.045 81.5 14.545 66.5 -0.455 58 -8.955 10.5 -56.45 736.5 0
(X-Xbar)
2
181.025 627.275 16.366 2.388 226.366 4.184 290.548 211.570 0.207 80.184 3187.116 4827.227
(X-Xbar)
3
-2435.606 15710.382 66.207 3.691 3405.775 8.558 4952.515 3077.385 -0.094 -718.010 -179927.168 -155856.366
(X-Xbar)
32769.976 393473.666 267.836 5.705 51241.431 17.505 84417.862 44761.970 0.043 6429.455 10157706.501 10771091.950
Rata-rata hitung ( Mean) Mean) : 66. 66. 955 955 Menghitung standart deviasi(simpangan baku) : Berdasarkan persamaan (6) maka besar s s :
21.971 a.
Menghitung Koefisien Variasi (C (C V ) : V): Berdasarkan Persamaan (7) maka besar C besar C v :
C v = 0.381
b.
4
Menghitung Koefisien Asimetri/Skewnes Asimetri/ Skewnes/kemencengan /kemencengan (C (C )) :
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30
= C s = - 1.7961 c.
Menghitung Koefisien Koefisien Kurtosisis Kurtosisis (C k k ) : Berdasarkan Persamaan (10) maka besar C besar C k k :
C k k = 7.76814 Tabel 5.3 Perhitungan Analisa Frekuensi Log Normal Normal No. 1 2 3 4 5 6 7 8 9 10 11 ∑
X y = logX y - ybar (mm (mm) (mm (mm) 53.5 1.728 -0.051 92 1.964 0. 0.184 71 1.851 0. 0.072 68.5 1.836 0.056 82 1.914 0. 0.134 69 1.839 0. 0.059 84 1.924 0. 0.145 81.5 1.911 0.132 66.5 1.823 0.043 58 1.763 -0.016 10.5 1.021 -0.758 736.5 19.575 0
(y-ybar)
2
0.003 0.034 0.005 0.003 0.018 0.004 0.021 0.017 0.002 0.000 0.575 0.682
Rata-rata hitung ( Mean) Mean) : 1.7795 Menghitung standart deviasi(simpangan baku) : Berdasarkan persamaan (6) maka besar S :
(y-ybar)
3
- 0.00013 0.006 0.00037 0.00018 0.002 0.00021 0.003 0.002 0.00008 -0.000004 -0.436 -0.421
(y-ybar)
4
0.000007 0.001 0.000026 0.000010 0.00033 0.000012 0.00044 0.000300 0.000004 0.0000001 0.331 0.333
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31
Berdasarkan Persamaan (7) maka besar C besar C v : =0.1467 b.
Menghitung Koefisien Skewnes/ kemencengan kemencengan (C (C S S ) : Berdasarkan persamaan (9) maka besar C besar C s :
C s= -2.8922 c.
Menghitung Koefisien Koefisien Kurtosisis Kurtosisis (C k k ) : Berdasarkan Persamaan (10) maka besar C besar C k k :
C k k = 12.0355
Tabel 5.4 Pemilihan Jenis Distribusi
No 1
Jenisdistribus Jenisdistribusii
Syarat
HasilPerhitung HasilPerhitungan an
Keputusan Keputusan
Cs = 0
-1.7961
Tidak
Ck= 3
7.7681 -2.8922
Tidak Tidak
12.034
Mendekati
-1.7961
Tidak
7.7681
Tidak
Normal Cs (lnx) = 1,33
2
Log Normal Ck (lnx) = 11,73 Cs = 1,14
3
Gumbel Ck = 5,4
4
Log person III
Selain dari nilai diatas
Sumber : Hidrologi Terapan,Bambang Triatmodjo (1998)
Dari Dari tabel tabel di atas terlihat bahwa perbed perbedaan aan antara antara parame parameter ter statist statistik ik hasil hasil
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32
meyakinkan dilakukan penggambaran pada kertas Probabilitas dan di uji dengan Metode Chi-Kuadrat dan Smirnov-Kolmogorov
3.
Penentuan Jenis Distribusi
Penent Penentuan uan jenis jenis distrib distribusi usi ini dilaku dilakukan kan dengan dengan cara pengu pengujian jian distrib distribusi usi probabilitas probabilitas yang dimana maksudnya maksudnya adalah untuk mengetahui apakah persamaan persamaan distribusi probabilitas yang dipilih dapat mewakili distribusi statistik sampel yang dianali dianalisis. sis. Penguj Pengujian ian distrib distribusi usi probab probabilita ilitass ini ada 2 Metode Metode penguj pengujian, ian, yaitu yaitu pengujian pengujian dengan cara Metode Metode Chi-Kuadarat Chi-Kuadarat dan pengujian Smirnov-Kolm Smirnov-Kolmogoro ogorov. v. (I Made Kamiana. 2011) a. Uji Chi-Ku Chi-Kuadr adrat at
Uji Chi-Ku Chi-Kuadra adratt mengg menggunak unakan an nilai nilai X2 yang dapat dapat dihitu dihitung ng denga dengan n persamaan persamaan berikut berikut : X n2
Dengan : X2 = Nilai Chi-Kuadrat terhitung Ef = Frekuensi yang diharapkan sesuai pembagian kelasnya. Of = Frekuensi yang terbaca pada kelas yang sama Nilai x2 yang yang dipe diperol roleh eh haru haruss lebih lebih kecil kecil dari dari nilai nilai x2cr (Chi-kuadrat (Chi-kuadrat kritik). Derajat kebebasan dapat dihitung dengan persamaan : DK = K - (α+1) K
= 1 + 3,3 log n
Dengan : Dk = Derajat kebebasan K = Bany Banyak akny nyaa kelas kelas α
= banyaknya banyaknya keterikatan, keterikatan, untuk uji Chi-Kuadrat Chi-Kuadrat adalah 2
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n = Ban Banya yakn knya ya data data Syarat dalam pengujian Chi-Kuadrat adalah distribusi probabilatas yang mempunyai nilai simpangan maksimum terkecil dan lebih kecil dari simpangan kritis, atau dirumuskan sebagai berikut : X 2
= parameter Chi-Kuadrat kritis(lihat tabel lampiran 3.7)
Prosed Prosedur ur perhitu perhitunga ngan n denga dengan n Metode Metode uji chi-Ku chi-Kuadra adratt adalah adalah sebaga sebagaii berikut (I (I Made Kamiana. Kamiana. 2011): 2011): 1) Urutkan data dari besar ke kecil atau sebaliknya.
2) Mengh Menghitun itung g jumlah jumlah Kelas 3) Menghitung derajat kebebasan (DK) dan X dan X 2cr
4) Menghitung Menghitung kelas distribusi distribusi 5) Menghitung Menghitung Interval Interval kelas. kelas. 6) Perhitungan nilai X nilai X 2. 7) Bandingkan nilai X nilai X 2 terhadap X terhadap X 2cr.
Tabel 5.5 Pengurutan Data Hujan Dari Besar ke Kecil
No
xi (mm)
Xi (urutandarib (urutandaribesarkek esarkekecil) ecil)
1
53.5
92
2
92
84
3
71
82
4
68.5
81.5
5
82
71
6
69
69
7
84
68.5
8
81.5
66.5
9
66.5
58
10
58
53.5
11
10.5
10.5
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34
Dk = 5- (2+1) DK = 2 Jadi nilai X2cr dengan dengan jumlah data data n=11, α=5% dan DK DK = 2, maka nilai X2cr adalah adalah 5,991 5,991 dapat dapat dari dari tabel tabel 3.7 (dibuku (dibuku Teknik Teknik Perhitu Perhitunga ngan n Debit Debit Rencana Bangunan Air,I Made Kamiana (2011)) Tabel 5.6 Uji Chi-Kuadrat Distribusi Normal
NO 1 2 3 4 5 ∑
P(X≥Xm) P(X≥Xm) >90 80-90 70-80 60-70 <60
Ef 2 2 2 3 2 11
Of 1 3 1 3 3 11
Ef-Of 1 -1 1 -1 -1 X2
(Ef-Of)2/Ef 0.5 0.5 0.5 0.33 0.5 2.33
Tabel 5.7 Uji Chi-Kuadrat Distribusi Log Normal
NO 1 2 3 4 5
P(X≥Xm) P(X≥Xm) >90 80-90 70-80 60-70 <60
Ef 2 2 2 3 2 11
Of 1 3 1 3 3 11
Ef-Of 1 -1 1 -1 -1 X2
(Ef-Of)2/Ef 0.5 0.5 0.5 0.33 0.5 2.33
Tabel 5.8 Uji Chi-Kuadrat Distribusi Gumbel
NO 1
P(X≥Xm) P(X≥Xm) >90
Ef 2
Of 1
Ef-Of 1
(Ef-Of)2/Ef 0.5
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35
3 4 5
70-80 60-70 <60
2 3 2 11
1 3 3 11
1 -1 -1 X2
0.5 0.33 0.5 2.33
Tabel 5.10 Rekapitulasi Nilai X2 danX2cr untuk 4 Distribusi
Dist istrib ribusiPro iProb babil abilit itas as Normal Normal Log-Normal Gumbel Log Person type III
X2 terhitung 2.33 2.33 2.33 2.33
X2cr 5.991 5.991 5.991 5.991
Keterangan Diterima Diterima Diterima Diterima Diterima
Nilai X2
Uji Smirnov-Ko Uji Smirnov-Kolmogorov lmogorov
Penguj Pengujian ian distrib distribusi usi probab probabilit ilitas as dengan dengan Metode Metode Smirnov-Kolmogorov dilak dilakuk ukan an deng dengan an langk langkah ah-la -lang ngka kah h perhi perhitu tung ngan an seba sebaga gaii berik berikut ut ( I Made Made Kamiana,2011). : 1)
Urutka Urutkan n data data hujan hujan (Xi) (Xi) dari besa besarr ke kecil kecil atau atau sebali sebalikny knyaa
2) Tentukan Tentukan peluang peluang empiris empiris masing-mas masing-masing ing data data yang sudah sudah diurut diurut tersebut tersebut
(Xi) dengan rumus tertentu, Rumus Weilbul misalnya P (Xi)
= (i/(n+1)
keterangan :
P
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36
5.
Tentu Tentuka kan n apak apakah ah ΔPi < ΔP kritis, kritis, jika jika “tida “tidak” k” artinya artinya distrib distribus usii proba probabi bilit litas as yang dipilih tidak dapat diterima, demikian sebaliknya.
6.
ΔP kritis dicari dari tabel pada Lampiran (3.28) distribusi Normal
Tabel 11. Perhitungan Uji Distribusi dengan Metode SmirnovKolmogorov untuk Distribusi Normal i Xi P(Xi) F(t) P’(Xi) ΔP 1 53.5 12 -0.612379 0.2946 -11.7054 2 92 6 1.139935 0.9452 -5 -5.0548 3 71 4 0.184127 0.1814 -3 -3.8186 4 68.5 3 0.070341 0.3632 -2 - 2.6368 5 82 2.4 0.684788 0.8925 -1 - 1.5075 6 69 2 0.093098 0.7673 -1 -1.2327 7 84 1.714 0.775818 0.0307 -1.683586 8 81.5 1.5 0.662031 0.3085 -1.1915 9 66.5 1.333 -0.020688 0.5832 -0.750133 10 58 1.2 -0.407563 0.4443 -0.7557 11 10.5 1.091 -2.569508 0.7054 -0.385509 Keterangan Tabel 11: i
= nomor urut
Xi
= data hu hujan di diurut da dari ke kecil ke ke be besar (m (mm)
P(Xi P(Xi))
= pelu peluang ang emp empiri iriss (dihit (dihitung ung deng dengan an persa persama maan an Wei Weilb lbull ull))
f(t f(t)
= untuk distr istrib ibu usi pro prob babil abilit itaas No Normal K T
=
dimana K T = f(t) P’(X P’(Xi) i)
= 1-Luas 1-Luas diba dibawa wah h kurv kurvee Nor Norma mall
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37
Tabel 12. Perhitungan Uji Distribusi dengan Metode SmirnovKolmogorov untuk Distribusi Log Normal I Lo Log Xi P(Xi) F(t) P’(Xi) 1 1.728 6.943 19.773 0.028 2 1.964 6.111 16.586 0.001 3 1.851 6.482 18.008 0.002 4 1.836 6.537 18.219 0.078 5 1.914 6.270 17.197 0.019 6 1.839 6.526 18.176 0.024 7 1.924 6.236 17.066 0.008 8 1.911 6.279 17.230 0.034 9 1.823 6.583 18.395 0.583 10 1.763 6.805 19.245 0.201 11 1.021 11.751 38.185 0.903 ∑ 19.5746
ΔP -6.915 -6.109 -6.480 -6.459 -6.251 -6.502 -6.228 -6.245 -6 -6.604 -10.848
Keterangan Tabel 12 : i
= nomor urut data
Log Xi = nilai log hujan hujan diurutkan dari kecil ke besar (mm) P(Xi P(Xi))
= pelu peluang ang emp empiri iriss (dihit (dihitung ung deng dengan an persa persama maan an Wei Weilb lbull ull))
f(t f(t)
= un untuk dis distr trib ibu usi pro prob babil abilit itaas Lo Log No Normal K T
=
dimana K T = f(t) P’(Xi)
= 1-Luas dibawah kurve Normal Normal sesuai sesuai dengan dengan nilai f(t), yang
ditentukan dengan tabel pada Lampiran (3.9) ΔPi
= P (Xi) – P’(Xi)
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38
Tabel 13. Perhitungan Uji Distribusi dengan Metode SmirnovKolmogorov untuk Distribusi Gumbel i Xi P(Xi) F(t) P’(Xi) ΔP 1 53.5 6.943022965 19.77338 0.2 0.2639219 -6. -6.679101 2 92 6.110639771 16.58582 0.2590003 -5. -5.85164 3 71 6. 6.482077452 18.00822 0. 0.2129925 -6. -6.269085 4 68.5 6.537049428 18.21873 0.2 0.2997602 -6. -6.237289 5 82 6.27020229 17.19685 0.1185115 -6. -6.151691 6 69 6.525820993 18.17573 0.5 -6.025821 7 84 6.23610101 17.06626 0.0930665 -6. -6.143034 8 81.5 6.278917 17.23022 0.2699784 -6.008939 9 66.5 6.583200299 18.39546 0.5 -6.0832 10 58 6.8049277 19.24455 1.5772871 -5.227641 11 10.5 11.75100445 38.18528 0.5 -11.251 Keterangan Tabel 13 : i
= nomor urut
Xi
= data hujan diurut dari kecil ke besar (mm)
P (Xi (Xi))
= pel pelua uang ng empir empiris is (dihi (dihitu tung ng deng dengan an persa persama maan an We Weilb ilbull ull))
f(t f(t)
= untuk distribusi probabili ilitas Gumbel K T
=
dimana K T = f(t) P’(Xi P’(Xi))
= dite ditentu ntuka kan n berda berdasa sarka rkan n nilai nilai Yn, Yn, Sn, Sn, dan dan jika jika f(t) f(t) pada pada pers persam amaan aan
(3.20) dan (3.21). (I Made Kamiana. 2011) contoh untuk nilai f(t) = -1,111 , Yn = 0,4987, Sn = 0,964 maka berdasarkan persamaan (3.20) didapat nilai Yt =1,499. kemudian melaui
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39
Tabel 14. Perhitungan Uji Distribusi dengan Metode Smirnov-Kolmogorov untuk Distribusi Log Person type III I Lo Log Xi Xi P(Xi) F(t) P'(Xi) 1 1.72835 53.5 6.943023 1.91 0.465 2 1.96379 92 6.11064 -6.01 0.08 3 1. 1.85126 71 6.482077 2.822 0.29 4 1.83569 68.5 6.537049 1.421 0.315 5 1. 1.91381 82 6.270202 -4.145 0.18 6 1.83885 69 6.525821 -1.983 0.31 7 1. 1.92428 84 6.236101 4.835 0.16 8 1.91116 81.5 6.278917 1.82 0.185 9 1.82282 66.5 6.5832 -0.209 0.335 10 1.76343 58 6.804928 0.841 0.42 11 1.02119 10.5 11.751 -1.301 0.895 ∑ 19.5746 736.5 76.52296 0.001 3.635 P(Xi)
=
G
= (Log X - LogXrt)/ s s
P’(Xi)
= (100-53 -53,5)/100
ΔP
[P(Xi) P’(Xi)]
ΔP -6.478 -6.031 -6.192 -6.222 -6.09 -6.216 -6.076 -6.094 -6.248 -6.385 -10.86 -72.89
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40
4.
Analisis Hujan Rencana
Penelitian hujan rencana menggunakan distribusi Gumbel sesuai dengan hasil analisi analisiss frekuen frekuensi si di atas. atas. Langka Langkah h perhitu perhitunga ngan n tersebu tersebutt adalah adalah sebaga sebagaii berikut berikut dibawah ini. Berdasarkan Pada tabel 2 dan perhitungan metode statistik sebagai berikut berikut : = 66.955 s
= 3.683
C s
= - 2.892
C k k
= 0.0003
Untuk saluran sekunder periode masa ulang yang digunakan untuk drainase salu saluran ran terb terbuk ukaa yaitu yaitu perio periode de ulan ulang g 5(lim 5(lima) a) dan dan 10ta 10tahu hun n (W (Wes esli. li.20 2008 08)da )dan n persamaan persamaan yang digunakan digunakan adalah adalah persamaan persamaan (16) yaitu yaitu :
x = x –
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41
x = x – mm x = _____ mm Tabel 16. Hasil Perhitungan Hujan Rencana Metode Gumbel
No 1
T 2
Yt 0,366513
p (mm) (mm) 68,37645278
2
5
1,49994
69,39315336
3
10
2,250367
69,52576648
4
25
3,198534
69,54786867
5
50
3,901939
69,56260346
6
100
4,600149
69,55523606
7
200
5,295812
69,55523606
Berdas Berdasarka arkan n tabel tabel di atas dapat dapat disimpu disimpulka lkan n bahwa bahwa hujan hujan rencana rencana dengan dengan periode ulang 5 tahun yaitu sebesar sebesar 69,393153 69,39315336 36 mm dan periode ulang 10 tahun yaitu sebesar 69,52576648 mm untuk analisa saluran sekunder.
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42
Didapat Didapat kemiring kemiring dasar dasar salura saluran n =3,0/3 =3,0/343 43 =0,00 =0,0093(S 93(Sumb umber er : Kantor Kantor Pemasar Pemasaran an Perumahan PT.Bumi Cipta Rahayu. 2011) Qmaks = 0,278.C.Cs.I.A yang dimana: C
= 0,75 ,75 (tab (tabeel 2.3. Koefis fisien ien Pengalir aliraan)
Cs
= 1 (kare (karena na di di peru peruma maha han n Pam Pamara araya yan-C n-Cad adasa asari ri tid tidak ak ada ada tamp tampun unga gan, n, jadi jadi
nilai Cs tidak berpengaruh)
t
= 6 jam untuk wilayah Indonesia (Sumber: Hidrologi Praktis.2010)
Maka didapat nilai intensitas hujannya adalah
It
= 6,979343 mm/jam
A
=
0, 0,018045km 2 (luas Chathment saluran saluran yang yang diamati diamati di Peruma Perumahan han
Pamarayan-Cadasari) jadi Q5
= 0,278x0,75x1x6,979343x0,018045 0,278x0,75x1x6,979343x0,018045
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43
Cs
= 1 (kare (karena na di di peru peruma maha han n Pam Pamara araya yan-C n-Cad adasa asari ri tid tidak ak ada ada tamp tampun unga gan, n, jadi jadi
nilai Cs tidak berpengaruh)
t
= 6 jam untuk wilayah Indonesia (Sumber: Hidrologi Praktis.2010)
Maka didapat nilai intensitas hujannya adalah
It
= 8,581 mm/jam
A
=
0, 0,018045km 2 (luas Chathment saluran saluran yang yang diamati diamati di Peruma Perumahan han
Pamarayan-Cadasari) jadi Q10= 0,278x0,75x1x8,581x0 0,278x0,75x1x8,581x0,018045 ,018045 = 0,032285 m 3/dtk ≈ 0,0323 m3/dtk Dari perhitungan diatas dapat dihasilkan nilai debit dengan periode ulang 10 tahun (Q10) sebesar 0,0323m 3/dtk.
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44
(mm/jam)
(m3/det)
(m3/det)
(m3/det)
43,43409
4,560294
0,0172
0,001502
0,0187
5
66,47406
6,979343
0,0263
0.001502
0,0278
10
81,7285
8,581
0.0323
0.001502
0,0338
(tahunan)
(mm)
2
Dapat Dapat disimp disimpulk ulkan an bahwa bahwa dari dari perhitu perhitunga ngan n diatas diatas diperole diperoleh h debit debit dengan dengan periode ulang 2 tahun sebesar sebesar 0,0187 0,0187 m 3/dtk, dan debit dengan periode ulang 5 tahu tahun n sebe sebesa sarr 0,0338m3/det.
0,02 0,0267 678m 8m3/dtk /dtk,d ,dan an untu untuk k peri period odee ulan ulang g 10 tahu tahun n sebe sebesa sar r
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45
b (lebar saluran) saluran)
= 0,40m 0,40m
d (kedalaman saluran)
= H/1,3 =0,36/1,3 = 0,277 m
F (tingg (tinggii jagaan jagaan salu saluran ran))
= 30%.d 30%.d (sum (sumbe ber:W r:Wes esli. li.200 2008) 8) = 0,0831m
R (jari-jari hidolis)
= 0,5.d = 0,1385 m
As ( luas saluran)
= bxd = 0,40m x 0,277m
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46
Dari hasil perhitungan dapat disimpulkan bahwa dimensi saluran yang ada di perumahan perumahan Pamaraya Pamarayan-Cadas n-Cadasari ari dapat mengalirkan mengalirkan debit debit rencana rencana 5 dan dan 10 tahun. tahun.
7.
Data Teknis Saluran
Dari analisis perhitungan kapasitas saluran didapat data teknis dimensi saluran sebagai berikut: b = 0,40m 0,40m F d
d = 0,277m H
F = 0,0831m