Perhitungan Debit Pada Sistem Jaringan Pipa Dengan Metoda Hardy-Cross Menggunakan Rumus Hazen-Williams dan Rumus Manning.
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ρ
= Massa jenis
(kg/m3)
υ
= Viscositas kinematik fluida
(m2/det)
A’
= Luas basah
(m2)
A
= Luas penampang pipa
(m2)
An
= Luas penampang pipa n
(m2)
D
= Diameter pipa
(m)
Dn
= Diameter pipa n
(m)
De
= Diameter pipa ekivalen
(m)
f
= Faktor gesekan Darcy&Weisbach
fn
= Faktor gesekan Darcy&Weisbach ke&n
fe
= Faktor gesekan ekivalen
g
= Percepatan gravitasi bumi
hf
= Tinggi kehilangan energi
(m)
hfn
= Tinggi kehilangan energi ke&n
(m)
hm
= Tinggi kehilangan energi sekunder
(m)
Hn
= Tinggi energi pada titik n
(m)
k
= Konstanta hambatan pipa
K
= Koefisien energi sekunder
L
= Panjang pipa
(m)
Ln
= Panjang pipa n
(m)
Le
= Panjang pipa ekivalen
(m)
P’
= Keliling basah
(m)
(m/det2)
P
= Tekanan
(kg/m2)
Pn
= Tekanan pada titik n
(kg/m2)
Q
= Debit aliran
(m3/det, lt/det)
Qn
= Debit aliran ke&n
(m3/det, lt/det)
Q0
= Debit terkaan awal
(m3/det, lt/det)
= Koreksi debit
(m3/det, lt/det)
Q
n’
= Koefisien Manning
n
= Konstanta
R
= Jari&jari hidraulik
Re
= Bilangan Reynolds
V
= Kecepatan rerata aliran
(m/det)
Vn
= Kecepatan rerata aliran pipa n
(m/det)
Sf
= Kemiringan garis energi/gradien energi
Z
= Tinggi datum
(m)
Zn
= Tinggi datum di titik n
(m)
(m)
(m/m)
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Tabel 3.2 Konstanta hambatan pipa (k) menurut rumus Hazen Williams dan rumus Manning pada tiap tiap kasus
Pipa
1 ( AB )
4 ( BD )
5 ( AE )
6 ( DE )
6 ( DE )
7 ( DF )
8 ( EF )
2 ( BC )
3 ( CD )
4 ( BD )
L
(m)
Jaring
50
200
350
80
80
100
200
75
300
200
I
II
III
D
(in)
3
2
2
2
2
2
2
3
2
2
Kasus h
Koefisien
Hazen
Manning
Williams
15359,69
442595,46
774542,06
177038,18
177038,18
221297,73
442595,46
23039,54
663893,19
442595,46
57158,07
1987425,88
3477995,30
794970,35
794970,35
993712,94
1987425,88
85737,11
2981138,83
1987425,88
D
(in)
2
2
2
2
2
2
2
2
2
2
Kasus 2
Koefisien
Hazen
Manning
Williams
110648,87
442595,46
774542,06
177038,18
177038,18
221297,73
442595,46
165973,30
663893,19
442595,46
Rumus Hazen Williams:
k=
10,68 L
C HW
di mana:
1,852
3
3
3
3
3
3
3
3
3
3
15359,69
61438,77
107517,85
24575,51
24575,51
30719,39
61438,77
23039,54
92158,16
61438,77
10,29 n ′ 2 L
D
L
: Panjang pipa (m)
D
: Diameter pipa (m)
CHW : Koefisien gesekan Hazen,Willams
: Koefisien gesekan Manning
57158,07
228632,29
400106,50
91452,91
91452,91
114316,14
228632,29
85737,11
342948,43
228632,29
Rumus Manning:
k=
D 4,87
n’
496856,47
1987425,88
3477995,30
794970,35
794970,35
993712,94
1987425,88
745284,71
2981138,83
1987425,88
D
(in)
Kasus 3
Koefisien
Hazen
Manning
Williams
16
3
D
(in)
2
3
3
2
2
2
3
2
3
3
Kasus 4
Koefisien
Hazen
Manning
Williams
110648,87
61438,77
107517,85
177038,18
177038,18
221297,73
61438,77
165973,30
92158,16
61438,77
496856,47
228632,29
400106,50
794970,35
794970,35
993712,94
228632,29
745284,71
342948,43
228632,29
D
(in)
3
2
2
3
3
3
2
3
2
2
Kasus 5
Koefisien
Hazen
Manning
Williams
15359,69
442595,46
774542,06
24575,51
24575,51
30719,39
442595,46
23039,54
663893,19
442595,46
57158,07
1987425,88
3477995,30
91452,91
91452,91
114316,14
1987425,88
85737,11
2981138,83
1987425,88
Tabel 3.3 Debit pada tiap tiap Kasus
Pipa
Jaring
1 ( AB )
4 ( BD )
5 ( AE )
6 ( DE )
6 ( DE )
7 ( DF )
8 ( EF )
2 ( BC )
3 ( CD )
4 ( BD )
I
II
III
L
(m)
Q0
(lt/det)
50
200
350
80
80
100
200
75
300
200
20
10
10
15
15
5
5
15
10
10
Kasus h
Kasus 2
3Q =
Σ k Q0
Kasus 4
Manning
Hazen
Williams
Manning
Hazen
Williams
Manning
Hazen
Williams
Manning
Hazen
Williams
Manning
30,47
4,52
0,47
3,26
3,26
6,27
3,73
19,99
5,01
4,52
30,28
4,64
0,28
3,51
3,51
6,21
3,79
19,92
5,08
4,64
24,34
6,39
5,66
7,85
7,85
7,80
2,20
15,73
9,27
6,39
23,75
6,74
6,25
8,29
8,29
7,96
2,04
15,50
9,50
6,74
24,34
6,39
5,66
7,85
7,85
7,80
2,20
15,73
9,27
6,39
23,75
6,74
6,25
8,29
8,29
7,96
2,04
15,50
9,50
6,74
19,07
6,03
10,93
11,09
11,09
9,84
0,16
10,10
14,90
6,03
18,35
6,39
11,65
11,43
11,43
10,22
0,22
9,73
15,27
6,39
29,95
4,85
0,05
1,92
1,92
8,13
1,87
19,80
5,20
4,85
29,71
5,01
0,29
2,18
2,18
8,11
1,89
19,72
5,28
5,01
Rumus Hardy Cross menurut Manning:
n=2
1,852
Σ 1,852 k Q 0
0,852
Kasus 5
Hazen
Williams
Rumus Hardy Cross menurut Hazen Williams:
n = 1,852
Q (lt/det)
Kasus 3
2
Σ k Q0
3Q =
Σ 2 k Q0
Tabel 4.3 Debit pada Tiap Kasus dengan Rumus Hazen Williams dan Rumus Manning
Q (lt/det)
Kasus 1
(m)
1 (AB )
2 ( BC )
3 (CD )
4 (BD )
5 ( AE )
6 ( DE )
7 ( DF )
8 ( EF )
Kasus 2
Kasus 3
Kasus 4
Kasus 5
Q0
(lt/det)
50
75
300
200
350
80
100
200
%=
20
15
10
10
10
15
5
5
(in)
Hazen
Williams
Manning
∆%
(in)
Hazen
Williams
Manning
∆%
(in)
Hazen
Williams
Manning
∆
%
(in)
Hazen
Williams
Manning
∆%
(in)
Hazen
Williams
Manning
∆%
3
3
2
2
2
2
2
2
30,47
19,99
5,01
4,52
0,47
3,26
6,27
3,73
30,28
19,92
5,08
4,64
0,28
3,51
6,21
3,79
0,63
0,35
1,38
2,59
67,86
7,12
0,97
1,58
2
2
2
2
2
2
2
2
24,34
15,73
9,27
6,39
5,66
7,85
7,80
2,20
23,75
15,50
9,50
6,74
6,25
8,29
7,96
2,04
2,48
1,48
2,42
5,19
9,44
5,31
2,01
7,84
3
3
3
3
3
3
3
3
24,34
15,73
9,27
6,39
5,66
7,85
7,80
2,20
23,75
15,50
9,50
6,74
6,25
8,29
7,96
2,04
2,48
1,48
2,42
5,19
9,44
5,31
2,01
7,84
2
3
3
2
2
2
3
2
19,07
10,10
14,90
6,03
10,93
11,09
9,84
0,16
18,35
9,73
15,27
6,39
11,65
11,43
10,22
0,22
3,92
3,80
2,42
5,63
6,18
2,97
3,72
27,27
3
2
2
3
3
3
2
3
29,95
19,80
5,20
4,85
0,05
1,92
8,13
1,87
29,71
19,72
5,28
5,01
0,29
2,18
8,11
1,89
0,81
0,41
1,52
3,19
82,76
11,93
0,25
1,06
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ρ
= Massa jenis
(kg/m3)
υ
= Viscositas kinematik fluida
(m2/det)
A’
= Luas basah
(m2)
A
= Luas penampang pipa
(m2)
An
= Luas penampang pipa n
(m2)
D
= Diameter pipa
(m)
Dn
= Diameter pipa n
(m)
De
= Diameter pipa ekivalen
(m)
f
= Faktor gesekan Darcy&Weisbach
fn
= Faktor gesekan Darcy&Weisbach ke&n
fe
= Faktor gesekan ekivalen
g
= Percepatan gravitasi bumi
hf
= Tinggi kehilangan energi
(m)
hfn
= Tinggi kehilangan energi ke&n
(m)
hm
= Tinggi kehilangan energi sekunder
(m)
Hn
= Tinggi energi pada titik n
(m)
k
= Konstanta hambatan pipa
K
= Koefisien energi sekunder
L
= Panjang pipa
(m)
Ln
= Panjang pipa n
(m)
Le
= Panjang pipa ekivalen
(m)
P’
= Keliling basah
(m)
(m/det2)
P
= Tekanan
(kg/m2)
Pn
= Tekanan pada titik n
(kg/m2)
Q
= Debit aliran
(m3/det, lt/det)
Qn
= Debit aliran ke&n
(m3/det, lt/det)
Q0
= Debit terkaan awal
(m3/det, lt/det)
= Koreksi debit
(m3/det, lt/det)
Q
n’
= Koefisien Manning
n
= Konstanta
R
= Jari&jari hidraulik
Re
= Bilangan Reynolds
V
= Kecepatan rerata aliran
(m/det)
Vn
= Kecepatan rerata aliran pipa n
(m/det)
Sf
= Kemiringan garis energi/gradien energi
Z
= Tinggi datum
(m)
Zn
= Tinggi datum di titik n
(m)
(m)
(m/m)
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Tabel 3.2 Konstanta hambatan pipa (k) menurut rumus Hazen Williams dan rumus Manning pada tiap tiap kasus
Pipa
1 ( AB )
4 ( BD )
5 ( AE )
6 ( DE )
6 ( DE )
7 ( DF )
8 ( EF )
2 ( BC )
3 ( CD )
4 ( BD )
L
(m)
Jaring
50
200
350
80
80
100
200
75
300
200
I
II
III
D
(in)
3
2
2
2
2
2
2
3
2
2
Kasus h
Koefisien
Hazen
Manning
Williams
15359,69
442595,46
774542,06
177038,18
177038,18
221297,73
442595,46
23039,54
663893,19
442595,46
57158,07
1987425,88
3477995,30
794970,35
794970,35
993712,94
1987425,88
85737,11
2981138,83
1987425,88
D
(in)
2
2
2
2
2
2
2
2
2
2
Kasus 2
Koefisien
Hazen
Manning
Williams
110648,87
442595,46
774542,06
177038,18
177038,18
221297,73
442595,46
165973,30
663893,19
442595,46
Rumus Hazen Williams:
k=
10,68 L
C HW
di mana:
1,852
3
3
3
3
3
3
3
3
3
3
15359,69
61438,77
107517,85
24575,51
24575,51
30719,39
61438,77
23039,54
92158,16
61438,77
10,29 n ′ 2 L
D
L
: Panjang pipa (m)
D
: Diameter pipa (m)
CHW : Koefisien gesekan Hazen,Willams
: Koefisien gesekan Manning
57158,07
228632,29
400106,50
91452,91
91452,91
114316,14
228632,29
85737,11
342948,43
228632,29
Rumus Manning:
k=
D 4,87
n’
496856,47
1987425,88
3477995,30
794970,35
794970,35
993712,94
1987425,88
745284,71
2981138,83
1987425,88
D
(in)
Kasus 3
Koefisien
Hazen
Manning
Williams
16
3
D
(in)
2
3
3
2
2
2
3
2
3
3
Kasus 4
Koefisien
Hazen
Manning
Williams
110648,87
61438,77
107517,85
177038,18
177038,18
221297,73
61438,77
165973,30
92158,16
61438,77
496856,47
228632,29
400106,50
794970,35
794970,35
993712,94
228632,29
745284,71
342948,43
228632,29
D
(in)
3
2
2
3
3
3
2
3
2
2
Kasus 5
Koefisien
Hazen
Manning
Williams
15359,69
442595,46
774542,06
24575,51
24575,51
30719,39
442595,46
23039,54
663893,19
442595,46
57158,07
1987425,88
3477995,30
91452,91
91452,91
114316,14
1987425,88
85737,11
2981138,83
1987425,88
Tabel 3.3 Debit pada tiap tiap Kasus
Pipa
Jaring
1 ( AB )
4 ( BD )
5 ( AE )
6 ( DE )
6 ( DE )
7 ( DF )
8 ( EF )
2 ( BC )
3 ( CD )
4 ( BD )
I
II
III
L
(m)
Q0
(lt/det)
50
200
350
80
80
100
200
75
300
200
20
10
10
15
15
5
5
15
10
10
Kasus h
Kasus 2
3Q =
Σ k Q0
Kasus 4
Manning
Hazen
Williams
Manning
Hazen
Williams
Manning
Hazen
Williams
Manning
Hazen
Williams
Manning
30,47
4,52
0,47
3,26
3,26
6,27
3,73
19,99
5,01
4,52
30,28
4,64
0,28
3,51
3,51
6,21
3,79
19,92
5,08
4,64
24,34
6,39
5,66
7,85
7,85
7,80
2,20
15,73
9,27
6,39
23,75
6,74
6,25
8,29
8,29
7,96
2,04
15,50
9,50
6,74
24,34
6,39
5,66
7,85
7,85
7,80
2,20
15,73
9,27
6,39
23,75
6,74
6,25
8,29
8,29
7,96
2,04
15,50
9,50
6,74
19,07
6,03
10,93
11,09
11,09
9,84
0,16
10,10
14,90
6,03
18,35
6,39
11,65
11,43
11,43
10,22
0,22
9,73
15,27
6,39
29,95
4,85
0,05
1,92
1,92
8,13
1,87
19,80
5,20
4,85
29,71
5,01
0,29
2,18
2,18
8,11
1,89
19,72
5,28
5,01
Rumus Hardy Cross menurut Manning:
n=2
1,852
Σ 1,852 k Q 0
0,852
Kasus 5
Hazen
Williams
Rumus Hardy Cross menurut Hazen Williams:
n = 1,852
Q (lt/det)
Kasus 3
2
Σ k Q0
3Q =
Σ 2 k Q0
Tabel 4.3 Debit pada Tiap Kasus dengan Rumus Hazen Williams dan Rumus Manning
Q (lt/det)
Kasus 1
(m)
1 (AB )
2 ( BC )
3 (CD )
4 (BD )
5 ( AE )
6 ( DE )
7 ( DF )
8 ( EF )
Kasus 2
Kasus 3
Kasus 4
Kasus 5
Q0
(lt/det)
50
75
300
200
350
80
100
200
%=
20
15
10
10
10
15
5
5
(in)
Hazen
Williams
Manning
∆%
(in)
Hazen
Williams
Manning
∆%
(in)
Hazen
Williams
Manning
∆
%
(in)
Hazen
Williams
Manning
∆%
(in)
Hazen
Williams
Manning
∆%
3
3
2
2
2
2
2
2
30,47
19,99
5,01
4,52
0,47
3,26
6,27
3,73
30,28
19,92
5,08
4,64
0,28
3,51
6,21
3,79
0,63
0,35
1,38
2,59
67,86
7,12
0,97
1,58
2
2
2
2
2
2
2
2
24,34
15,73
9,27
6,39
5,66
7,85
7,80
2,20
23,75
15,50
9,50
6,74
6,25
8,29
7,96
2,04
2,48
1,48
2,42
5,19
9,44
5,31
2,01
7,84
3
3
3
3
3
3
3
3
24,34
15,73
9,27
6,39
5,66
7,85
7,80
2,20
23,75
15,50
9,50
6,74
6,25
8,29
7,96
2,04
2,48
1,48
2,42
5,19
9,44
5,31
2,01
7,84
2
3
3
2
2
2
3
2
19,07
10,10
14,90
6,03
10,93
11,09
9,84
0,16
18,35
9,73
15,27
6,39
11,65
11,43
10,22
0,22
3,92
3,80
2,42
5,63
6,18
2,97
3,72
27,27
3
2
2
3
3
3
2
3
29,95
19,80
5,20
4,85
0,05
1,92
8,13
1,87
29,71
19,72
5,28
5,01
0,29
2,18
8,11
1,89
0,81
0,41
1,52
3,19
82,76
11,93
0,25
1,06
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