Latihan Soal
Luas daerah
pengaliran suatu sungai sampai ke pelepasannya 2400 km2. Panjang L =
75 km. Hujan efektif dalam daerah pengaliran adalah sebagai berikut:
|
t
|
1
|
2
|
3
|
(jam)
|
|
Hujan Efektif
|
20
|
40
|
10
|
mm/jam
|
Ditanyakan: Hitung
ordinat hidrograf satuan sintetik Nakayasu! (Daerah Pengaliran Biasa = α = 2)
Penyelesaian:
Diketahui: A =
2400 km2
L = 75 km
R0 = 1
(Perubahan Waktu “t” )
Jawab:
Karena L = 75 km
> 15 km,
Maka tg = 0,4 + (0,058 x 75) = 4,75 jam
tr
= 0,75 x tg = 0,75 x 4,75 = 3,56 jam
Tp
= tg + (0,8 tr) = 4,75 + (0,8 . 3,56) = 7,6 jam
To,3 = α . tg = 2 . 4,75 = 9,5 jam
Qp =
m3/det
m3/det
Menentukan Nilai Q
atau U:
*Untuk t = 0 s/d t =
7, menggunakan rumus Qa:
Qa = Qp 
2,4
2,4
t = 0 => Qa =
56.59 
2,4
= 0
2,4
= 0
t = 1 => Qa =
56.59 
2,4 = 0,4353
2,4 = 0,4353
t = 2 => Qa =
56.59 
2,4 = 2,2975
2,4 = 2,2975
t = 3 => Qa =
56.59 
2,4 =6,0796
2,4 =6,0796
t = 4 => Qa =
56.59 
2,4 = 12,12
2,4 = 12,12
t = 5 => Qa =
56.59 
2,4 = 20,71
2,4 = 20,71
t = 6 => Qa =
56.59 
2,4 = 32,08
2,4 = 32,08
t = 7 => Qa =
56.59 
2,4 = 46,45
2,4 = 46,45
*Untuk t = 8 s/d t =
17, menggunakan rumus Qd1:
Qd1 = Qp x 
t = 8 => Qd1 =
56,59 x 
= 53,79
= 53,79
t = 9 => Qd1 =
56,59 x 
= 47,38
= 47,38
t = 10 => Qd1 =
56,59 x 
= 41,74
= 41,74
t = 11 => Qd1 =
56,59 x 
= 36,77
= 36,77
t = 12 => Qd1 =
56,59 x 
= 32,40
= 32,40
t = 13 => Qd1 =
56,59 x 
= 28,54
= 28,54
t = 14 => Qd1 =
56,59 x 
= 25,14
= 25,14
t = 15 => Qd1 =
56,59 x 
= 22,15
= 22,15
t = 16 => Qd1 =
56,59 x 
= 19,51
= 19,51
t = 17 => Qd1 =
56,59 x 
= 17,19
= 17,19
*Untuk t = 18 s/d t
= 31, menggunakan rumus Qd2:
Qd2 = Qp x 
t = 18 => Qd2 =56,59
x 
= 15,73
= 15,73
t = 19 => Qd2
=56,59 x 
= 14,45
= 14,45
t = 20 => Qd2
=56,59 x 
= 13,28
= 13,28
t =21 => Qd2
=56,59 x 
= 12,21
= 12,21
t = 22 => Qd2
=56,59 x 
= 11,22
= 11,22
t = 23 => Qd2
=56,59 x 
= 10,31
= 10,31
t = 24 => Qd2
=56,59 x 
= 9,47
= 9,47
t = 25 => Qd2
=56,59 x 
= 8,709
= 8,709
t = 26 => Qd2
=56,59 x 
= 8,003
= 8,003
t = 27 => Qd2
=56,59 x 
= 7,35
= 7,35
t = 28 => Qd2
=56,59 x 
= 6,75
= 6,75
t = 29 => Qd2
=56,59 x 
= 6,211
= 6,211
t = 30 => Qd2
=56,59 x 
= 5,708
= 5,708
t = 31 => Qd2
=56,59 x 
=5,245
=5,245
*Untuk t = 32 s/d t
= 35, menggunakan rumus Qd3:
Qd3 = Qp x 
t = 32 => Qd3 =
56,59 x 
= 4,887
= 4,887
t = 33 => Qd3 =
56,59 x 
= 4,587
= 4,587
t = 34 => Qd3 =
56,59 x 
= 4,305
= 4,305
t = 35 => Qd3 =
56,59 x 
= 4,041
= 4,041
Mengisi Kolom Akibat
Hujan:
** 20 mm ** 40 mm **
10 mm
t = 0 => 20 x 0 =
0 =>
bergeser satu jam = 0 =>
bergeser satu jam = 0
t = 1 => 20 x
0,435 = 8,705 => 40 x 0 = 0 =>
bergeser satu jam = 0
t = 2 => 20 x
2,297 = 45,95 => 40 x 0,435
= 17,411 => 10 x 0 =
0
t = 3 => 20 x
6,079 = 121,5 => 40 x 2,297
= 91,901 => 10 x
0,435 = 4,35
t = 4 => 20 x
12,12 = 242,5 => 40 x 6,079
= 243,18 => 10 x
2,297 = 22,97
dan seterusnya . . .
s/d t = 35
Mengisi kolom Total:
Kolom 3 + Kolom 4 +
Kolom 5
t = 0 => 0 + 0 + 0 = 0
t = 1 => 8,7059 +
0 + 0 = 8,7059
t = 2 => 2,297 +
45,95 + 17,41 = 63,36
t = 3 => 121,59 +
91,09 + 4,35 = 217,84
t = 4 => 242,52 +
243,18 + 22,97 = 508,68
t = 5 => 414,3288 + 485,0551 + 60,79643 = 960,1803
t = 6 => 641,771+ 828,6575+ 121,2638= 1591,692
t = 7 => 929,0784+ 1283,542+ 207,1644= 2419,785
t = 8 => 1075,855+ 1858,157+ 320,8855= 3254,897
t = 9 => 947,7938+ 2151,71+ 464,5392= 3564,043
dan seterusnya . .
. s/d t = 35
|
Tabel
Ordinat Hidrograf Satuan Sintetik Nakayasu
|
|||||||
|
t
|
Q atau U
|
Akibat Hujan
|
Total
|
Keterangan
|
|||
|
(Jam)
|
m3/det
|
20 mm
|
40 mm
|
10 mm
|
m3/det
|
||
|
|
|
m3/det
|
m3/det
|
m3/det
|
|
||
|
0
|
0
|
0
|
0
|
0
|
0
|
Qa
|
|
|
1
|
0,435298
|
8,705968
|
0
|
0
|
8,705968
|
0 - 7
|
|
|
2
|
2,297519
|
45,95037
|
17,41194
|
0
|
63,36231
|
|
|
|
3
|
6,079643
|
121,5929
|
91,90075
|
4,352984
|
217,8466
|
|
|
|
4
|
12,12638
|
242,5275
|
243,1857
|
22,97519
|
508,6884
|
|
|
|
5
|
20,71644
|
414,3288
|
485,0551
|
60,79643
|
960,1803
|
|
|
|
6
|
32,08855
|
641,771
|
828,6575
|
121,2638
|
1591,692
|
|
|
|
7
|
46,45392
|
929,0784
|
1283,542
|
207,1644
|
2419,785
|
|
|
|
8
|
53,79275
|
1075,855
|
1858,157
|
320,8855
|
3254,897
|
Qd1
|
|
|
9
|
47,38969
|
947,7938
|
2151,71
|
464,5392
|
3564,043
|
8 s/d 17
|
|
|
10
|
41,7488
|
834,976
|
1895,588
|
537,9275
|
3268,491
|
|
|
|
11
|
36,77936
|
735,5872
|
1669,952
|
473,8969
|
2879,436
|
|
|
|
12
|
32,40144
|
648,0287
|
1471,174
|
417,488
|
2536,691
|
|
|
|
13
|
28,54463
|
570,8926
|
1296,057
|
367,7936
|
2234,744
|
|
|
|
14
|
25,1469
|
502,9381
|
1141,785
|
324,0144
|
1968,738
|
|
|
|
15
|
22,15362
|
443,0724
|
1005,876
|
285,4463
|
1734,395
|
|
|
|
16
|
19,51663
|
390,3326
|
886,1447
|
251,469
|
1527,946
|
|
|
|
17
|
17,19353
|
343,8705
|
780,6652
|
221,5362
|
1346,072
|
|
|
|
18
|
15,73392
|
314,6785
|
687,741
|
195,1663
|
1197,586
|
Qd2
|
|
|
19
|
14,45918
|
289,1837
|
629,3569
|
171,9353
|
1090,476
|
18-31
|
|
|
20
|
13,28772
|
265,7544
|
578,3674
|
157,3392
|
1001,461
|
|
|
|
21
|
12,21117
|
244,2234
|
531,5089
|
144,5918
|
920,3241
|
|
|
|
22
|
11,22184
|
224,4368
|
488,4468
|
132,8772
|
845,7608
|
|
|
|
23
|
10,31266
|
206,2532
|
448,8736
|
122,1117
|
777,2385
|
|
|
|
24
|
9,477146
|
189,5429
|
412,5065
|
112,2184
|
714,2678
|
|
|
|
25
|
8,709321
|
174,1864
|
379,0858
|
103,1266
|
656,3989
|
|
|
|
26
|
8,003705
|
160,0741
|
348,3729
|
94,77146
|
603,2184
|
|
|
|
27
|
7,355256
|
147,1051
|
320,1482
|
87,09321
|
554,3465
|
|
|
|
28
|
6,759344
|
135,1869
|
294,2103
|
80,03705
|
509,4342
|
|
|
|
29
|
6,211712
|
124,2342
|
270,3738
|
73,55256
|
468,1606
|
|
|
|
30
|
5,708448
|
114,169
|
248,4685
|
67,59344
|
430,2309
|
|
|
|
31
|
5,245958
|
104,9192
|
228,3379
|
62,11712
|
395,3742
|
|
|
|
32
|
4,887584
|
97,75168
|
209,8383
|
57,08448
|
364,6745
|
Qd3
|
|
|
33
|
4,587481
|
91,74963
|
195,5034
|
52,45958
|
339,7126
|
32-35
|
|
|
34
|
4,305805
|
86,1161
|
183,4993
|
48,87584
|
318,4912
|
|
|
|
35
|
4,041424
|
80,82849
|
172,2322
|
45,87481
|
298,9355
|
|
|
|
--
|
--
|
--
|
161,657
|
43,05805
|
204,715
|
|
|
|
--
|
--
|
--
|
--
|
40,41424
|
40,41424
|
|
|
Diagram Histograf
Nakayasu
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