1. The document describes the Nakayasu unit hydrograph method for calculating peak discharge values. It provides the Nakayasu equation and defines the parameters. 2. It then applies the Nakayasu method to calculate hydrographs for the Deli River basin in Medan, Indonesia using basin characteristics and rainfall data. Discharge values are calculated for different time intervals on the hydrograph curve. 3. Tables of results show the calculated hydrographs for return periods of 2 years and 5 years, with discharge values over time.

1. 5. Menghitung Nilai Debit
1. Menghitung Hidrograf Satuan Sintesis Metode Nakayashu
Nakayashu memiliki persamaan sebagai berikut
푄푝 =
퐴. 푅표
3,6. (0,3푇푝 + 푇0,3)
푇푝 = 푇푔 + 0,8푇푟
푡푔 = 0,4 + 0,058퐿 untuk L > 15 km
푇푔 = 0,21퐿0,7 untuk L < 15 km
푇0,3 = ∝ 푡푔
dengan :
푄푝 = debit puncak banjir
A = luas DAS (km2)
Re = curah hujan efektif (mm)
Tp = waktu dari permulaan banjir sampai puncak hidrograf banjir (jam)
T0,3 = waktu dari puncak banjir sampai 0,3 kali debit puncak banjir (jam)
tg = waktu konsentrasi
Tr = satuan waktu dari curah hujan (jam)
∝ = kefisien karakteristik DAS
L = panjang sungai utama (km)
Perhitungan HSS Nakayashu memakai parameter sebagai berikut :
Data DAS Sungai Deli di Medan
L = 71,91 km
Luas DAS (A) = 167,65 km2
α = 2
Mencari nilai waktu konsentrasi (tg) (untuk L > 15 km)
푇푔 = 0,4 + 0,058퐿

2. 푇푔 = 0,4 + 0,058(71,91)
푇푔 = 4.57078 jam
Mencari nilai satuan waktu dari curah hujan (Tr)
푇푟 = (1 − 0,5)푇푔
푇푟 = (0,75)(4.57078 )
푇푟 =3.428085 jam
Mencari waktu permulaan banjir sampai puncak hidrograf banjir (Tp)
푇푝 = 푇푔 + 0,8푇푟
푇푝 = 4,7078 + 0,8(3.428085 )
푇푝 = 7.313248 jam
Mencari waktu dari puncak banjir sampai 0,3 kali puncak banjir (T0,3)
푇0,3 = ∝ 푇푔
푇0,3 = (2)(4.57078)
푇0,3 = 9.14156
Mencari nilai hidrograf untuk tiap interval tertentu:
푄푝 =
퐴. 푅표
3,6. (0,3푇푝 + 푇0,3)
푄푝 =
167,65푥1
3,6. (0,3(6.399092) + (9.14156))
푄푝 = 4.108271 m3/det

3. Tabel Debit dasar untuk 1 jam
Periode
(tahun)
Qp
(m3/det)
2 4.108271
5 4.108271
10 4.108271
25 4.108271
50 4.108271
100 3,081203
Contoh Perhitungan
1. Pada kurva naik sebelum mencapai debit puncak (Qp)
interval = (0 < t < Tp)
= (0 < t < 7,313248 )
푄푡 = 푄푝
푡2,4
푇푝
푄1 = 4,108 (1)2,4
(7,313248 )
=0.034657269 m3/det
Tabel untuk kurva 0 < t < 7,313248
waktu T (jam) Q (m3/det)
0 0
1 0.034657269
2 0.182922162
3 0.484044563
4 0.965468957
5 1.649386158
6 2.554802522
7 3.698534135
7.313248 4.108270753

4. 2. Pada kurva turun (Qr)
Interval = (Tp < t < Tp+T0,3)
= (7,313248 < t <(7,313248 +9,14156))
= (7,313248 < t < 16,45481)
푄푟 = 푄푝 + 0,3(푡−푇푝 )/푇0,3
푄8 = 4.108 + 0,3(8−7,313248 )/9,14156 = 3.752997129 m3/det
Tabel untuk kurva 7,313248 < t < 16,45481
waktu T (jam) Q (m3/det)
7.313248 4.108270753
8 3.752997129
9 3.289881495
10 2.88391381
11 2.528042082
12 2.216084526
13 1.942622182
14 1.702904785
15 1.492768245
16 1.308562319
16.454808 1.232481226
3. Pada kurva turun (Qt)
Interval = (Tp+T0,3 < t < Tp+T0,3+1,5T0,3)
= (16.454808< t < 16.454808+(1,5. 9,14156))
= (16.454808< t < 30.16715)
푄푡 = 푄푝 + 0,3[(푡 −푇푝 )+(0,5푇0,3)]/(1,5푇0,3)
푄17 = 4.108 + 0,3[(17−7,313)+(0,5.9,141) ]/(1,5.9,141) =1.17487m3/det

5. Tabel untuk kurva 16.454808< t < 30.16715
waktu T (jam) Q (m3/det)
16.454808 1.232481226
17 1.174873368
18 1.076115964
19 0.985659901
20 0.902807387
21 0.826919282
22 0.757410172
23 0.693743853
24 0.635429193
25 0.582016341
26 0.533093261
27 0.488282554
28 0.447238542
29 0.409644603
30 0.375210732
30.167148 0.369744368
4. Pada kurva turun (Qt)
Interval = t > Tp+T0,3+1,5T0,3
= (t > 30.167148)
푄푡 = 푄푝 + 0,3[(푡−푇푝 )+ (1,5푇0,3)]/(2푇0,3)
푄31 = 4.108 + 0,3[(11−7,313248) +(1,5.9 ,141)]/(2.9 ,141 ) =0.35001 m3/det

6. Tabel untuk kurva t > 30.167148
waktu T (jam) Q (m3/det)
30.167148 0.369744368
31 0.350011926
32 0.327705593
33 0.306820847
34 0.28726709
35 0.268959499
36 0.251818654
37 0.235770198
Hasil dari perhitungan diatas kemudian dimasukkan ke dalam tabel Hidrograf Banjir Periode T

7. Tabel Hidrograf Banjir Periode 2 tahun
PERIODE 2 TAHUN
t Q
R1 R2 R3 R4 R5
Qtot
98.954383 111.56739 115.2661 117.50058 118.3218
0 0.000 0.000 0
1 0.035 3.429 0.000 3.429
2 0.183 18.101 3.867 0.000 21.968
3 0.484 47.898 20.408 3.995 0.000 72.301
4 0.965 95.537 54.004 21.085 4.072 0.000 174.698
5 1.649 163.214 107.715 21.085 21.493 4.101 317.608
6 2.555 252.809 184.018 55.794 56.876 21.644 571.140
7 3.699 365.986 285.033 190.118 113.443 57.273 1011.853
7.313 4.108 406.531 412.636 294.482 193.804 114.236 1421.689
8 3.753 371.376 458.349 426.316 300.191 195.158 1751.389
9 3.290 325.548 418.712 473.544 434.580 302.289 1954.673
10 2.884 285.376 367.043 432.593 482.724 437.617 2005.354
11 2.528 250.161 321.751 379.212 440.979 486.098 1878.201
12 2.216 219.291 282.047 332.417 386.563 444.061 1664.380
13 1.943 192.231 247.243 291.398 338.862 389.265 1458.998
14 1.703 168.510 216.733 255.439 297.046 341.230 1278.959
15 1.493 147.716 189.989 223.918 260.391 299.123 1121.137
16 1.309 129.488 166.544 196.287 228.259 262.211 982.790
16.455 1.232 121.959 145.993 172.066 200.092 229.855 869.965
17 1.175 116.259 137.505 150.833 175.401 201.491 781.488
18 1.076 106.486 131.078 142.063 153.757 176.627 710.011
19 0.986 97.535 120.059 135.423 144.817 154.831 652.667
20 0.903 89.337 109.967 124.040 138.048 145.829 607.222
21 0.827 81.827 100.724 113.613 126.444 139.013 561.622
22 0.757 74.949 92.257 104.063 115.816 127.328 514.413
23 0.694 68.649 84.502 95.316 106.080 116.625 471.172
24 0.635 62.879 77.399 87.304 97.163 106.822 431.567
25 0.582 57.593 70.893 79.965 88.996 97.843 395.290
26 0.533 52.752 64.934 73.243 81.515 89.618 362.063
27 0.488 48.318 59.476 67.087 74.663 82.085 331.629
28 0.447 44.256 54.476 61.448 68.387 75.185 303.753
29 0.410 40.536 49.897 56.282 62.639 68.865 278.220
30 0.375 37.129 45.703 51.551 57.373 63.077 254.833
30.167 0.370 36.588 41.861 47.218 52.551 57.774 235.993
31 0.350 34.635 41.251 47.218 48.133 52.918 224.156
32 0.328 32.428 39.050 43.249 44.087 48.470 207.284

8. 33 0.307 30.361 36.561 40.345 43.445 44.396 195.108
34 0.287 28.426 34.231 37.773 41.127 43.749 185.306
35 0.269 26.615 32.050 35.366 38.506 41.414 173.950
36 0.252 24.919 30.007 33.112 36.052 38.775 162.864
37 0.236 23.330 28.095 31.002 33.754 36.304 152.485
26.304 29.026 31.603 33.990 120.923
27.176 29.589 31.824 88.589
27.703 29.796 57.499
27.897 27.897

9. Tabel Hidrograf Banjir Periode 5 tahun
PERIODE 5TAHUN
t Q
R1 R2 R3 R4 R5
Qtot
62.3373553 70.2830494 72.61309 74.02073 74.538075
0 0.000 0.000 0.000
1 0.035 2.160 0.000 2.160
2 0.183 11.403 2.436 0.000 13.839
3 0.484 30.174 12.856 2.517 0.000 45.547
4 0.965 60.185 34.020 13.283 2.565 0.000 110.053
5 1.649 102.818 67.856 35.148 13.540 2.583 221.946
6 2.555 159.260 115.924 70.106 35.829 13.635 394.753
7 3.699 230.557 179.559 119.767 71.465 36.080 637.428
7.313 4.108 256.099 259.944 185.512 122.089 71.964 895.608
8 3.753 233.952 288.742 268.562 189.108 122.942 1103.306
9 3.290 205.083 263.772 298.314 273.768 190.430 1231.367
10 2.884 179.776 231.223 272.517 304.097 275.682 1263.294
11 2.528 157.591 202.690 238.888 277.800 306.223 1183.192
12 2.216 138.145 177.679 209.410 243.519 279.741 1048.494
13 1.943 121.098 155.753 183.569 213.469 245.221 919.111
14 1.703 106.155 136.533 160.917 187.128 214.961 805.694
15 1.493 93.055 119.685 141.060 164.036 188.435 706.272
16 1.309 81.572 104.916 123.653 143.794 165.183 619.119
16.455 1.232 76.830 91.970 108.395 126.050 144.799 548.043
17 1.175 73.238 86.623 95.019 110.496 126.931 492.307
18 1.076 67.082 82.574 89.494 96.861 111.268 447.279
19 0.986 61.443 75.633 85.311 91.229 97.538 411.154
20 0.903 56.279 69.275 78.140 86.965 91.867 382.526
21 0.827 51.548 63.452 71.572 79.655 87.573 353.800
22 0.757 47.215 58.118 65.556 72.959 80.212 324.060
23 0.694 43.246 53.233 60.045 66.826 73.469 296.820
24 0.635 39.611 48.758 54.998 61.209 67.294 271.870
25 0.582 36.281 44.660 50.375 56.064 61.637 249.017
26 0.533 33.232 40.906 46.140 51.351 56.456 228.085
27 0.488 30.438 37.467 42.262 47.035 51.710 208.913
28 0.447 27.880 34.318 38.710 43.081 47.364 191.352
29 0.410 25.536 31.433 35.456 39.460 43.382 175.267
30 0.375 23.390 28.791 32.475 36.143 39.736 160.535
30.16715 0.370 23.049 26.371 29.746 33.105 36.396 148.666
31 0.350 21.819 25.987 27.245 30.322 33.336 138.709
32 0.328 20.428 24.600 26.848 27.773 30.534 130.184

10. 33 0.307 19.126 23.032 25.415 27.369 27.967 122.910
34 0.287 17.907 21.564 23.796 25.908 27.560 116.736
35 0.269 16.766 20.190 22.279 24.257 26.089 109.582
36 0.252 15.698 18.903 20.859 22.711 24.427 102.598
37 0.236 14.697 17.699 19.530 21.264 22.870 96.059
16.571 18.285 19.909 21.412 76.177
17.120 18.640 20.048 55.808
17.452 18.770 36.222
17.574 17.574

11. Tabel Hidrograf Banjir Periode 10 tahun
PERIODE 10 TAHUN
t Q
R1 R2 R3 R4 R5
Qtot
47.57231 53.63601 55.41416 56.48839 56.883197
0 0.000 0.000 0.000
1 0.035 1.649 0.000 1.649
2 0.183 8.702 1.859 0.000 10.561
3 0.484 23.027 9.811 1.921 0.000 34.759
4 0.965 45.930 25.962 10.136 1.958 0.000 83.986
5 1.649 78.465 51.784 26.823 10.333 1.971 169.376
6 2.555 121.538 88.466 53.501 27.343 10.405 301.253
7 3.699 175.948 137.029 91.399 54.538 27.534 486.448
7.31325 4.108 195.440 198.375 141.572 93.171 54.919 683.477
8 3.753 178.539 220.351 204.951 144.317 93.822 841.980
9 3.290 156.507 201.296 227.656 208.924 145.325 939.709
10 2.884 137.194 176.456 207.969 232.070 210.384 964.074
11 2.528 120.265 154.682 182.306 212.001 233.692 902.945
12 2.216 105.424 135.594 159.810 185.840 213.482 800.151
13 1.943 92.415 118.862 140.089 162.908 187.139 701.413
14 1.703 81.011 104.194 122.802 142.805 164.046 614.859
15 1.493 71.014 91.337 107.649 125.183 143.803 538.986
16 1.309 62.251 80.066 94.365 109.736 126.058 472.476
16.4548 1.232 58.632 70.186 82.720 96.194 110.503 418.235
17 1.175 55.891 66.105 72.513 84.324 96.867 375.700
18 1.076 51.193 63.016 68.297 73.919 84.913 341.338
19 0.986 46.890 57.719 65.105 69.621 74.435 313.769
20 0.903 42.949 52.867 59.632 66.367 70.107 291.922
21 0.827 39.338 48.423 54.620 60.788 66.831 270.000
22 0.757 36.032 44.353 50.028 55.678 61.213 247.304
23 0.694 33.003 40.624 45.823 50.998 56.067 226.516
24 0.635 30.229 37.210 41.971 46.711 51.355 207.476
25 0.582 27.688 34.082 38.443 42.785 47.038 190.036
26 0.533 25.360 31.217 35.212 39.188 43.084 174.062
27 0.488 23.229 28.593 32.252 35.894 39.462 159.430
28 0.447 21.276 26.190 29.541 32.877 36.145 146.029
29 0.410 19.488 23.988 27.058 30.114 33.107 133.754
30 0.375 17.850 21.972 24.783 27.582 30.324 122.511
30.1671 0.370 17.590 20.125 22.700 25.264 27.775 113.453
31 0.350 16.651 19.832 20.792 23.140 25.440 105.855
32 0.328 15.590 18.773 20.489 21.195 23.302 99.349

12. 33 0.307 14.596 17.577 19.396 20.886 21.343 93.798
34 0.287 13.666 16.457 18.160 19.772 21.032 89.086
35 0.269 12.795 15.408 17.002 18.512 19.910 83.626
36 0.252 11.980 14.426 15.919 17.332 18.641 78.297
37 0.236 11.216 13.507 14.904 16.227 17.453 73.307
12.646 13.954 15.193 16.341 58.134
13.065 14.225 15.299 42.589
13.318 14.324 27.643
13.411 13.411

13. Tabel Hidrograf Banjir Periode 25 tahun
PERIODE 25 TAHUN
t Q
R1 R2 R3 R4 R5
Qtot
39.27007 44.27555 45.74338 46.63014 46.95604
0 0.000 0.000 0.000
1 0.035 1.361 0.000 1.361
2 0.183 7.183 1.534 0.000 8.718
3 0.484 19.008 8.099 1.585 0.000 28.693
4 0.965 37.914 21.431 8.367 1.616 0.000 69.329
5 1.649 64.772 42.747 22.142 8.530 1.627 139.817
6 2.555 100.327 73.027 44.164 22.571 8.589 248.679
7 3.699 145.242 113.115 75.448 45.020 22.729 401.554
7.31325 4.108 161.332 163.755 116.865 76.911 45.335 564.198
8 3.753 147.380 181.896 169.183 119.131 77.449 695.039
9 3.290 129.194 166.166 187.926 172.463 119.963 775.713
10 2.884 113.252 145.661 171.675 191.569 173.669 795.825
11 2.528 99.276 127.687 150.490 175.003 192.908 745.364
12 2.216 87.026 111.930 131.920 153.408 176.226 660.510
13 1.943 76.287 98.118 115.641 134.477 154.480 579.004
14 1.703 66.873 86.011 101.371 117.883 135.417 507.555
15 1.493 58.621 75.397 88.862 103.336 118.707 444.923
16 1.309 51.387 66.093 77.897 90.585 104.059 390.020
16.4548 1.232 48.400 57.937 68.284 79.407 91.218 345.246
17 1.175 46.137 54.569 59.858 69.608 79.962 310.134
18 1.076 42.259 52.018 56.378 61.018 70.094 281.768
19 0.986 38.707 47.646 53.743 57.471 61.445 259.011
20 0.903 35.453 43.641 49.225 54.785 57.872 240.976
21 0.827 32.473 39.972 45.087 50.179 55.167 222.880
22 0.757 29.744 36.612 41.297 45.961 50.530 204.145
23 0.694 27.243 33.535 37.826 42.098 46.283 186.985
24 0.635 24.953 30.716 34.647 38.559 42.392 171.267
25 0.582 22.856 28.134 31.734 35.318 38.829 156.871
26 0.533 20.935 25.769 29.067 32.349 35.565 143.685
27 0.488 19.175 23.603 26.623 29.630 32.575 131.607
28 0.447 17.563 21.619 24.385 27.140 29.837 120.544
29 0.410 16.087 19.802 22.336 24.858 27.329 110.412
30 0.375 14.735 18.137 20.458 22.769 25.032 101.131
30.1671 0.370 14.520 16.613 18.739 20.855 22.928 93.654
31 0.350 13.745 16.371 17.163 19.102 21.001 87.381
32 0.328 12.869 15.497 16.913 17.496 19.235 82.011

14. 33 0.307 12.049 14.509 16.011 17.241 17.618 77.429
34 0.287 11.281 13.585 14.990 16.321 17.362 73.539
35 0.269 10.562 12.719 14.035 15.281 16.435 69.032
36 0.252 9.889 11.908 13.141 14.307 15.388 64.633
37 0.236 9.259 11.149 12.303 13.395 14.407 60.514
10.439 11.519 12.542 13.489 47.988
10.785 11.742 12.629 35.157
10.994 11.824 22.818
11.071 11.071

15. Tabel Hidrograf Banjir Periode 50 tahun
PERIODE 50 TAHUN
t Q
R1 R2 R3 R4 R5
Qtot
33.84192 38.155509 39.42045 40.184632 40.46549
0 0.000 0.000 0.000
1 0.035 1.173 0.000 1.173
2 0.183 6.190 1.322 0.000 7.513
3 0.484 16.381 6.979 1.366 0.000 24.727
4 0.965 32.673 18.469 7.211 1.393 0.000 59.746
5 1.649 55.818 36.838 19.081 7.351 1.402 120.491
6 2.555 86.459 62.933 38.059 19.451 7.402 214.305
7 3.699 125.166 97.480 65.020 38.797 19.587 346.049
7.31325 4.108 139.032 141.119 100.711 66.280 39.068 486.211
8 3.753 127.009 156.753 145.798 102.664 66.743 598.967
9 3.290 111.336 143.198 161.950 148.624 103.381 668.489
10 2.884 97.597 125.527 147.945 165.089 149.663 685.821
11 2.528 85.554 110.037 129.689 150.813 166.243 642.336
12 2.216 74.997 96.459 113.685 132.203 151.867 569.210
13 1.943 65.742 84.556 99.657 115.889 133.127 498.970
14 1.703 57.630 74.122 87.359 101.588 116.699 437.398
15 1.493 50.518 64.975 76.579 89.053 102.298 383.423
16 1.309 44.284 56.957 67.129 78.064 89.675 336.109
16.4548 1.232 41.710 49.929 58.846 68.431 78.609 297.524
17 1.175 39.760 47.026 51.584 59.986 68.909 267.265
18 1.076 36.418 44.828 48.585 52.584 60.406 242.820
19 0.986 33.357 41.060 46.314 49.527 52.952 223.209
20 0.903 30.553 37.608 42.421 47.212 49.873 207.667
21 0.827 27.985 34.447 38.855 43.243 47.542 192.072
22 0.757 25.632 31.552 35.589 39.608 43.546 175.927
23 0.694 23.478 28.899 32.598 36.279 39.885 161.139
24 0.635 21.504 26.470 29.857 33.229 36.533 147.594
25 0.582 19.697 24.245 27.348 30.436 33.462 135.187
26 0.533 18.041 22.207 25.049 27.878 30.649 123.824
27 0.488 16.524 20.340 22.943 25.534 28.073 113.415
28 0.447 15.135 18.631 21.015 23.388 25.713 103.882
29 0.410 13.863 17.065 19.248 21.422 23.552 95.150
30 0.375 12.698 15.630 17.630 19.621 21.572 87.152
30.1671 0.370 12.513 14.316 16.148 17.972 19.759 80.708
31 0.350 11.845 14.108 14.791 16.461 18.098 75.303
32 0.328 11.090 13.355 14.575 15.078 16.576 70.675

16. 33 0.307 10.383 12.504 13.798 14.858 15.183 66.726
34 0.287 9.722 11.707 12.918 14.065 14.962 63.374
35 0.269 9.102 10.961 12.095 13.169 14.163 59.490
36 0.252 8.522 10.262 11.324 12.329 13.261 55.699
37 0.236 7.979 9.608 10.603 11.544 12.416 52.149
8.996 9.927 10.808 11.624 41.355
9.294 10.119 10.884 30.297
9.474 10.190 19.664
9.541 9.541
Yang kemudian di buat Grafik HSS Nakayasu
2500
2000
1500
1000
500
0
0
2
4
6
7.31…
9
11
13
15
16.4…
18
20
22
24
26
28
30
31
33
35
37
PERIODE 2 TAHUN
PERIODE 5 TAHUN
PERIODE 10 TAHUN
PERIODE 25 TAHUN
PERIODE 50 TAHUN