02 Hidrograf Contoh Soal HSS Nakayasu [PDF]

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Contoh Soal Metode HSS Nakayasu Diketahui: - Luas Daearh Aliran Sungai - Panjang sungai utama - Data intensitas hujan :



A = L =



2400 km2 75 km



waktu (jam)



1



2



3



intensitas (mm/jam)



20



40



10



Ditanya: - Hitung debit maksimum ! - Gambar hidrografnya ! Dijawab: a. Menghitung debit puncak L tg



tr



= 75 km > 15 km = 0,21 x L0,7 = 4.3128284044



jam



waktu kelambatan



3.2346213033



jam



satuan lama hujan (antara 0,5 tg s/d tg, diambil 0,75 tg)



= tg + 0,8 tr = 6.9005254471



jam



waktu puncak



= α x tg = 8.6256568089



jam



waktu saat debit sama dengan 0,3 kali debit puncak (jam), koefisien α diambil nilai 2



=



jam



= 0,75tg =



tp



t0,3



1,5t0,3



12.9384852133



= (1/3.6) x A x R0 x (1/(0.3tp + t0,3)) debit puncak = 62.3296776716 m3/det Jadi debit puncaknya (Q) = 62.3296776716 Qp



m3/det



b. Menggambar grafik hidrograf bagian lengkung naik puncak



0 < t < tp



→



tp



Q



=



Qp x (t/tp)2,4



→ Qp



=



(1/3.6) x A x R0 x (1/(0.3tp + t0,3))



bagian lengkung turun 1



tp < t < (tp+t0,3)



→



Q



=



Qp x 0,3^((t-tp)/t0,3)



bagian lengkung turun 2



(tp+t0,3) < t < ((tp+t0,3) + 1,5t0,3)



→



Q



=



Qp x 0,3^((t-tp+0,5 x t0,3)/(1,5 x t0,3))



bagian lengkung turun 3



((tp+t0,3) + 1,5t0,3) < t



→



Q



=



Qp x 0,3^((t-tp+1,5 x t0,3)/(2 x t0,3))



tp+t0,3



15.526182256



1,5t0,3



12.938485213



tp+t0,3+1,5t0,3



28.464667469



untuk selanjutnya lihat Tabel Perhitungan



Tabel Perhitungan No



t (jam)



Q (m3/det)



20 mm



akibat hujan 40 mm



10 mm



Q total (m3/det)



1 2



0 1



0.0000 0.6045



0.0000 12.0895



0.0000 0.0000



0.0000 0.0000



0.0000 12.6940



3



2



3.1904



63.8087



24.1790



0.0000



91.1781



4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22



3 4 5 6 6.9005254471 7 8 9 10 11 12 13 14 15 15.526182256 16 17 18 19 20



8.4425 16.8392 28.7677 44.5595 62.3297 61.4702 53.4621 46.4972 40.4397 35.1713 30.5893 26.6042 23.1383 20.1239 18.6989 17.8924 16.3025 14.8540 13.5341 12.3315



168.8491 336.7842 575.3547 891.1908 1246.5936 1229.4046 1069.2415 929.9440 808.7938 703.4266 611.7864 532.0847 462.7664 402.4786 373.9781 357.8474 326.0508 297.0794 270.6823 246.6307



127.6173 337.6982 673.5683 1150.7095 1782.3816 2493.1871 2458.8092 2138.4831 1859.8881 1617.5876 1406.8532 1223.5727 1064.1694 925.5327 804.9572 804.9572 747.9561 715.6948 652.1015 594.1588



6.0447 31.9043 84.4245 168.3921 287.6774 445.5954 623.2968 614.7023 534.6208 464.9720 404.3969 351.7133 305.8932 266.0424 231.3832 231.3832 201.2393 186.9890 178.9237 163.0254



310.9536 723.2259 1362.1154 2254.8519 3378.9822 4229.6573 4204.8096 3729.6266 3243.7423 2821.1576 2453.6258 2133.9750 1855.9673 1614.1776 1429.0173 1412.0801 1291.5487 1214.6173 1115.2417 1016.1465



23 24 25



21 22 23



11.2358 10.2375 9.3278



224.7163 204.7490 186.5560



541.3646 493.2615 449.4326



148.5397 135.3412 123.3154



925.8564 843.5891 768.6317



26 27



24 25



8.4990 7.7438



169.9795 154.8759



409.4981 373.1120



112.3581 102.3745



700.3347 638.1062



lengkung naik



puncak



lengkung turun I



lengkung turun II



28



26



7.0557



141.1144



339.9590



93.2780



581.4070



29 30 31 32 33 34 35 36



27 28 28.464667469 29 30 31 32 33 34



6.4288 5.8575 5.6097 5.4040 5.0397 4.6999 4.3831 4.0877 3.8121



128.5756 117.1510 112.1934 108.0791 100.7934 93.9989 87.6624 81.7530 76.2420



309.7518 282.2287 257.1512 224.3868 216.1582 201.5869 187.9978 175.3247 163.5060



84.9897 77.4380 70.5572 58.5755 56.0967 54.0396 50.3967 46.9994 43.8312



529.7459 482.6752 445.5114 396.4454 378.0880 354.3252 330.4400 308.1648 287.3913



37 38



35 36



3.5551 3.3155



71.1025 66.3094



152.4840 142.2049



40.8765 38.1210



268.0181 249.9508



39 40



37 38



3.0920 2.8835



61.8395 57.6708



132.6188 123.6789



35.5512 33.1547



233.1015 217.3880



41 42



39 40



2.6892 2.5079



53.7832 50.1577



115.3417 107.5664



30.9197 28.8354



202.7338 189.0674



43 44 45



41 42 43



2.3388 2.1812 2.0341



46.7765 43.6233 40.6826



100.3153 93.5530 87.2465



26.8916 25.0788 23.3882



176.3222 164.4362 153.3515



46



44



1.8970



37.9402



81.3652



21.8116



143.0140



47



45



1.7691



35.3826



75.8803



20.3413



133.3733



48 49 50 51 52 53 54 55 56 57 58 dst



46 47 48 49 50 51 52 53 54 55 56



1.6499 1.5387 1.4349 1.3382 1.2480 1.1639 1.0854 1.0122 0.9440 0.8804 0.8210 dst



32.9974 30.7731 28.6986 26.7640 24.9599 23.2773 21.7082 20.2448 18.8801 17.6074 16.4205 dst



70.7652 65.9949 61.5461 57.3973 53.5281 49.9197 46.5546 43.4163 40.4896 37.7602 35.2148 dst



18.9701 17.6913 16.4987 15.3865 14.3493 13.3820 12.4799 11.6387 10.8541 10.1224 9.4400 dst



124.3826 115.9979 108.1784 100.8860 94.0852 87.7429 81.8281 76.3120 71.1678 66.3703 61.8963 dst



dst



lengkung turun III



Grafik Hidrograf HSS Nakayasu 4500.0000



Debit Q (m3/det)



4000.0000



Q (m3/det) akibat hujan 20 mm akibat hujan 40 mm akibat hujan 10 mm Q total (m3/det)



3500.0000



3000.0000



2500.0000



2000.0000



1500.0000



1000.0000



500.0000



0.0000 1



2



3



4



5



6



7



8



9



10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



Waktu t (jam)