Contoh Perhitungan HSS Nakayasu.docx

(1)

a)

a) PerhitPerhitungaungan n Debit Debit BanjiBanjirr(Metode Nakayasu)(Metode Nakayasu) Waktu konsentrasi :

Waktu konsentrasi :

Jika nilai L < 15 Km

Jika nilai L < 15 Km maka,maka,

7 7 .. 0 0 * * 21 21 .. 0 0 LL t t _g_g

=

!.10) !.10) Jika nilai L " 15 Km

Jika nilai L " 15 Km maka,maka,

L L t t _g_g

==

00..!!

++

00..05#05#**

!.11) !.11)

Dalam $erhitungan ini nilai L < 15 Km, maka %aktu Dalam $erhitungan ini nilai L < 15 Km, maka %aktu

k&n'entra'in(a aalah * k&n'entra'in(a aalah *

Jam

L

tg

+7+

,,

0

27

27 ,,

2

21

21 ,,

0

21

21 ,,

0

7 7 ,, 0 0 7 7 .. 0 0 = = × × = = × × = = g g g g r r

t t

s

d

t t

==

00..55**  !.12) !.12)

Diambil nilai tr - 0,75 tg, 'ehingga nilai tr * Diambil nilai tr - 0,75 tg, 'ehingga nilai tr *

tr

tr - - 0,75 0,75 tgtg - 0,75  0,+7+ - 0,75  0,+7+

(2)

- 0,2#0 jam

Tenggang waktu dari permulaan hujan sampai puncak banjir (jam) : r g p

t

T

=

+

0 .

#

*

!.1+)

/ehingga nilai tenggang %aktu ari $ermulan hujan 'am$ai $unak banjir ialah 'ebagai berikut *

jam t t T _p _g _r 5 , 0 ) 2#0 , 0 # , 0  +7+ , 0 * # . 0

=

×

+

=

+

=

Waktu yang diperlukan untuk penurunan debit puncak sampai 30 % dari debit puncak (jam) :

g

t T ₀_.₊

=

α *

!.1!) Dimana *

α - 2, untuk aerah $engaliran bia'a

- 1.5 untuk aerah $engaliran bia'a, untuk bagian naik hir&gra3 (ang lambat an bagian menurun (ang e$at - +, untuk bagian naik hir&gra3 (ang e$at an bagian

menurun (ang lambat

4tau bi'a iari engan $er'amaan berikut *

Tg L A )0,25  !7 , 0

×

=

α !.15)

(3)

Perhitungan nilai 0+ * Jam t T _g #+2 , 0 +7+ , 0 #+27 , 1 * + . 0

=

∗

=

α

Debit puncak banjir akibat hujan satuan : ) * + . 0  *  . + * + . 0 T T R A Qp p o

+

=

!.1) Perhitungan nilai 6$ * . et  ++ , 0 ) #+2 , 0 5 , 0 * + . 0  *  . + 1 * 5 , 1 ) * + . 0  *  . + * + + . 0 m T T R A Qp p o

=

+

=

+

=

ersamaan bagian lengkung naik (rising limb) pada

hidrogra! satuan "akayasu adalah :

! . 2 *

_













=

p p a T t Q Q !.17) Perhitungan nilai 6a * 0 5 , 0 * ++ , 0 * ! . 2 ! . 2

=













=













=

t T t Q Q p p a

(4)

Sehingga, 0 < t < tp , maka nilai t untuk Qa adalah t = 0 - 0,6

ersamaan bagian lengkung turun (decreasing limb) pada

hidrogra! satuan "akayasu adalah :

ntuk * 1 * + . 0 Q_p

<

Q_d → + . 0 + . 0 * 1 T T t p d p Q Q −

=

!.1#) p d p Q Q Q 0.+* * + . 0 2

<

₂

<

→ + . 0 + . 0 * 5 . 1 * 5 . 0 2 *0.+ T T T t p d p Q Q + −

=

_!.1) p d Q Q ₊

<

0.+2* → + . 0 + . 0 * 2 * 5 . 1 + *0.+ T T T t p d p Q Q + −

=

!.20) Perhitungan * 0#+0 , 0 + . 0 * +! , 0 + . 0 * #+ , 0 5 , 0 1 + . 0

=

− − t T T t p d p Q Q

Sehingga, tp < t < (tp+T03) , maka nilai t untuk Qd1 adalah t = 0,75 - 1,25 1!7 , 0 + . 0 * +! , 0 + . 0 * #+2 , 0 * 5 . 1 #+2 , 0 * 5 . 0 5! , 0 * 5 . 1 * 5 . 0 2 + . 0 + . 0

=

+ − + − t T T T t p d p Q Q

(5)

Sehingga, (tp+T03) < t < (tp+T03) + (1,5  T03) , maka nilai t untuk Qd2 adalah t = 1,5 - 2,25

001# , 0 + . 0 * +! , 0 + . 0 * #+2 , 0 * 2 #+2 , 0 * 5 . 1  , 0 * 2 * 5 . 1 + + . 0 + . 0

=

+ − + − t T T T t p d p Q Q

Sehingga, t ! (tp+T03) + (1,5  T03) , maka nilai t untuk Qd3 adalah t = 6,25 - 2"

#e$da%a$kan hitungan &aktu Qp, Qa, Qd1, Qd2 dan Qd3' idapatkan tael %e$ta g$a*k hid$g$a nakaa%u, dimana nantina tael ini akan men.adi a/uan untuk menghitung deit an.i$ e$da%a$kan metde hidg$a nakaa%u'

Tael "'5 $dinat id$g$a akaa%u

Waktu #idrogra! ($am) Debit aluran & (m3'detik) et Waktu #idrogra! ($am) Debit aluran & (m3'detik) et 4 B 8 4 B 8 0.00 0.0000 6a 12.00 0.0000 6+ 0.25 0.07# 12.25 0.0000 0.50 0.!150 12.50 0.0000

(6)

0.0 0.++ 6$ 12.75 0.0000 0.75 0.!#+! 61 1+.00 0.0000 1.00 0.+111 1+.25 0.0000 1.25 0.200+ 1+.50 0.0000 1.50 0.1!7 62 1+.75 0.0000 1.75 0.10! 1!.00 0.0000 2.00 0.0#15 1!.25 0.0000 2.25 0.00# 1!.50 0.0000 2.50 0.0!#0 6+ 1!.75 0.0000 2.75 0.0+#5 15.00 0.0000 +.00 0.0+0 15.25 0.0000 +.25 0.02!# 15.50 0.0000 +.50 0.01 15.75 0.0000 +.75 0.010 1.00 0.0000

(7)

!.00 0.012# 1.25 0.0000 !.25 0.010+ 1.50 0.0000 !.50 0.00#2 1.75 0.0000 !.75 0.00 17.00 0.0000 5.00 0.005+ 17.25 0.0000 5.25 0.00!+ 17.50 0.0000 5.50 0.00+! 17.75 0.0000 5.75 0.0027 1#.00 0.0000 .00 0.0022 1#.25 0.0000 .25 0.001# 1#.50 0.0000 .50 0.001! 1#.75 0.0000 .75 0.0011 1.00 0.0000 7.00 0.000 1.25 0.0000 7.25 0.0007 1.50 0.0000

(8)

7.50 0.000 1.75 0.0000 7.75 0.0005 20.00 0.0000 #.00 0.000! 20.25 0.0000 #.25 0.000+ 20.50 0.0000 #.50 0.0002 20.75 0.0000 #.75 0.0002 21.00 0.0000 .00 0.0002 21.25 0.0000 .25 0.0001 21.50 0.0000 .50 0.0001 21.75 0.0000 .75 0.0001 22.00 0.0000 10.00 0.0001 22.25 0.0000 10.25 0.0001 22.50 0.0000 10.50 0.0000 22.75 0.0000 10.75 0.0000 2+.00 0.0000

(9)

11.00 0.0000 2+.25 0.0000

11.25 0.0000 2+.50 0.0000

11.50 0.0000 2+.75 0.0000

11.75 0.0000 2!.00 0.0000

Bera'arkan tabel !.5 ia$atkan gra3ik $erbaningan antara %aktu engan ebit

9ambar !.2 9ra3ik :ir&gra3 Debit Banjir

0 * + 3 , -. /  1 *0 ** *+ *3 *, *-*. */ * *1 +0 +* ++ +3 +, 0 0* 0+ 03 0, 0-0. 0/

Waktu ($am)

Debit (m2'detik)

(10)

$am

456D 789"

&+ &- &*0 &+0 &-0 &*00 &*000

4 B 8 D ;  9 : 0.00 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.25 1.25 2.72 +.757 !.02 7.51# 10.+1## 2#.7#!0 0.50 11.+21 1.!##5 22.1+2 2#.15+ !!.#0+0 0.1!5 170.005 0.0 22.2!+0 +2.+772 !+.52++ 5.7#5 #7.25 11.+## +++.17! 0.75 2!.0+ +5.0277 !7.0#5 1.!+52 5.172 12.!+! +1.20+ 1.00 20.++7 2.01 +.72+ 51.177 #0.!!#5 10.+#1! +05.2#70 1.25 1.+712 2+.#20 +2.0+1! !1.71+ !.752 ##.0!! 2!5.7+1 1.50 1+.#+ 1.202 2.775 +!.+!# 5!.1+10 7+.577 205.!077 1.75 11.7#7 17.1722 2+.0#22 +0.11!5 !.12 +.!!11 177.05#7 2.00 10.2#!2 1!.7+ 20.11#1 2.2! !0.7 55.221 15!.+1++ 2.25 .0!12 1+.157# 17.#55 2+.072 +5.7!2 !#.0!2 1+5.!1

(11)

2.50 7.!! 11.51+ 15.5+2 20.272! +1.!0! !2.70+5 11.175 2.75 .!700 .!1!5 12.5+1 1.50 25.57+ +!.70 7.022 +.00 !.77# .527 .+!+5 12.1##2 1#.##1 25.700 71.+20 +.25 +.50!0 5.0 .#!#+ #.+25 1+.#+7 1#.#101 52.!#!7 +.50 2.!25 +.#!2! 5.122 .7+2 10.!27 1!.17!7 +.5!! +.75 2.051+ 2.#1# !.0052 5.222 #.0##2 10.+ +0.#1 !.00 1.072 2.++52 +.1+5 !.0##7 .++05 #.0+ 2+.7+ !.25 1.2#5 1.#!22 2.!7+2 +.22+ !.0! .7#1 1#.11 !.50 1.00! 1.!50 1.0 2.522 +.50 5.+#7 15.01 !.75 0.#10! 1.1752 1.57! 2.05+ +.177+ !.+15 12.0+0! 5.00 0.521 0.!!# 1.27 1.!# 2.5511 +.!51 .5+# 5.25 0.5252 0.700 1.01#+ 1.+25 2.0!#7 2.7#1 7.7!70 5.50 0.!2++ 0.117 0.#1# 1.055 1.!5 2.2++ .217+ 5.75 0.+!1 0.!27 0.50 0.#5# 1.+222 1.7!2 !.00

(12)

.00 0.270 0.+7+ 0.5+07 0.#+ 1.02# 1.!!1! !.005! .25 0.22+! 0.+207 0.!277 0.5550 0.#5! 1.15#! +.215! .50 0.1#12 0.25+ 0.+!51 0.!!7+ 0.#7 0.+1+ 2.5#1 .75 0.1!7! 0.2100 0.27# 0.+0# 0.55+ 0.7!2 2.07+2 7.00 0.1202 0.1705 0.2257 0.215 0.!!1 0.0+0 1.5+ 7.25 0.0#! 0.1+#7 0.1#+1 0.2+5# 0.+5 0.!#5# 1.++#0 7.50 0.0#0 0.11++ 0.1!## 0.112 0.207 0.+17 1.075! 7.75 0.0 0.02 0.121! 0.155+ 0.2+52 0.+12 0.#!# #.00 0.0557 0.075 0.0! 0.12 0.107 0.2557 0.5# #.25 0.0! 0.0++ 0.0#17 0.10+5 0.1550 0.2071 0.502 #.50 0.0+! 0.052# 0.075 0.0#51 0.12+ 0.1#1 0.!51! #.75 0.0++ 0.0!!+ 0.051 0.0702 0.10++ 0.1+ 0.+!1 .00 0.02# 0.0+75 0.0!70 0.05#+ 0.0#! 0.111# 0.2!1 .25 0.0252 0.0+21 0.0+7 0.0!## 0.0701 0.017 0.2+7

(13)

.50 0.0222 0.0277 0.0++# 0.0!11 0.05#2 0.0755 0.12 .75 0.01# 0.02!2 0.021 0.0+! 0.0!#7 0.02 0.157 10.00 0.017# 0.021! 0.025+ 0.0+00 0.0!10 0.0522 0.1277 10.25 0.01+ 0.012 0.022+ 0.021 0.0+! 0.0!+# 0.10!! 10.50 0.0150 0.017+ 0.01 0.022 0.0+00 0.0+71 0.0#5# 10.75 0.01!0 0.015 0.017 0.020+ 0.020 0.0+1# 0.070# 11.00 0.01+2 0.01!7 0.01! 0.01#+ 0.022# 0.0275 0.05## 11.25 0.012 0.01+# 0.0151 0.017 0.020+ 0.02!0 0.0!1 11.50 0.0121 0.01+0 0.01!1 0.015+ 0.01#+ 0.0212 0.0!1! 11.75 0.0117 0.012! 0.01++ 0.01!+ 0.01 0.010 0.0+52 12.00 0.011+ 0.0120 0.012 0.01+! 0.015+ 0.0172 0.0+02 12.25 0.0111 0.011 0.0121 0.012# 0.01!+ 0.015# 0.022 12.50 0.010 0.011+ 0.0117 0.0122 0.01+! 0.01!7 0.02+0 12.75 0.0107 0.0110 0.011! 0.011# 0.0127 0.01+7 0.020!

(14)

1+.00 0.010 0.010# 0.0111 0.011! 0.0122 0.01+0 0.01#! 1+.25 0.010! 0.0107 0.010 0.0111 0.011# 0.012! 0.017 1+.50 0.010! 0.0105 0.0107 0.010 0.011! 0.011 0.015! 1+.75 0.010+ 0.010! 0.010 0.0107 0.0111 0.0115 0.01!+ 1!.00 0.0102 0.010+ 0.0105 0.010 0.010 0.0112 0.01+5 1!.25 0.0102 0.010+ 0.010! 0.0105 0.0107 0.0110 0.012# 1!.50 0.0101 0.0102 0.010+ 0.010! 0.010 0.010# 0.0122 1!.75 0.0101 0.0102 0.0102 0.010+ 0.0105 0.010 0.011# 15.00 0.0101 0.0101 0.0102 0.0102 0.010! 0.0105 0.011! 15.25 0.0101 0.0101 0.0102 0.0102 0.010+ 0.010! 0.0112 15.50 0.0101 0.0101 0.0101 0.0102 0.0102 0.010+ 0.010 15.75 0.0100 0.0101 0.0101 0.0101 0.0102 0.010+ 0.0107 1.00 0.0100 0.0101 0.0101 0.0101 0.0102 0.0102 0.010 1.25 0.0100 0.0100 0.0101 0.0101 0.0101 0.0102 0.0105

(15)

1.50 0.0100 0.0100 0.0100 0.0101 0.0101 0.0101 0.010! 1.75 0.0100 0.0100 0.0100 0.0101 0.0101 0.0101 0.010+ 17.00 0.0100 0.0100 0.0100 0.0100 0.0101 0.0101 0.0102 17.25 0.0100 0.0100 0.0100 0.0100 0.0101 0.0101 0.0102 17.50 0.0100 0.0100 0.0100 0.0100 0.0100 0.0101 0.0102 17.75 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0101 1#.00 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0101 1#.25 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0101 1#.50 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0101 1#.75 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0101 1.00 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 1.25 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 1.50 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 1.75 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100

(16)

20.00 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 20.25 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 20.50 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 20.75 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 21.00 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 21.25 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 21.50 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 21.75 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 22.00 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 22.25 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 22.50 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 22.75 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 2+.00 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 2+.25 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100

(17)

2+.50 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100

2+.75 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100

2!.00 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100

9ambar !.+ :ir&gra3 Banjir Peri&e lang 9abungan

0 * + 3 , - . /  1 *0 ** *+ *3 *, *- *. */ * *1 +0 +* ++ +3 +, 0 ,0 0 *+0 *.0 +00 +,0 +0 3+0 3.0

2 ahun 5 ahun 10 ahun 20 ahun 50 ahun 100 ahun

1000 ahun

Waktu ($am)

(18)

Bera'arkan tabel ter'ebut ia$atkan ebit mak'imum ebit renana) (ang

terjai engan kala ulang 50 tahun 'ebe'ar 5,17 m+_etik.

abel !.7 abel :ir&gra3 /atuan =aka(a'u

"o eriode 7lang T (jam) & ;aks (m3'dt) 4 B 8 D 1 2 0.75 2!.0! 2 5 0.75 +5.02# + 10 0.75 !7.0#7 ! 20 0.75 1.!+5 5 50 0.75 5.17