bab iii perancang banggunan air

8/18/2019 bab III perancang banggunan air

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BAB III

ANALISIS HIDROLOGI

3.1 PERHITUNGAN CURAH HUJAN SEMENTARA

Data curah hujan yang digunakan adalah data curah hujan dari tiga stasiun hujan di

sekitar daerah aliran Sungai Cibatarua dengan pengamatan 15 (lima belas) tahun. Berikut adalah

data curah hujan yang telah diurutkan.

Tahun

Curah Hujan

Stasiun

Marasari

Stasiun Du!uh

"arinin

Stasiun

#a$i%a!un

1 159 153 13

! 1!" 1#" 1!

3 1$9 199 !$!

" 1"! 1! 13$

5 !53 !"3 1!5

% !15 !5 1!9

# 155 1#5 159

1%3 153 11

9 1## 1!# 1%5

1$ 15# 13% 1!

11 1$9 15 1!#

1! 1! 151 15%

13 15 1%# 1!9

1" 13 1#% 1!5

15 !"# 1#" 19

P&rhitunan Curah Hujan R&n'ana

1. M&t()a Gu*%&$

Tahun Sta Sta Sta CH +,-,n/ +,-,n3 +,-,n0


2/10

Marasar

i

Du!uh

"arinin

#a$i%a!un

i$a2ah

+,

1 159 153 13 15$.$$$ !".93 &39!#.%93 %19#$.!%3

! 1!" 1#" 1! 1%$.$$$ 33.33 &19!.# 111"."$%

3 1$9 199 !$! 1#$.$$$ 1#.!# #5.!#$ 31#.$

" 1"! 1! 13$ 151.333 !$.%"! &3$13.#1# "3531."#"

5 !53 !"3 1!5 !$#.$$$ 1%99.!#! #$$"#.#5!!#5!3.9

#

% !15 !5 1!9 !$9.%%# 19!%.!35 "5"$.!95 3#1$3#9.%11

# 155 1#5 159 1%3.$$$ #.#1% &!1."33 59.53#

1%3 153 11 1%5.%%# $.$1! &$.$$1 $.$$$

9 1## 1!# 1%5 15%.333 9.19 &"!."!1 #95%.!$$

1$ 15# 13% 1! 1"$.333 %"#."!$

&

1%"#3.!3% "1915!.33#

11 1$9 15 1!# 1"$.333 %"#."!$

&

1%"#3.!3% "1915!.33#

1! 1! 151 15% 1%3.$$$ #.#1% &!1."33 59.53#13 15 1%# 1!9 1%$.333 !9.%"! &1%1.3" #.%"#

1" 13 1#% 1!5 1"%.333 3#.$% ş.%$ 1"!9"9.3"1

15 !"# 1#" 19 !$3.333 1"1$."!$ 5!9%9.$9#

199!3.

$

Ju*$ah /04.445 5361.7/4

167163.38

8

7403/7.34

0

Rata-rata +,n 146.55

St).D&9iasi +S: //.714

S!&n&s +Cs 1.878

#urt(sis +C! 3.41

#T/6 /.806

#T 68 /.670

#T 188 3.13

R/6 +Gu*%&$ /1/.43

R68 +Gu*%&$ //6./1/

R188 +Gu*%&$ /35.470

P&rhitunan Stan)ar D&9iasi +S:

Sx=√∑i=1

n

( X − X n)2

n−1

Sx=√ 7351,92615−1 =22,916


3/10

P&rhitunan #(&;&si&n S!&n&ss +Cs

Cs= n

( n−1 )(n−2)Sx3∑ ( X − X n)3

Cs= 15

(15−1 ) x (15−2 ) x 22,9163 x 159153,300=1,090

P&rhitunan #(&;&si&n #urt(sis +C!

Ck = n

2

( n−1)(n−2)(n−3) Sx4∑( X n− X )4

Ck = 15

2

(15−1 )(15−2) (15−3 ) x 22,9164 x 9684329,364=3,618

P&rhitunan Curah Hujan R&n'ana +R/6< R68 )an R 188

KT =−√ 6

π {0,5772+ln [ ln ( T T −1 )]} KT 25=

−√ 6π {0,5772+ ln [ ln( 2525−1 )]}=¿ !'$"5

KT 50=−√ 6

π {0,5772+ ln [ ln( 5050−1 )]}=¿ !'59"

KT 100=−√ 6

π {0,5772+ ln [ ln( 100100−1 )]}=¿ 3'13 R= Xn+ KT . Sx

R25=165,778+22,916 (2,045 )=212,638mm

3

det


4/10

R50=165,778+22,916 (2,594 )=225,212mm

3

det

R100=165,778+22,916 (3,138 )=¿ /35.470mm

3

det

TahunSta Sta Sta CH

L( , +L( : - $( :/ +L( : - $(

Marasari Du!uh"arinin #a$i%a!un i$a2ah +,

1 159 153 13 15$.$$$ !.1#% $.$$15555! &%.3135

! 1!" 1#" 1! 1%$.$$$ !.!$" $.$$$139$1 &1.%39

3 1$9 199 !$! 1#$.$$$ !.!3$ $.$$$!113#3 3.$#3$

" 1"! 1! 13$ 151.333 !.1$ $.$$1!9"!" &".%5%1

5 !53 !"3 1!5 !$#.$$$ !.31% $.$1$$1!$!! $.$$1$

% !15 !5 1!9 !$9.%%# !.3!! $.$11155"$! $.$$11

# 155 1#5 159 1%3.$$$ !.!1! 1.351&$5 &5.15

1%3 153 11 1%5.%%# !.!19 1.1$5"&$5 3.%#5

9 1## 1!# 1%5 15%.333 !.19" $.$$$"##$1 &1.$"""

1$ 15# 13% 1! 1"$.333 !.1"# $.$$"#!%"1 &$.$$$3

11 1$9 15 1!# 1"$.333 !.1"# $.$$"#!%"1 &$.$$$3

1! 1! 151 15% 1%3.$$$ !.!1! 1.351&$5 &5.15

13 15 1%# 1!9 1%$.333 !.!$5 $.$$$1151" &1.!9$

1" 13 1#% 1!5 1"%.333 !.1%5 $.$$!55#$! &$.$$$1

15 !"# 1#" 19 !$3.333 !.3$ $.$$5191 $.$$$#

Ju*$ah /04.4445 33./3463 8.8066415 8.88

Rata-rata +,n /./167183

St).D&9iasi +S: 8.86580534

#(&;isi&n Asi*&tri +G: 8.7154/510

#T/6 /.8//08515

#T68 /.686564430

#T188 /.7406440

R/6 /10.0/6

R68 //.004744

R188 /0/.8/0046

/. M&t()& L( P&rs(n III


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L(arit*a Rata-rata

log ´ X n=

Σ log x

n 33,239

15 !'!159


Sx=√∑i=1n

( log X −log Xn)2

n−1

Sx=√ 0,045561715−1 =0,0570474

P&rhitunan #(&;&si&n Asi*&tri +G:

Gx= n

( n−1 )(n−2)Sx3∑ (log X −log Xn )3

Gx= 15

(15−1 ) x (15−2) x0,05703 x 0,002067=0,9176287

Ta%&$ =a!t(r =r&!u&nsi +# =unsi )ari Niai #(&;isi&n Asi*&tri +G:


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*ntuk +ilai ,-' dilakukan interplasi /

#(&;isi&n # 0eride ulang

!5 5$ 1$$

8.7 /.81 /.07 /.765

1 /.803 /.60/ 3.8//

8.7154/510

/.8//08

5

/.68656

5

/.7406

7

KT 25 !'$1(0,917628714−0,9)

(1−0,9) 2(!'$"3&!'$1)

¿2,02440 #

KT 50

!'"9

(0,917628714−0,9)

(1−0,9) 2(!'5"!&!'"9)

¿2,50575

KT 100 !'95#(0,917628714−0,9)

(1−0,9) 2(3'$!!&!'95#)

¿2,968459

L(arit*a hujan ran'anan )&nan !a$a t&rt&ntu )&nan ru*us >

log R=log Xn+ KT . Sx

log R25=2,2159+2,02440 (0,0570 )=2,331283294


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R25=10(2,331283294)=214,42889

log R50=2,2159+2,50575 (0,0570 )=2,358857117

R50=10(2,358857117)=228,4847

log R100=2,2159+2,968459 (0,0570 )=¿ !.35!53$5

R100=10(2,385253058)=¿ !"!.$!""%5

3. M&t()a L( N(r*a$

ahunSta Sta Sta CH

Log X(Log x -log x)2

(Log x -log x)3

(Log x log x)4Margas

ari DukuhWaringin

Kalibak ung

ila!ah(X)

1159 153 138 150.0000 2.1761 0.0016 -0.0001

2.51398

2

124 174 182 160.0000 2.2041 0.0001 0.0000

1.93239

3109 199 202 170.0000 2.2304 0.0002 0.0000

4.46785

4142 182 130 151.3333 2.1799 0.0013 0.0000

1.67508

5253 243 125 207.0000 2.3160 0.0100 0.0010

0.0001

2

6 215 285 129 209.6667 2.3215 0.0112 0.0012 0.0001


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4

7155 175 159 163.0000 2.2122 0.0000 0.0000

1.92047

8163 153 181 165.6667 2.2192 0.0000 0.0000

1.2221

9 177 127 165 156.3333 2.1941 0.0005 0.0000

2.28294

10157 136 128 140.3333 2.1472 0.0047 -0.0003

2.23396

11109 185 127 140.3333 2.1472 0.0047 -0.0003

2.23396

12182 151 156 163.0000 2.2122 0.0000 0.0000

1.92047

13185 167 129 160.3333 2.2050 0.0001 0.0000

1.40457

14138 176 125 146.3333 2.1653 0.0026 -0.0001

6.53835

15 247 174 189 203.3333 2.3082 0.0085 0.00087.2573

"u#lah24$%&%%%

%%'33&23

$%&4%*

%+&2%'

%%&3

+

,ata-rata (Xn)2&2*

+*

St&D./iasi (Sx)&'4'

3$%

0aktor 0r.ku.nsi (K2)*&'$333

333

0aktor 0r.ku.nsi (K) 2&

0aktor 0r.ku.nsi (K*) 2&33

,22&'%24

$$

,2*&2'4

+2

,*223&2'*

4$2

L(arit*a Rata-rata

log Xn= Σ log ´ X

n

33,23865

15 !'!1591


Sx=√∑i=1n

( log X −log ´ X )2

n−1


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Sx=√ 0.0455616615−1 =0,0570474

=a!t(r =r&!u&nsi

enghitung 4actr 4rekuensi dengan cara interplasi /

KT 25 1'%"(25−20)(50−20) 2(!'$5&1'%")

¿1.708333

L(arit*a hujan ran'anan )&nan !a$a t&rt&ntu )&nan ru*us >

log R=log Xn+ KT . Sx

Y 25=2,21591+1,70833 (0.0570474 )=2,313366203

R25=10(2,313366203)=205,76249

Y 50=2,21591+2,05 (0.0570474 )=2,332857393

R50=10(2,332857393)=215,2075

Y 100=2,21591+2,33 (0.0570474 )=¿ !.3"3$%%1

R100=10(2,348830661)=¿ !!3.!#$1"!

Para*&t&r P&n&ntu J&nis S&%aran

J&nis S&%aran S2arat

+rmal Cs $ Ck 3

KT &$4

KT* *&2$

KT2 *&%4

KT2*&'$

333

KT 2&KT* 2&33


10/10

g +rmal Cs $'#%3 Ck 3

g 0earsn 666 Cs 7 $Ck 1'5Cs 3

Ck 3'#3

8umbel Cs 1'139% Ck 5'"$$!

Dari table diatas diperleh nilai Cs1'139% (ke4. Ske:ness) dan nilai Ck5'"$$! (,e4.

,urtsis)' maka termasuk kedalam jenis sebaran Gumbel .

bab iii perancang banggunan air

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