pembahasan hidrologi insyaallah yovi

7/23/2019 Pembahasan Hidrologi Insyaallah Yovi

1/26

BAB III

PENYELESAIAN SOAL

A. PerhitunganLuas DaerahdenganMetodePoligonThiessen

KoefisienThiessen (n) =An A

Ket :

An : Luaspoligon

A : Luaspoligon total

ContohperhitungankoefisienThiesssenpada STA A :

A =A A

A

A =8,3142

85,2252

A = 0,0!"

YOVI DWIANA

11!"1111#


2/26

Ta$el .A.1 Perhitunganluasdaerahdan%oe&isienThissen

B.

Perhitungan'urah(u)an *ata+*ata denganMetodePoligonThiessen

Curah#u$an %ata %ata ( % ) = % A A& % ' ' & %C C & % & %

Ket :

% : #u$an rata rata AS padasuatuhari (**)

%+%n : #u$an -ang ter.atatpadastasiun + sa*paistasiun n (**)

Contohperhitungan*en.arihu$an rata rata di Stasiun A padatahun+!! :

% = % A A& % ' ' & %C C & % & % % = (+/0,+00,10"!) & (2,+00,+2++) & (,+00,2/3) & (14,"00,0/++) &

(2/,00,2322)

% = 41,!!**

YOVI DWIANA

11!"1111#

5o

Stasiun

#u$anKode

STA

Luas

6oligon

(.*2)

Skala

7arak

Luas

aerah

(k*2)

Koefissien

Thiessen

+ 8599ALAA

3,/ +: 1000 3,1+/2 0,0!"

2 8T%'

+,4 +: 1000 +3,4414 0,2+!!

1 KTA';8ln%) (ln%>ln%)2 (ln%>ln%)1 (ln%>ln%)/

+1,//1+ >0,/422 0,20/4 >0,024 0,0/+3

21,"+3/ >0,2!" 0,0!"! >0,02+2 0,004

11,"20 >0,2""/ 0,0!+0 >0,0+3 4,01//>01

/1,!/"2 >0,+/2 0,0222 >1,1+3+>01 /,/+>0/

41,313+ >0,04!1 1,23+2>01 >+,3!4>0/ +,0!"">04

"1,313+ >0,04!1 1,23+2>01 >+,3!4>0/ +,0!"">04

!1,3"2+ >0,0112 0,00++ >1,"!44>04 +,2220>0"

3/,031 0,+334 0,0144 0,00"! 0,00+1

/,1"2+ 0,/""! 0,2+!3 0,+0+! 0,0/!/

+0/,412" 0,"1!1 0,/0"+ 0,2433 0,+"/

;u5la 13,414 +,0/+4 0,2103 0,2""

YOVI DWIANA

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9/26

$/. Si56angan$a%u 7

ln% =

lnRlnR2

= 1,0415

101

= 0,1/02

8/. Perhitungan%oe&isien%e5en8engan -'s/ 7

Cs(ln%) =

lnRlnR 3

n .

=10x (0,2308)

9x 8x0,34023

= 0,3+/2

d/. Perhitungan%oe&isien %urtosis -'%/

Ck(ln%) =

lnR lnR4

(n22n+3) .

=(1022.10+3)x 0,2669

(9 ) (8 ) (7 ) .0,34024

= 1,23+!

YOVI DWIANA

11!"1111#


10/26

arihasilperhitungan, didapatkankoefisienke*en.engan (Cs) dankoefisien kurtosis (Ck)

pada :

+ 6erhitunganCurah#u$an %ata>rata non logarit*ik

Cs = +,1+!

Ck = /,0+1

2 6erhitunganCurah#u$an %ata>rata Logarit*ik

Cs= 0,3+/2

Ck=1,23+!

8akadapatdisi*pulkan?ah@a*etode -ang paling *endekatiadalah*etode Log 6earson


11/26

D. Pengu)ianDistri$usi

1. 2)i S5irno9 ol5ogro9

Ta$el .D.1.2)i S5irno9 ol5ogro9

5* terurut

-55/Y : log*

P= m

n+1

-2/F

=1F

= 0,1

7u*lahtahunpenga*atan = +0tahun

= 4 F = 0,04

kritik =0,/+ (darita?el)

Che.king :

YOVI DWIANA

11!"1111#


12/26

*aksBkritik

0,1B 0,/+ KGGG

0. 2)i 'hi uadrat

22

2 )(cr

F

FFx

E

OEx

=

k = K> (6 & +)

i*ana:

2= #arga Chi Kuadratterhitung

H = Hrekuensi -ang diharapkan

H = Hrekuensi -ang ter?a.a

.r2 = #arga Chi Kuadratkritis

k = era$atKe?a?asan

K = 'an-akn-aKelas

6 = 'an-akn-aketerikatanuntuku$i .hi kuadrat

a 'an-akn-a data Curah#u$an= +0

YOVI DWIANA

11!"1111#


13/26

di?agi*en$adi / kelas (K = /)

F24/

F+006r ==obabilitasNilai

Ta$el .D.0.Ta$el2)i 'hi uadrat

6ro?a?ilitas

(F)H H (H>H)

(H>>

H)2

H

2

HH

):(

6ro?a?ilitasI24 2,4 2 0,4 0,24 0,+

24B6ro?a?ilitasI40 2,4 1 >0,4 0,24 0,+

40B6ro?a?ilitasI!4 2,4 1 >0,4 0,24 0,+

!4B6ro?a?ilitasI+00 2,4 2 0,4 0,24 0,+

;u5lah +0 +0 0 + 0,/

k = / J ( 2 &+) = +

5ilai Chi Kuadratterhitung (2) = 0,/

'erdasarkanTa?el, didapat: .r2 = 0,!"/4

Che.king :

2 I .r2

0,/ I 0,!"/4 KGGG

YOVI DWIANA

11!"1111#


14/26

E. Perhitungan(u)an*an8angandenganMetode Log Pearson III

a/. *ata rata Data 7

Curah#u$an %ata %ata (log % ) = log%

n

=16,9173

10

= +,"+! **

Ta$el .E.1.PerhitunganMetode Log Pearson III

5o % Log % (Log % > Log %) (Log % > Log %)2 (Log % > Log %)1

+ 1+,23// +,/41 >0,+"/ 0,013" >0,00!"

2 1!,2!30 +,4!+4 >0,+201 0,0+/4 >0,00+!

1 1!,"!/2 +,4!"0 >0,++4! 0,0+1/ >0,00+4/ /2,144 +,"2!0 >0,0"/3 0,00/2 >0,0001

4 /",/144 +,""" >0,02/ 0,000" 0,0000

" /",/144 +,""" >0,02/ 0,000" 0,0000

! /!,4"40 +,"!!1 >0,0+// 0,0002 0,0000

3 4,1!4/ +,!!1" 0,03+ 0,00"! 0,0004

!3,/+3 +,3// 0,202! 0,0/++ 0,0031

+0 2,! +,"34 0,2!"3 0,0!"" 0,02+2

7u*lah 4+,32"2 +",+! 0,0000 0,+"/ 0,0+3

$/. Standarde9iasi data 7

Std (log (%)) =+n

))%log()%(log( 2

YOVI DWIANA

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15/26

= 0,1477

101

= 0,+/!!

8/. oe&isiens%=enessdata 7

Cs =

1

1

)))%(log(std)(2n)(+n(

))%log()%(log(n

=

1

1

)+/!!,0)(2+0)(++0(

)0,03+(+0

= 0,021!

d/.(u)an*an8angan -*T/ 7

Log t = log % & std(log(%))9

%T = +0log t

ari Ta?el, didapat:

;ntuk T = 4 dan, Cs = 0,021! *aka 9 = 0,3/+

;ntuk T = 24 dan, Cs = 0,021! *aka 9 = +,!4

;ntuk T = 40 dan, Cs = 0,021! *aka 9 = 2,+0+

;ntuk T = +00 dan, Cs = 0,021! *aka 9 = 2,1/1

#u$an%an.angan 4 tahunanLog t = +,"/"0 & 0,+++0,3/+

= +,30"!

%4 = +0 +,30"!

= "/,0!"! **

#u$an%an.angan 24 tahunanLog t = +,"/"0 & 0,+++ +,!4

= +,322

%24 = +0+,322

YOVI DWIANA

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16/26

= 4,3/1**

#u$an%an.angan 40 tahunan

Log t = +,"/"0 & 0,+++ 2,+0+

= 2,0/!4

%24 = +02,0/!4

= +++,44!3 **

#u$an%an.angan +00 tahunanLog t = +,"/"0& 0,+++ 2,1/1

= 2,01!

%+00 = +02,01!

= +2/,0!4 **

>. Menghitung De$it *an8angan


17/26

+0 F ta*andanke?un (C/= 0,1+)

. = (C+ F) & (C2 F)&(C1 F)&(C/ F)

= (0,4+ 0,14) & (0," 0,+4) & (0,4 0,/0) & (0,1+ 0,+0)

= 0,/4

A =34,2242 k*2

Ta?el 1H+6erhitungan2

/0F

7a* ke>1

/0 F

7a* ke>/

+0F

+ 4 "/,0!"! 4!,""0 4,!"" 21,0"!" 21,0"!" 4,!""

2 24 4,3/1 3",134 3,"13" 1/,44/1 1/,44/1 3,"13"

1 40 +++,44!3 +00,/020 +0,0/02 /0,+"03 /0,+"03 +0,0/02

/ +00 +2/,0!4 +++,"!+" ++,+"!2 //,""3" //,""3" ++,+"!2

Ket :#u$anefektif -ang ter$adihan-alah 0 F dengan rata>rata hu$an -ang ter$adisela*a

/ $a* ?erturut>turutdenganpe*?agian +0 F, /0F, /0F, dan +0F

a e?it 4 tahunan


18/26

4 =c x I5x A

3,6

=

0,4995x 23,0676x 85,2252

3,6

= 2!2,!!// *1Ms

? e?it 24 tahunan


19/26

a e?it 4 tahunan

ata : ran.angan= 4 = 2!2,!!//*1Ms

itentukan :

?+ =4 * < =0,0003 *

?2 =+/ * * = +,4

h+ = 1 * n = 0,024

h2 = / *

t =1

n N ( b2+m. h2 )h2+(b1+m . h1 ) h1

(2.2 )+ (2h22 )+b1+(2h12) O2M1 I PN?2& *h2) h2& (?+& *h+)

h+O

t =1

0,025 N (14+1,5.4 )4+ (5+1,5.3 )3

(2.2 )+(2.4 2 )+5+(2.32) O2M1 0,0008 PN(+/&+,4/)/&

(4&+,41)1O

t =1//,"!1*1Ms

'he8%ing 7

?teoritis @ ?ran8angan

1//,"!1 *1Ms Q 2!2,!!// *1Ms o%

? e?it 24tahunan

ata : ran.angan= 24 =/03,"040*1Ms

itentukan :

YOVI DWIANA

11!"1111#


20/26

?+ =" * < =0,0003 *

?2 = +3 * * = +,4

h+ = / * n = 0,024

h2 = / *

t =1

n N ( b2+m . h2 )h2+(b1+m . h1 ) h1

(2.2 )+ (2h22 )+b1+(2h12) O2M1 I PN?2& *h2) h2& (?+&

*h+) h+O

t =1

0,025 N (18+1,5.4 )4+ (4+1,5.4 )4

(2.2 )+(2.4 2 )+6+(2.4 2) O2M1 0,0008 PN(+3&+,4/)/&

("&+,4/)/O

t = /13,1/!*1Ms

'he8%ing 7


/13,1/!*1Ms Q /03,"040*1Ms o%

. e?it 40tahunan

ata : ran.angan= 40=/!/,0+/*1Ms

itentukan :

?+ =4 * < =0,0003 *

?2 = +! * * = +,4

YOVI DWIANA

11!"1111#


21/26

h+ = / * n = 0,024

h2 = 4 *

t =1

n N (b2+m . h2 )h2+(b1+m . h1 ) h1(2.2 )+ (2h22 )+b1+(2h12) O

2M1 I PN?2& *h2) h2& (?+&

*h+) h+O

t =1

0,025

N

(17+1,5.5 )5+(5+1,5.4 )4

(2.2 )+(2.6 2 )+6+(2.62) O

2M1

0,0008 PN(+!&+,44)4& (4&+,4/)/O

t = 413,/+3! *1Ms

'he8%ing 7

?teoritis @?ran8angan

413,/+3!*1Ms Q /!/,0+/*1Ms o%

d e?it tahunan +00 tahun

ata : ran.angan= +00=423,20"1*1Ms

itentukan :

?+ =1 * < =0,0003 *

?2 = +3 * * = +,4

h+ = 4 * n = 0,024

h2 = 4 *

YOVI DWIANA

11!"1111#


22/26

t =1

n N ( b2+m . h2) h2+(b1+m . h1 ) h1

(2.2)+ (2h22 )+b1+(2h12) O2M1 I PN?2& *h2) h2& (?+& *h+)

h+O

t =1

0,025 N (18+1,5.5 )5+ (3+1,5.5 )5

(2.2 )+(2.52 )+3+(2.52) O2M1 0,0008 PN(+3&+,44)4&

(1&+,44)4O

t = "01,/21*1Ms

'he8%ing 7


"01,/21*1Ms Q423,20"1*1Ms o%

Ta$el .D.13. Data hasil6erhitungan

e?itteoritis(*1M

s)?+(*)

?2(*)

h+(*)

h2(*)

#

(h+& h2)

4 1//,"!1 4 +/ 1 / !

24 /13,1/! " +3 / / 3

YOVI DWIANA

11!"1111#


23/26

40 413,/+3! 4 +! / 4

+00 "01,/21 1 +3 4 4 +0

300.0000 400.0000 500.0000 600.0000 700.0000

0

2

4

6

8

10

12

f(x) = 0x^2 + 0x + 5.25

Qteoritis (m3/s)

H (m)

9rafik 1C+9rafikhu?unganteoritisdan #

esi56ulan

9rafik?erupagarislengkungdenganpersa*aanse?agai?erikut:

- = +0>42>0,00+" & 4,2/2

E. 2)i S5irno9 ol5ogro9

Ta$el .E.1!.2)i S5irno9 ol5ogro9

*%

terurutR = Log %

6 =m

n+1

(F)

T =1

P

+ 21,+111 +,1"/2 ,00 0,++

2 2!,4!04 +,//0/ +3,+3+3 0,044

YOVI DWIANA

11!"1111#


24/26

1 1",33+2 +,4""3 2!,2!2! 0,01"!

/ 13,11+ +,431" 1",1"1" 0,02!4

4 /0,"""" +,"02 /4,/4/4 0,022

" /4,222 +,"4" 4/,4/44 0,0+31

! /3,//30 +,"341 "1,"1"/ 0,0+4!

3 42,1"2 +,!++ !2,!2!1 0,0+13

43,10 +,!!03 3+,3+32 0,0+22

+0 !0,42"" +,3/3/ 0,0+ 0,0++

*u5us 7 *aks Bkritik

i*ana : *aks = 7arak*aksi*u* horiDontal titikgarissinggung

kritik = 7arakketentuanu$i S*irnoE Kol*ogoroE

ari 9rafikdidapat :

*aks= "0F>/4,/4F

= +/,44F

= 0,+/44

7u*lahtahunpenga*atan= +0tahun

= 4 F = 0,04

kritik =0,/+ (darita?el)

Che.king :

*aksBkritik

0,+/44B 0,/+

>. 2)i 'hi uadrat

2

.r

H

2

HH2 0

):(0

=

k = K> (6 & +)

YOVI DWIANA

11!"1111#


25/26

i*ana :

2 = #arga Chi Kuadratterhitung

H = Hrekuensi -ang diharapkan

H = Hrekuensi -ang ter?a.a

.r2 = #arga Chi Kuadratkritis

k = era$atKe?a?asan

K = 'an-akn-aKelas

6 = 'an-akn-aketerikatanuntuku$i .hi kuadrat

a 'an-akn-a data Curah#u$an = +0

di?agi*en$adi / kelas (K = /)

F24

/

F+00o?a?ilitas6r5ilai ==

YOVI DWIANA

11!"1111#


26/26

Ta$el .>.14.Ta$el2)i 'hi uadrat

6ro?a?ilitas

(F)H H (H>H)

(H>>

H)2

H

2

HH

):(

6ro?a?ilitasI24 2,4 2 0,4 0,24 0,+

24B6ro?a?ilitasI40 2,4 1 >0,4 0,24 0,+

40B6ro?a?ilitasI!4 2,4 1 >0,4 0,24 0,+

!4B6ro?a?ilitasI+00 2,4 2 0,4 0,24 0,+

;u5lah +0 +0 0 + 0,/

k = / J ( 2 &+) = +

5ilai Chi Kuadratterhitung (2) = 0,/

'erdasarkanTa?el, didapat: .r2 = 0,!"/4

Che.king :

2 I .r2

0,/ I 0,!"/4 KGGG

YOVI DWIANA

11!"1111#

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