Nama : Punto Ajie Ramadhan

NPM : 93213032

Jurusan : Teknik Sipil

Mata Kuliah : Teknik Hidrologi

1. Make Unit Hydrograph using The Excess Rainfall Hyetograph & Direct Runoff ?

Jawab :

A. The Excess Raifall

Tabel 1.1 Direct Runoff

Time

(1/2 hr)

Excess Rainfall

(in)

Excess Rainfall

(cm)

Direct Runoff

(cfs)

Direct Runoff

(cms) U

1 1.06 2.6924 428 12.12 4.50

2 1.93 4.9022 1923 54.45 12.03

3 1.81 4.5974 5297 149.99 26.12

4 0 0 9131 258.56 27.93

5 0 0 10625 300.87 16.285

6 0 0 7834 221.83 5.05

7 0 0 3921 111.03 4.24

8 0 0 1846 52.27 3.07

9 0 0 1402 39.70 1.91

10 0 0 830 23.50 0.010

11 0 0 313 8.86 0.020

Tabel 1.2 Direct Runoff Koreksi

Time

(1/2 hr)

Excess Rainfall

(in)

Excess Rainfall

(cm)

Direct Runoff

(cfs)

Direct Runoff

(cms) Ukoreksi

1 2 5.08 428 22.87 4.50

2 3 7.62 1923 95.41 12.03

3 2.5 6.35 5297 252.95 26.12

4 1.5 3.81 9131 434.48 27.93

5 0 0 10625 507.27 16.28

6 0 0 7834 426.62 5.05

7 0 0 3921 269.83 4.24

8 0 0 1846 142.03 3.07

9 0 0 1402 79.27 1.91

10 0 0 830 50.25 0.010

11 0 0 313 23.99 0.020

Tabel 1.3 Volume Rainfall

Time

(1/2 hr)

P V

(m) (m3)

1 0.027 21815.299

2 0.049 98015.933

3 0.046 269989.806

4 465410.027

5 541559.691

6 399301.517

7 199854.640

8 94091.218

9 71460.394

10 42305.369

11 15953.711

0.122 2219757.604 18206673.264 18.207

Tabel 1.4 Volume Rainfall Koreksi

Time

(1/2 hr)

P V

I x T QXT

(m) (m3)

1 0.051 41160.941

2 0.076 171733.156

3 0.064 455301.284

4 0.038 782060.150

5 913091.002

6 767922.055

7 485701.717

8 255657.030

9 142684.095

10 90455.091

11 43183.777

0.229 4148950.298 18149388.882 18.149

Gambar 1.1 Grafik Direct Runoff

Gambar 1.2 Grafik Direct Runoff Koreksi

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B. Unit Hidrograph

Tabel 1.5 Hasil Perhitungan

Unit Besaran Satuan

tR 6 hr

A 2500 km2

L 100 km2

Lc 50 km2

Ct 2.64

tp 25.4892 hr

tr 4.6344

tpr 25.8306 m3/skm2cm

qp 0.060418

qpr 0.059619

peak discharge 149.048

tb 93.25853

w50 44.97764

w70 25.64146

Gambar 1.3 Grafik Unit Hidrograph

2. Make Unit Hydrograph Convolution ?

Jawab :

0

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0 20 40 60 80 100

Series1

A. S – Curve 2-1

Tabel 2.1 Data S-Curve 2-1

Time 2-Hr Total

(hr) Uh

0 0.0

0.0

1 75.0

75.0

2 250.0 0.0

250.0

3 300.0 75.0

375.0

4 275.0 250.0 0.0

525.0

5 200.0 300.0 75.0

575.0

6 100.0 275.0 250.0 0.0

625.0

7 75.0 200.0 300.0 75.0

650.0

8 50.0 100.0 275.0 250.0 0.0 675.0

9 25.0 75.0 200.0 300.0 75.0 675.0

10 0.0 50.0 100.0 275.0 250.0 0.0 675.0

11 25.0 75.0 200.0 300.0 75.0 675.0

Tabel 2.2 Perhitungan S-Curve 2-1

Time

S-Curve

S-Curved

lagged 1

HR

Diff 1-HR UH-

ORDINATES (hr)

0 0.0

0.0 0.0

1 75.0 0.0 75.0 150.0

2 250.0 75.0 250.0 500.0

3 375.0 250.0 125.0 250.0

4 525.0 375.0 150.0 300.0

5 575.0 525.0 50.0 100.0

6 625.0 575.0 50.0 100.0

7 650.0 625.0 25.0 50.0

8 675.0 650.0 25.0 50.0

9 675.0 675.0 0.0 0.0

10 675.0 675.0 0.0 0.0

11 675.0 675.0 0.0 0.0

Gambar 2.1 Grafik S-Curve 2-1

Gambar 2.2 Grafik Persamaan S-Curve 2-1

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1-HR-UH

S-Curve

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0 2 4 6 8 10 12

S-Curve

Series2

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Series4

Series5

Series6

Series7

Gambar 2.3 Grafik Perbandingan S-Curve 2-1

B. S – Curve 2-3

Tabel 2.3 Data S-Curve 2-3

Time 2-Hr Total

(hr) Uh

0 0.0

0.0

1 75.0

75.0

2 250.0 0.0

250.0

3 300.0 75.0

375.0

4 275.0 250.0 0.0

525.0

5 200.0 300.0 75.0

575.0

6 100.0 275.0 250.0 0.0

625.0

7 75.0 200.0 300.0 75.0

650.0

8 50.0 100.0 275.0 250.0 0.0

675.0

9 25.0 75.0 200.0 300.0 75.0

675.0

10 0.0 50.0 100.0 275.0 250.0 0.0 675.0

11 25.0 75.0 200.0 300.0 75.0 675.0

0.0

100.0

200.0

300.0

400.0

500.0

600.0

700.0

800.0

0 2 4 6 8 10 12

S-CURVE

1-hr-Uh

Tabel 2.4 Perhitungan S-Curve 2-3

Time

S-Curve

S-Curved

lagged 3

HR

Diff 3-HR UH-

ORDINATES (hr)

0 0.0

0.0 0.0

1 75.0

75.0 50.0

2 250.0

250.0 166.7

3 375.0 0.0 375.0 250.0

4 525.0 75.0 450.0 300.0

5 575.0 250.0 325.0 216.7

6 625.0 375.0 250.0 166.7

7 650.0 525.0 125.0 83.3

8 675.0 575.0 100.0 66.7

9 675.0 625.0 50.0 33.3

10 675.0 650.0 25.0 16.7

11 675.0 675.0 0.0 0.0

Gambar 2.4 Grafik S-Curve 2-3

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3-HR-UH

3-HR-UH

Gambar 2.5 Grafik Persamaan S-Curve 2-3

Gambar 2.6 Grafik Perbandingan S-Curve 2-3

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S-Curve

Series2

Series3

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Series7

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S-CURVE

3-hr-Uh

C. S – Curve 3-1

Tabel 2.5 Data S-Curve 3-1

Time 3-Hr Total

(hr) Uh

0 0.0

0.0

1 50.0

50.0

2 166.7

166.7

3 250.0 0.0

250.0

4 300.0 50.0

350.0

5 216.7 166.7

383.3

6 166.7 250.0 0.0

416.7

7 83.3 300.0 50.0

433.3

6 66.7 216.7 166.7

450.0

9 33.3 166.7 250.0 0.0 450.0

10 16.7 83.3 300.0 50.0 450.0

11 0.0 66.7 216.7 166.7 450.0

12 0.0 33.3 166.7 250.0 0.0 450.0

Tabel 2.6 Perhitungan S-Curve 3-1

Time

S-Curve

S-Curved

lagged 1

HR

Diff 1-HR UH-

ORDINATES (hr)

0 0.0

0.0 0.0

1 50.0 0.0 50.0 150.0

2 166.7 50.0 116.7 350.0

3 250.0 166.7 83.3 250.0

4 350.0 250.0 100.0 300.0

5 383.3 350.0 33.3 100.0

6 416.7 383.3 33.3 100.0

7 433.3 416.7 16.7 50.0

8 450.0 433.3 16.7 50.0

9 450.0 450.0 0.0 0.0

10 450.0 450.0 0.0 0.0

11 450.0 450.0 0.0 0.0

12 450.0 450.0 0.0 0.0

Gambar 2.7 Grafik S-Curve 3-1

Gambar 2.8 Grafik Persamaan S-Curve 3-1

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S-Curve

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S-Curve

Series2

Series3

Series4

Series5

Series6

Gambar 2.9 Grafik Perbandingan S-Curve 3-1

3. Make Flood Routing ?

Jawab :

A. EXAMPLE 1

Gambar 3.1 Contoh Soal 1

Diketahui Intensitas Hujan (I) dan Debit (Q) pada suatu hari pada Tabel 1.1 berikut

ini dimana Convert satuan 1 cfs = 0.0283 cms (m3/s).

Tabel 3.1 Rata-Rata Intensitas Hujan (I) dan Debit Air (Q)

Time I Q Δt Δt

(days) (cfs) (cfs) (cfs) (cms)

0.5 500 250 250 7.079

0

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400

450

500

0 2 4 6 8 10 12 14

S-CURVE

1-hr-Uh

1.5 3500 1000 2500 70.792

2.5 9000 3000 6000 169.901

3.5 9750 4500 5250 148.663

4.5 8000 5750 2250 63.713

5.5 4500 6000 -1500 -42.475

6.5 2250 5250 -3000 -84.951

7.5 1250 4250 -3000 -84.951

8.5 250 3250 -3000 -84.951

9.5 0 2500 -2500 -70.792

10.5 0 1500 -1500 -42.475

11.5 0 1000 -1000 -28.317

12.5 0 750 -750 -21.238

13.5 0 0 0 0.000

Note : ∆S = I – Q

Gambar 3.2 Grafik Inflow & Outflow

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Q (c

ms)

Time (days)

Inflow (I)

Outflow (Q)

Tabel 3.2 Storage Water

Time ΔS S

(days) (m3) (m3)

0 0.0 0.0

1 611643.9 611643.9

2 6116438.9 6728082.8

3 14679453.3 21407536.0

4 12844521.6 34252057.6

5 5504795.0 39756852.6

6 -3669863.3 36086989.3

7 -7339726.6 28747262.7

8 -7339726.6 21407536.0

9 -7339726.6 14067809.4

10 -6116438.9 7951370.5

11 -3669863.3 4281507.2

12 -2446575.5 1834931.7

13 -1834931.7 0.0

14 0.0 0.0

Note : ∆Si = ∆ti*24*3600

Gambar 3.3 Grafik Storage

-5000000.00.0

5000000.010000000.015000000.020000000.025000000.030000000.035000000.040000000.045000000.0

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Stor

age

(m3)

Time (days)

Storage (m3 - day)

S (m3)

B. EXAMPLE 3

Gambar 3.4 Contoh Soal 2

Intensitas Hujan (I) dan Debit (Q) pada suatu hari pada Tabel 2.1 berikut ini dimana

Convert satuan 1 cfs = 0.0283 cms (m3/s). Dimana diketahui :

K = 2 days

∆t = 1 days

x = 0.20

D = K – (K*x) + (0.5*∆t)

= 2 – (2*0.2) + (0.5*1)

= 2.10

C0 = [(–∆t*x) + (0.5*∆t)]/D

= [(–1*0.20) + (0.5*1)]/2.10

= 0.05

C1 = [(∆t*x) + (0.5*∆t)]/D

= [(1*0.20) + (0.5*1)]/2.10

= 0.43

C2 = [∆t – (∆t*x) + (0.5*∆t)]/D

= [1 – (1*0.20) + (0.5*1)]/2.10

= 0.52

∑C = C0 + C1 + C2 = 1

Tabel 3.3 Inflow dan Outflow

Time I Q Q

(days) (cfs) (cms) (cms)

1 4000 113.27 113.27

2 7000 198.22 117.31

3 11000 311.49 161.23

4 17000 481.39 240.87

5 22000 622.97 362.14

6 27000 764.55 493.09

7 30000 849.51 626.40

8 28000 792.87 729.95

9 25000 707.92 755.87

10 23000 651.29 730.34

11 20000 566.34 688.65

12 17000 481.39 626.36

13 14000 396.44 553.28

14 11000 311.49 474.55

15 8000 226.53 392.85

16 5000 141.58 309.61

17 4000 113.27 228.25

18 4000 113.27 173.50

19 4000 113.27 144.82

20 4000 113.27 129.79

Note : Q1 = I1

Qi = (C0*Ii) + (C1*Ii-1) + (C2*Qi-1)

C. EXAMPLE 4

Gambar 3.5 Contoh Soal 3

Diketahui Intensitas Hujan (I) dan Debit (Q) pada suatu hari pada Tabel 3.1 berikut

ini dimana Convert satuan yaitu :

1 cfs = 0.0283 cms (m3/s)

1 cfs-days = 86400 m3

Tabel 3.4 Inflow dan Outflow

Time I Q S S S

(days) (cfs) (cfs) (cfs-days) (cms-days) m3

1 59 42 17 0.481 41591.784

2 93 70 40 1.133 97863.022

3 129 76 93 2.633 227531.526

4 205 142 156 4.417 381665.785

5 210 183 183 5.182 447723.325

6 234 185 232 6.570 567605.527

7 325 213 344 9.741 841621.988

8 554 293 605 17.132 1480178.205

9 627 397 835 23.645 2042890.581

10 526 487 874 24.749 2138307.027

11 432 533 773 21.889 1891202.897

12 400 487 686 19.425 1678350.824

13 388 446 628 17.783 1536449.443

14 270 400 498 14.102 1218394.622

15 162 360 300 8.495 733972.664

16 124 230 194 5.493 474635.656

17 102 140 156 4.417 381665.785

18 81 115 122 3.455 298482.217

19 60 93 89 2.520 217745.224

20 51 71 69 1.954 168813.713

Tabel 3.5 Weighted Discharge

S Wxn (m3/s)

(m3) x = 0.1 x = 0.2 x = 0.3

41591.784 1.237 0.951 1.334

97863.022 2.047 1.586 2.178

227531.526 2.302 1.722 2.602

381665.785 4.199 3.217 4.556

447723.325 5.258 4.146 5.411

567605.527 5.377 4.191 5.655

841621.988 6.349 4.825 6.983

1480178.205 9.036 6.637 10.514

2042890.581 11.893 8.993 13.196

2138307.027 13.901 11.032 14.122

1891202.897 14.807 12.074 14.235

1678350.824 13.544 11.032 13.051

1536449.443 12.465 10.103 12.137

1218394.622 10.959 9.061 10.222

733972.664 9.633 8.155 8.512

474635.656 6.213 5.210 5.612

381665.785 3.857 3.171 3.642

298482.217 3.160 2.605 2.968

217745.224 2.540 2.107 2.353

168813.713 1.954 1.608 1.841

Note : Wxn = (xn*Ii)+[(1-xn)*Q]

Gambar 3.6 Grafik Storage vs Weighted Discharge untuk x = 0.1

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0 500000 1000000 1500000 2000000 2500000

Wei

ghte

d D

isch

arge

(m3/

s)

Storage (m3)

x = 0.1

x = 0.1

Gambar 3.7 Grafik Storage vs Weighted Discharge untuk x = 0.2

Gambar 3.8 Grafik Storage vs Weighted Discharge untuk x = 0.3

Didapatkan :

m = 0.0000063 (Gradien Garis Linear)

K = 1/m

0

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Wei

ghte

d D

isch

arge

(m3/

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Storage (m3)

x = 0.2

x = 0.2

y = 6E-06x + 1.7327

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Wei

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d D

isch

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(m3/

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Storage (m3)

X = 0.3

X = 0,3

Linear (X = 0,3)

= 1/0.0000063

= 158730.16 s

= 1.83 days

D. EXAMPLE 5

Gambar 3.9 Contoh Soal 4

1 ft = 0.3048 m 1 ac-ft = 1233.4818 m3 1 cfs = 0.0283 cms (m3/s)

Tabel 3.6 Data Storage

Depth S Q (2*Si/Δt) + Qi

(m) (m3) (cms) (cms)

0 0 0 0

0.3048 1233.482 0.424753 4.536359

0.6096 2466.964 0.906139 9.129351

0.9144 3700.446 1.557427 13.89224

1.2192 4933.927 2.548516 18.99494

1.524 6167.409 3.539606 24.09764

1.8288 7400.891 4.474062 29.1437

2.1336 9251.114 5.238617 36.07566

2.4384 12951.56 5.946538 49.1184

2.7432 14801.78 6.512875 55.85215

3.048 16652 7.079212 62.58589

3.3528 24669.64 7.645549 89.87767

3.6576 27136.6 8.211886 98.66722

Gambar 3.10 Grafik Debit

Gambar 3.11 Grafik Kedalaman vs Debit

y = 1.4176x2 - 0.9254x + 6.3961

0

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2S/Δ

t + Q

(cm

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Q (cms)

Series1

Poly. (Series1)

y = 2.4053x - 0.2384

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Depth (m)

Series1

Linear (Series1)

Tabel 3.7 Perhitungan

n Time I I + (Ii+1) (2*Si/Δt) - Qi (2*Si+1/Δt) + (Qi+1) Q plot

(s) (cms) (cms) (cms) (cms) (cms)

0 0 0.000 1.699 0.000 1.699 0.000

1 600 1.699 5.097 1.416 6.513 0.142

2 1200 3.398 8.495 5.267 13.762 0.623

3 1800 5.097 11.893 10.704 22.597 1.529

4 2400 6.796 15.291 16.084 31.375 3.256

5 3000 8.495 18.689 21.917 40.606 4.729

6 3600 10.194 19.255 29.619 48.875 5.493

7 4200 9.061 16.990 36.982 53.972 5.947

8 4800 7.929 14.725 41.286 56.011 6.343

9 5400 6.796 12.459 42.928 55.388 6.541

10 6000 5.663 10.194 42.419 52.613 6.485

11 6600 4.531 7.929 40.153 48.082 6.230

12 7200 3.398 5.663 36.302 41.966 5.890

13 7800 2.265 3.398 30.865 34.263 5.550

14 8400 1.133 1.133 24.183 25.315 5.040

15 9000 0.000 0.000 17.783 17.783 3.766

16 9600 0.000 0.000 13.139 13.139 2.322

17 10200 0.000 0.000 10.251 10.251 1.444

18 10800 0.000 0.000 8.155 8.155 1.048

19 11400 0.000 0.000 6.570 6.570 0.793

20 12000 0.000 0.000 5.267 5.267 0.651

Note : Didapat Debit Maksimum, Qmaks = 6.541 m3/s dan tinggi maksimum,

hmaks = 2.81 m (tinggi didapat dari interpolasi linear)

Gambar 3.12 Grafik Waktu vs Inflow

0.000

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In (c

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Time (s)

Series1