Compute and plot problems about water resources in Excel file
ruowan
hw11.pdf
Page 1 of 9
Homework No. 11 -- Solution
1. Watershed Information
Watershed Drainage Area, Ad (mi 2 ) = 1,406
2. Observed Flood Hydrograph, Base Flow Separation, Direct Runoff Hydrograph Derivation, and Numerical Integration
Incremental
Flood Direct Runoff Direct Runoff Direct Runoff
Elapsed Time, ti Time Increment, Dti Hydrograph, Qi Hydrograph, QRi 1
Volume, DVRi 2
Hydrograph
Date and Time (hours) (hours) (cfs) (cfs) (ft 3 ) Index, i
3
7/10/1986 0:00 0 2 1,400 0 120,000 1
7/10/1986 2:00 2 2 1,433 33 360,000 2
7/10/1986 4:00 4 2 1,467 67 600,000 3
7/10/1986 6:00 6 2 1,500 100 840,000 4
7/10/1986 8:00 8 2 1,533 133 1,080,000 5
7/10/1986 10:00 10 2 1,567 167 1,320,000 6
7/10/1986 12:00 12 2 1,600 200 1,800,000 7
7/10/1986 14:00 14 2 1,700 300 2,520,000 8
7/10/1986 16:00 16 2 1,800 400 3,240,000 9
7/10/1986 18:00 18 2 1,900 500 4,680,000 10
7/10/1986 20:00 20 2 2,200 800 6,840,000 11
7/10/1986 22:00 22 2 2,500 1,100 9,000,000 12
7/11/1986 0:00 24 2 2,800 1,400 12,840,000 13
7/11/1986 2:00 26 2 3,567 2,167 18,360,000 14
7/11/1986 4:00 28 2 4,333 2,933 23,880,000 15
7/11/1986 6:00 30 2 5,100 3,700 31,680,000 16
7/11/1986 8:00 32 2 6,500 5,100 41,760,000 17
7/11/1986 10:00 34 2 7,900 6,500 54,720,000 18
7/11/1986 12:00 36 2 10,100 8,700 73,440,000 19
7/11/1986 14:00 38 2 13,100 11,700 84,060,000 20
7/11/1986 16:00 40 2 13,050 11,650 83,700,000 21
7/11/1986 18:00 42 2 13,000 11,600 83,280,000 22
7/11/1986 20:00 44 2 12,933 11,533 82,800,000 23
7/11/1986 22:00 46 2 12,867 11,467 82,320,000 24
7/12/1986 0:00 48 2 12,800 11,400 79,560,000 25
7/12/1986 2:00 50 2 12,100 10,700 74,520,000 26
7/12/1986 4:00 52 2 11,400 10,000 69,480,000 27
7/12/1986 6:00 54 2 10,700 9,300 65,520,000 28
7/12/1986 8:00 56 2 10,300 8,900 62,640,000 29
7/12/1986 10:00 58 2 9,900 8,500 59,760,000 30
7/12/1986 12:00 60 2 9,500 8,100 57,600,000 31
7/12/1986 14:00 62 2 9,300 7,900 56,160,000 32
7/12/1986 16:00 64 2 9,100 7,700 54,720,000 33
7/12/1986 18:00 66 2 8,900 7,500 53,040,000 34
7/12/1986 20:00 68 2 8,633 7,233 51,120,000 35
7/12/1986 22:00 70 2 8,367 6,967 49,200,000 36
7/13/1986 0:00 72 2 8,100 6,700 47,520,000 37
7/13/1986 2:00 74 2 7,900 6,500 46,080,000 38
7/13/1986 4:00 76 2 7,700 6,300 44,640,000 39
7/13/1986 6:00 78 2 7,500 6,100 43,200,000 40
7/13/1986 8:00 80 2 7,300 5,900 41,760,000 41
7/13/1986 10:00 82 2 7,100 5,700 40,320,000 42
7/13/1986 12:00 84 2 6,900 5,500 38,820,000 43
7/13/1986 14:00 86 2 6,683 5,283 37,260,000 44
7/13/1986 16:00 88 2 6,467 5,067 35,700,000 45
7/13/1986 18:00 90 2 6,250 4,850 34,140,000 46
7/13/1986 20:00 92 2 6,033 4,633 32,580,000 47
7/13/1986 22:00 94 2 5,817 4,417 31,020,000 48
7/14/1986 0:00 96 2 5,600 4,200 29,400,000 49
7/14/1986 2:00 98 2 5,367 3,967 27,720,000 50
7/14/1986 4:00 100 2 5,133 3,733 26,040,000 51
7/14/1986 6:00 102 2 4,900 3,500 24,360,000 52
7/14/1986 8:00 104 2 4,667 3,267 22,680,000 53
7/14/1986 10:00 106 2 4,433 3,033 21,000,000 54
7/14/1986 12:00 108 2 4,200 2,800 19,920,000 55
7/14/1986 14:00 110 2 4,133 2,733 19,440,000 56
7/14/1986 16:00 112 2 4,067 2,667 18,960,000 57
7/14/1986 18:00 114 2 4,000 2,600 18,480,000 58
7/14/1986 20:00 116 2 3,933 2,533 18,000,000 59
7/14/1986 22:00 118 2 3,867 2,467 17,520,000 60
Page 2 of 9
Incremental
Flood Direct Runoff Direct Runoff Direct Runoff
Elapsed Time, ti Time Increment, Dti Hydrograph, Qi Hydrograph, QRi 1
Volume, DVRi 2
Hydrograph
Date and Time (hours) (hours) (cfs) (cfs) (ft 3 ) Index, i
3
7/15/1986 0:00 120 2 3,800 2,400 16,980,000 61
7/15/1986 2:00 122 2 3,717 2,317 16,380,000 62
7/15/1986 4:00 124 2 3,633 2,233 15,780,000 63
7/15/1986 6:00 126 2 3,550 2,150 15,180,000 64
7/15/1986 8:00 128 2 3,467 2,067 14,580,000 65
7/15/1986 10:00 130 2 3,383 1,983 13,980,000 66
7/15/1986 12:00 132 2 3,300 1,900 13,380,000 67
7/15/1986 14:00 134 2 3,217 1,817 12,780,000 68
7/15/1986 16:00 136 2 3,133 1,733 12,180,000 69
7/15/1986 18:00 138 2 3,050 1,650 11,580,000 70
7/15/1986 20:00 140 2 2,967 1,567 10,980,000 71
7/15/1986 22:00 142 2 2,883 1,483 10,380,000 72
7/16/1986 0:00 144 2 2,800 1,400 9,900,000 73
7/16/1986 2:00 146 2 2,750 1,350 9,540,000 74
7/16/1986 4:00 148 2 2,700 1,300 9,180,000 75
7/16/1986 6:00 150 2 2,650 1,250 8,820,000 76
7/16/1986 8:00 152 2 2,600 1,200 8,460,000 77
7/16/1986 10:00 154 2 2,550 1,150 8,100,000 78
7/16/1986 12:00 156 2 2,500 1,100 7,800,000 79
7/16/1986 14:00 158 2 2,467 1,067 7,560,000 80
7/16/1986 16:00 160 2 2,433 1,033 7,320,000 81
7/16/1986 18:00 162 2 2,400 1,000 7,080,000 82
7/16/1986 20:00 164 2 2,367 967 6,840,000 83
7/16/1986 22:00 166 2 2,333 933 6,600,000 84
7/17/1986 0:00 168 2 2,300 900 6,360,000 85
7/17/1986 2:00 170 2 2,267 867 6,120,000 86
7/17/1986 4:00 172 2 2,233 833 5,880,000 87
7/17/1986 6:00 174 2 2,200 800 5,640,000 88
7/17/1986 8:00 176 2 2,167 767 5,400,000 89
7/17/1986 10:00 178 2 2,133 733 5,160,000 90
7/17/1986 12:00 180 2 2,100 700 4,860,000 91
7/17/1986 14:00 182 2 2,050 650 4,500,000 92
7/17/1986 16:00 184 2 2,000 600 4,140,000 93
7/17/1986 18:00 186 2 1,950 550 3,780,000 94
7/17/1986 20:00 188 2 1,900 500 3,420,000 95
7/17/1986 22:00 190 2 1,850 450 3,060,000 96
7/18/1986 0:00 192 2 1,800 400 2,850,000 97
7/18/1986 2:00 194 2 1,792 392 2,790,000 98
7/18/1986 4:00 196 2 1,783 383 2,730,000 99
7/18/1986 6:00 198 2 1,775 375 2,670,000 100
7/18/1986 8:00 200 2 1,767 367 2,610,000 101
7/18/1986 10:00 202 2 1,758 358 2,550,000 102
7/18/1986 12:00 204 2 1,750 350 2,490,000 103
7/18/1986 14:00 206 2 1,742 342 2,430,000 104
7/18/1986 16:00 208 2 1,733 333 2,370,000 105
7/18/1986 18:00 210 2 1,725 325 2,310,000 106
7/18/1986 20:00 212 2 1,717 317 2,250,000 107
7/18/1986 22:00 214 2 1,708 308 2,190,000 108
7/19/1986 0:00 216 2 1,700 300 2,100,000 109
7/19/1986 2:00 218 2 1,683 283 1,980,000 110
7/19/1986 4:00 220 2 1,667 267 1,860,000 111
7/19/1986 6:00 222 2 1,650 250 1,740,000 112
7/19/1986 8:00 224 2 1,633 233 1,620,000 113
7/19/1986 10:00 226 2 1,617 217 1,500,000 114
7/19/1986 12:00 228 2 1,600 200 1,380,000 115
7/19/1986 14:00 230 2 1,583 183 1,260,000 116
7/19/1986 16:00 232 2 1,567 167 1,140,000 117
7/19/1986 18:00 234 2 1,550 150 1,020,000 118
7/19/1986 20:00 236 2 1,533 133 900,000 119
7/19/1986 22:00 238 2 1,517 117 780,000 120
Page 3 of 9
Incremental
Flood Direct Runoff Direct Runoff Direct Runoff
Elapsed Time, ti Time Increment, Dti Hydrograph, Qi Hydrograph, QRi 1
Volume, DVRi 2
Hydrograph
Date and Time (hours) (hours) (cfs) (cfs) (ft 3 ) Index, i
3
7/20/1986 0:00 240 2 1,500 100 660,000 121
7/20/1986 2:00 242 2 1,483 83 540,000 122
7/20/1986 4:00 244 2 1,467 67 420,000 123
7/20/1986 6:00 246 2 1,450 50 300,000 124
7/20/1986 8:00 248 2 1,433 33 180,000 125
7/20/1986 10:00 250 2 1,417 17 60,000 126 n-1
7/20/1986 12:00 252 2 1,400 0 N/A 127 n
7/20/1986 14:00 254 2 1,383 N/A N/A N/A
7/20/1986 16:00 256 2 1,367 N/A N/A N/A
7/20/1986 18:00 258 2 1,350 N/A N/A N/A
7/20/1986 20:00 260 2 1,333 N/A N/A N/A
7/20/1986 22:00 262 2 1,317 N/A N/A N/A
7/21/1986 0:00 264 N/A 1,300 N/A N/A N/A
Total
Base Direct Runoff
Flow, QB (cfs) 4 = 1,400 Volume, VR (ft
3 )
5 = 2,544,480,000
VR (acre-ft) = 58,413
Notes: 1 Direct Runoff Hydrograph Ordinates, QRi = Qi - QB
2 Trapezoidal rule for numerical integration, DVRi = 1/2(QRi+QRi+1)Dti
3 Total number of direct runoff hydrograph ordinates, n = 127
4 QB = base flow at time t1 , where direct runoff begins
5 Total Direct Runoff Volume, VR = SDVRi , summation from i = 1 to i = n-1
3. Effective Rainfall Depth
Effective Rainfall Depth, R = Total Direct Runoff Volume, VR , in equivalent depth of rainfall uniformly spread over the watershed drainage area, Ad
R = VR / Ad
R (in) = 0.78
4. Mean Areal Precipitation and Rainfall Duration from the Precipitation data, and Rainfall Hyetograph
Mean Areal Precipitation, P (in) = 2.40
Rainfall duration, tR (hours) = 48.00
5. W-Index Value
W-Index = (P-R)/tR
W-Index (in/hr) = 0.0338
6. Effective Rainfall Duration and f-Index value from analysis of Precipitation data, rainfall Hyetograph, and PhiIndex hyetograph
Effective Rainfall Duration, tER (hours) = 24.00
f-Index = "Average infiltration rate" over tER that yields proper apportioning of P between R and (L+G)
f-Index (in/hr) = 0.0575
7. Runoff Coefficient
Runoff Coefficient, k = Ratio of Effective Rainfall Depth, R, to Mean Areal Precipitation, P
k = R / P
k = 0.325
Page 4 of 9
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
10,000
11,000
12,000
13,000
14,000
0 24 48 72 96 120 144 168 192 216 240 264 288
D is
c h
a rg
e (
c fs
)
Time (hours)
Flood Hydrograph
Base Flow, QB = 1,400 cfs
Horizontal Base Flow Separation Line
Page 5 of 9
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
9,000
10,000
11,000
12,000
13,000
14,000
0 24 48 72 96 120 144 168 192 216 240 264 288
D is
c h
a rg
e (
c fs
)
Time (hours)
Direct Runoff Hydrograph Derivation
Flood Hydrograph
Direct Runoff Hydrograph
1,400 cfs
Page 6 of 9
Rainfall Hyetograph and Effective Rainfall Hyetograph
f-Index (in/hr) = 0.0575
Recording Rain Gauge -- Observed Rainfall Hyetograph Effective Rainfall Hyetograph
Starting Ending Time Increment, Dt Elapsed Time, t Depth, DP Rate, i Elapsed Time, t Effective Rate, iR Effective Depth, DR
Date and Time Date and Time (hours) (hours) (inches) (in/hr) (hours) (in/hr) (inches)
7/9/1986 0:00 7/9/1986 1:00 1 1 0.01 0.01 0 0
7/9/1986 1:00 7/9/1986 2:00 1 2 0.01 0.01 0 0
7/9/1986 2:00 7/9/1986 3:00 1 3 0.00 0.00 0 0
7/9/1986 3:00 7/9/1986 4:00 1 4 0.00 0.00 0 0
7/9/1986 4:00 7/9/1986 5:00 1 5 0.01 0.01 0 0
7/9/1986 5:00 7/9/1986 6:00 1 6 0.00 0.00 0 0
7/9/1986 6:00 7/9/1986 7:00 1 7 0.01 0.01 0 0
7/9/1986 7:00 7/9/1986 8:00 1 8 0.00 0.00 0 0
7/9/1986 8:00 7/9/1986 9:00 1 9 0.02 0.02 0 0
7/9/1986 9:00 7/9/1986 10:00 1 10 0.00 0.00 0 0
7/9/1986 10:00 7/9/1986 11:00 1 11 0.02 0.02 0 0
7/9/1986 11:00 7/9/1986 12:00 1 12 0.02 0.02 0 0
7/9/1986 12:00 7/9/1986 13:00 1 13 0.00 0.00 0 0
7/9/1986 13:00 7/9/1986 14:00 1 14 0.00 0.00 0 0
7/9/1986 14:00 7/9/1986 15:00 1 15 0.02 0.02 0 0
7/9/1986 15:00 7/9/1986 16:00 1 16 0.00 0.00 0 0
7/9/1986 16:00 7/9/1986 17:00 1 17 0.03 0.03 0 0
7/9/1986 17:00 7/9/1986 18:00 1 18 0.03 0.03 0 0
7/9/1986 18:00 7/9/1986 19:00 1 19 0.00 0.00 0 0
7/9/1986 19:00 7/9/1986 20:00 1 20 0.00 0.00 0 0
7/9/1986 20:00 7/9/1986 21:00 1 21 0.03 0.03 0 0
7/9/1986 21:00 7/9/1986 22:00 1 22 0.03 0.03 0 0
7/9/1986 22:00 7/9/1986 23:00 1 23 0.00 0.00 0 0
7/9/1986 23:00 7/10/1986 0:00 1 24 0.00 0.00 0 0
7/10/1986 0:00 7/10/1986 1:00 1 25 0.10 0.10 1 0.0425 0.0425
7/10/1986 1:00 7/10/1986 2:00 1 26 0.10 0.10 2 0.0425 0.0425
7/10/1986 2:00 7/10/1986 3:00 1 27 0.10 0.10 3 0.0425 0.0425
7/10/1986 3:00 7/10/1986 4:00 1 28 0.10 0.10 4 0.0425 0.0425
7/10/1986 4:00 7/10/1986 5:00 1 29 0.10 0.10 5 0.0425 0.0425
7/10/1986 5:00 7/10/1986 6:00 1 30 0.10 0.10 6 0.0425 0.0425
7/10/1986 6:00 7/10/1986 7:00 1 31 0.10 0.10 7 0.0425 0.0425
7/10/1986 7:00 7/10/1986 8:00 1 32 0.10 0.10 8 0.0425 0.0425
7/10/1986 8:00 7/10/1986 9:00 1 33 0.08 0.08 9 0.0225 0.0225
7/10/1986 9:00 7/10/1986 10:00 1 34 0.08 0.08 10 0.0225 0.0225
7/10/1986 10:00 7/10/1986 11:00 1 35 0.08 0.08 11 0.0225 0.0225
7/10/1986 11:00 7/10/1986 12:00 1 36 0.08 0.08 12 0.0225 0.0225
7/10/1986 12:00 7/10/1986 13:00 1 37 0.09 0.09 13 0.0325 0.0325
7/10/1986 13:00 7/10/1986 14:00 1 38 0.09 0.09 14 0.0325 0.0325
7/10/1986 14:00 7/10/1986 15:00 1 39 0.09 0.09 15 0.0325 0.0325
7/10/1986 15:00 7/10/1986 16:00 1 40 0.09 0.09 16 0.0325 0.0325
7/10/1986 16:00 7/10/1986 17:00 1 41 0.08 0.08 17 0.0225 0.0225
7/10/1986 17:00 7/10/1986 18:00 1 42 0.08 0.08 18 0.0225 0.0225
7/10/1986 18:00 7/10/1986 19:00 1 43 0.08 0.08 19 0.0225 0.0225
7/10/1986 19:00 7/10/1986 20:00 1 44 0.08 0.08 20 0.0225 0.0225
7/10/1986 20:00 7/10/1986 21:00 1 45 0.09 0.09 21 0.0325 0.0325
7/10/1986 21:00 7/10/1986 22:00 1 46 0.09 0.09 22 0.0325 0.0325
7/10/1986 22:00 7/10/1986 23:00 1 47 0.09 0.09 23 0.0325 0.0325
7/10/1986 23:00 7/11/1986 0:00 1 48 0.09 0.09 24 0.0325 0.0325
Rainfall Duration, tR (hours) = 48 Effective Rainfall Duration, tER (hours) = 24
Mean Areal Precipitation Depth, P (inches) = 2.40 Trial Effective Rainfall Depth, R (inches) = 0.78
Known Effective Rainfall Depth, R (inches) = 0.78
Page 7 of 9
Observed Hourly Rainfall Hyetograph
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.11
0.12
0.13
0.14
0.15
1 2 3 4 5 6 7 8 9
1 0
1 1
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
2 0
2 1
2 2
2 3
2 4
2 5
2 6
2 7
2 8
2 9
3 0
3 1
3 2
3 3
3 4
3 5
3 6
3 7
3 8
3 9
4 0
4 1
4 2
4 3
4 4
4 5
4 6
4 7
4 8
Elapsed Time (hours)
R a in
fa ll R
a te
, i (i
n /h
r)
Page 8 of 9
f-Index Determination
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10 1 2 3 4 5 6 7 8 9
1 0
1 1
1 2
1 3
1 4
1 5
1 6
1 7
1 8
1 9
2 0
2 1
2 2
2 3
2 4
2 5
2 6
2 7
2 8
2 9
3 0
3 1
3 2
3 3
3 4
3 5
3 6
3 7
3 8
3 9
4 0
4 1
4 2
4 3
4 4
4 5
4 6
4 7
4 8
Elapsed Time (hours)
R a in
fa ll R
a te
, i (i
n /h
r)
f-Index = 0.0575 in/hr
0.09 in/hr
R = 0.78 inches
Checks with Direct Runoff Hydrograph
0.09 in/hr
0.10 in/hr
tER = 24 hours
tR = 48 hours
0.08 in/hr 0.08in/hr
Page 9 of 9
Effective Rainfall Hyetograph
0
0.01
0.02
0.03
0.04
0.05
0.06
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0.08
0.09
0.1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Elapsed Time (hours)
E ff
e c ti
v e R
a in
fa ll R
a te
, i
R (
in /h
r)
0.0425 in/hr
0.0225 in/hr 0.0225 in/hr
0.0325 in/hr 0.0325 in/hr
