Code: nec/DCE/Hydr/HKS/2007/Tuto3
Nepal Engineering College
Changunarayan, Bhaktapur
Program: B.E. Civil
Tutorial 3: Physical Hydrology
Year: III
Instructor: Dr. Hari Krishna Shrestha
Engineering Hydrology
1. A catchment has seven rain gauge stations. In a year the annual rainfall recorded
by the gauges are as follows:
Station
P
Q
R
S
T
U
V
Rainfall (cm) 130.0 142.1 118.2 108.5 165.2 102.1 146.9
For a 5% error in the estimation of the mean rainfall, calculate the minimum
number of additional stations required to be established in the catchment.
2. The normal annual precipitation of five rain gauges P, Q, R, S, and T are
respectively 125, 102, 76, 113 and 137 cm. During a particular storm the
precipitations recorded by stations P, Q, R and S are 13.2, 9.2, 6.8, and 102 cm,
respectively. The instrument at station T was inoperative during that storm.
Estimate the rainfall at station T during that storm.
3. Test the consistency of the 22 years of data of the annual precipitation measured at
station A. Rainfall data for the station A as well as the average annual rainfall
measured at a group of eight neighboring stations located in a meteorologically
homogeneous region are given below.
Year
Station A (cm)
8 station average (cm)
Year
Station A (cm)
8 station average (cm)
1946
177
143
1957
158
164
‘47
144
132
‘58
145
155
‘48
178
146
‘59
132
143
‘49
162
147
‘60
95
115
‘50
194
161
‘61
148
135
‘51
168
155
‘62
142
163
‘52
196
152
‘63
140
135
‘53
144
117
‘64
130
143
‘54
160
128
‘65
137
130
‘55
196
193
‘66
130
146
‘56
141
156
‘67
163
161
(a) In what year is a change in regime indicated?
(b) Adjust the recorded data at station A and determine the mean and annual
precipitation.
4. For a drainage basin of 600 km2, isohyetals drawn for a storm gave the following
data. Estimate the average depth of precipitation over the catchment.
Isohyetals (interval) (cm) 15-12 12-9 9-6 6-3 3-1
Inter-isohyetal area (km2) 92
128 120 175 85
5. There are ten rain gauge stations available to calculate he rainfall characteristics of
a catchment whose shape can be approximately described by straight lines joining
the following coordinates (distances in kilometers).
(30,0), (80,10), (110,30), (140,90), (130,115), (40,110), (15,60). The coordinates
of the rain gauge stations and the annual rainfall in them in the year 1981 are
given below. Determine the average annual rainfall over the catchment.
Station
Coordinates
Annual
rainfall
(cm)
1
(0,40)
132
2
(50,0)
136
3
(140,30)
93
4
(140,80)
81
5
(90,140)
85
6
(0,80)
124
7
(40,50)
156
8
(90,30)
128
9
(90,90)
102
10
(40,80)
128
6. Following date are from a self-recording rain gauge during a storm. (a) Plot the
hyetograph of the storm and (b) Obtain the values of maximum intensities of this
storm for various durations and plot a curve of maximum intensity versus duration.
Time from beginning of storm (min) 10 20 30 40 50 60 70 80 90
Accumulated rainfall (mm)
19 41 48 68 91 124 152 160 166
7. For the storm given below prepare the maximum depth-duration curve:
Time from beginning of storm (min) 0 10 20 30 40 50 60 70 80 90
Accumulated rainfall (mm)
0 8 15 25 30 46 55 60 64 67
8. The record of annual rainfall at a place is given for 25 years. Estimate the
recurrence interval for various magnitudes. By suitable extrapolation, determine
the magnitude of annual rainfall at the station corresponding to a recurrence
interval of (a) 50 years and (b) 100 years.
Year
Annual rainfall (cm)
Year
Annual rainfall (cm)
1950
113
1963
68.6
‘51
94.5
‘64
82.5
‘52
76
‘65
90.7
‘53
87.5
‘66
99.8
‘54
92.7
‘67
74.4
‘55
71.3
‘68
66.6
‘56
77.3
‘69
65
‘57
85.1
‘70
91
‘58 ‘59 ‘60 ‘61 ‘62
122.8 69.4 81 94.5 86.3
‘71 ‘72 ‘73 ‘74
106.8 102.2 87 84
9. The annual rainfall values in cm at a station P for a period of 20 years are:
120, 84, 68, 92, 102, 92, 95, 88, 76, 84, 101, 109, 106, 115, 95, 90, 70, 89, 80, 90.
Determine the: (a) rainfall with a recurrence interval of 15 years, and
(b) the probability of occurrence of an annual rainfall of magnitude 100 cms.
[Hint: If an event (rainfall magnitude in the present case) occurs more than once,
the rank m = number of times the event is equaled + number of times it is
exceeded.]
10. Plot the three-year moving mean for data of problem 8. Is there any apparent time
trend? [Hint: Average the annual precipitation value of overlapping three-year
periods and plot the average value at the middle year of the period.]
11. On the bases of isopluvial maps the 50-yr-24 hr maximum rainfall at Banglore is
found to be 16.0 cm. Determine the probability of a 24 h rainfall of magnitude
equal to or greater than 16.0 cm occurring at Banglore:
a) once in 10 successive years,
b) two times in 10 successive years and
c) at least once in 10 successive years.
12. A one-day rainfall of 15.0 cm at a place X was found to have a return period of
100 years. Calculate the probability that a one-day rainfall of this or larger
magnitude:
a) will not occur at X during the next 50 years, and
b) will occur in the next year
13. Results to determine the Horton infiltration capacity in the exponential form are
tabulated below. Determine the infiltration capacity exponential equation.
Time (h)
0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
fct (cm/hr) 5.60 3.20 2.10 1.50 1.20 1.10 1.00 1.00
14. The rainfalls on five successive days on a catchment were 2, 6, 9, 5 and 3 cm. If
the -index for the storm can be assumed as 3 cm/day, find the total surface runoff.
15. The mass curve of a rainfall of duration 100 min. is given below. If the catchment
had an initial loss of 0.6 cm and a index of 0.6 cm/h, calculate the total surface
runoff from the catchment.
Time from beginning of storm (min) 0 20 40 60 80 100
Accumulated rainfall (cm)
0 0.5 1.2 2.6 3.3 3.5
16. An isolated 3-h storm occurred over a basin in the following fashion. Estimate the
runoff from the catchment due to this storm.
% of
Rainfall (cm)
-index
catchment area (cm/hr) 1st hr 2nd hr 3rd hr
20
1.00
0.8
2.3
1.5
30
0.75
0.7
2.1
1.0
50
0.50
1.0
2.5
0.8
17. An isolated storm in a catchment produced a runoff of 3.5 cm. The mass curve of
the average rainfall depth over the catchment was as below. Calculate the -index
for the storm.
Time from beginning of storm (h)
0
1
2
3
4
5
6
Accumulated average rainfall (cm) 0 0.50 1.65 3.55 5.65 6.80 7.75
18. The average rainfall over a basin of area of 50 ha during a storm was as follows. If
the volume of runoff was measured as 25×103 m3, determine the -index for the
storm.
Time (h)
0 1 2 3 4 5 6 7
Rainfall (mm) 0 6 11 34 28 12 6 0
19. In a 140-min storm the following rates of rainfall were observed in successive 20minute intervals: 3.0, 3.0, 9.0, 6.6, 1.2, 1.2, and 6.0 mm/h. Assuming the -index
values as 3.0 mm/h and an initial loss of 0.8 mm, determine the total rainfall, net
runoff and W-index for the storm.
20. Determine the number of gauges required to be installed in a watershed of 500
km2 area if normal annual rainfall recorded at various stations are as under.
Station
A
B
C
D
E
F
Rainfall (mm) 500 1000 750 650 450 300
21. Determine the mean precipitation using Thiessen Polygon method. The data are as
follows.
Station
A
B
C
D
E
F
Rainfall (cm) 5.0 15.0 7.5 8.0 25.0 12.5
Ploygon area 175 300 100 250 300 400
22. Calculate the mean precipitation using isohyetal method, with the data as under.
Zone
I
II III IV
V
Mean isohyetal value (cm)
5.0 3.5 7.5 8.0 15.0
Area enclosed by isohyets (km2) 30 130 45 130 250
Source of the problems 1 to 12: Subramanya, K. 1994. Engineering Hydrology, 2nd ed., Tata
McGraw-Hill Publishing Company Ltd. New Delhi, ISBN: 0-07-462449-8, pp. 50-54.
Source of the problems 13 to 19: Subramanya, K. 1994. Engineering Hydrology, 2nd ed., Tata
McGraw-Hill Publishing Company Ltd. New Delhi, ISBN: 0-07-462449-8, pp. 93-94.
Source of the problems 20 to 22: Suresh, R. 1997. Watershed Hydrology, 1st ed., Standard
Publishers Distributors, Delhi, ISBN: 81-86308-23-7, pp. 78-79.