MINISTRY OF SCIENCE AND TECHNOLOGY

DEPARTMENT OF TECHNICAL AND VOCATIONAL EDUCATION

Sample Questions & Worked Out Examples

for CE-04026

ENGINEERING HYDROLOGY

B.Tech. (Second Year)

Civil Engineering

MINISTRY OF SCIENCE AND TECHNOLOGY

DEPARTMENT OF TECHNICAL AND VOCATIONAL EDUCATION

CE-04026 ENGINEERING HYDROLOGY

Sample Questions

B.Tech. (Second Year)

Civil Engineering

1

Problems for CE 04026 Engineering Hydrology

Chapter 1 * What is the hydrologic cycle? * Sketch the hydrologic cycle. * Explain the hydrologic cycle. * Describe the liquid transport phases of the hydrologic cycle. * Name the vapour-transport phases of the hydrologic cycle. * What is a catchment? * Give a brief description of different components of the hydrologic cycle. * How can you get the catchment area? Chapter 2 * What are the different forms of precipitation and rainfall? * Distinguish between the precipitation and rainfall. * What are the different methods for the measurement of precipitation. * Describe various types of recording type rain gauges. What are the advantages and

disadvantages of these gauges? * Explain the method for estimation of missing rainfall data. * When is the normal ratio method used to fill in missing precipitation records? What is a

double mass analysis? * What are different methods for the estimation of average rainfall depth over an area? * Describe the methods for plotting the mass rainfall curve and the hyetograph. * What is a double-mass curve? What is its use? * Differentiate between the infiltration capacity and infiltration index. * * Differentiate between - index and w- index. * * Explain the method for the determination of - index. * What are the various losses which occur in the precipitation to become runoff. * Draw the intensity duration curve from the following data. Duration (mts) 5 10 15 30 60 90 120 Precipitation (cm) 0.8 1.2 1.4 1.7 2.1 2.4 2.8 ** Storm precipitation occurred from 6 AM to 10 AM on a particular day over a basin of

1500 ha area. The precipitation was measured by 3 rain gauges suitably located on the basin. The rain gauge readings and the areas of the Thiessen polygons are as follows:

2

Rain gauge no. 1 2 3 Area of Thiessen polygon (ha) 450 750 300 Rain gauge reading 6 to 7 AM 0.8 1.2 2.0 7 to 8 AM 1.4 3.6 3.2 8 to 9 AM 6.2 5.8 5.6 9 to 10 AM 4.4 4.6 2.8

Compute and draw the storm hyetograph and mass rainfall curve of the basin. * * The computation of an isohyet map of a 2000 ha basin following a 6 hr storm gave the

following data. Determine the average precipitation for the basin.

Isohyet 35-40 cm 30-35 25-30 20-25 15-20 10-15 below 10 cm Area (ha) 40 80 170 310 480 670 250

* * Compute the index from the following data: Total runoff = 77 x 106 m3 Estimated ground water contribution = 2 x 106 m3 Area of basin = 250 km2 The rainfall distribution is as follows:

Hour 0-2 2-4 4-6 6-8 8-10 10-12 12-14 14-16 Rainfall(cm/hr) 2.5 5.0 5.0 3.5 2.0 2.0 1.5 1.5

** The following rainfall distribution was measured during a 6-hour storm

Time (hr) 0 1 2 3 4 5 6 Rainfall

intensity (cm/hr) 0.5 1.5 1.2 0.3 1.0 0.5

The runoff depth has been estimated at 2 cm. Calculate the - index.

* The precipitation gage for station X was inoperative during part of the month of

January. During that same period, the precipitation depths measured at three index stations A, B, and C were 25, 28, and 27 mm respectively. Estimate the missing precipitation data at X, given the following average annual precipitation at X, A, B and C: 285, 250, 225 and 275 mm, respectively.

* The annual precipitation at station z and the average annual precipitation at 10

neighbouring stations are as follows:

3

Year Precipitation at z (mm) 10 station Average (mm) 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987

35 37 39 35 30 25 20 24 30 31 35 38 40 28 25 21

28 29 31 27 25 21 17 21 26 31 36 39 44 32 30 23

Use double-mass analysis to correct for any data inconsistencies at station z. ** The following rainfall distribution was measured during a 12-h storm:

Time (hr) 0-2 2-4 4-6 6-8 8-10 10-12 Rainfall intensity (cm/hr)

1.0

2.0

4.0

3.0

0.5

1.5

Runoff depth was 16 cm. Calculate the -index for this storm.

*** Using the data of above problem, calculate the w-index, assuming the sum of the

interception loss and depth of surface storage is 1 cm. * The isohyets for annual rainfall over a catchment were drawn and the area enclosed by

the isohyets are given below. Determine the average depth of annual rainfall over the catchment.

Isohyet (cm) 40 35 30 25 20 15 10 Area enclosed (km2) - 20 70 150 320 450 600

* Precipitation station X was inoperative for part of a month during which a storm

occurred. The respective storm totals at three surrounding stations A, B and C were 98, 80 and 110 mm. The normal annual precipitation amounts at station X, A, B and C are, respectively, 800, 1008, 842 and 1080 mm.

4

*** The annual precipitation at station X and the average annual precipitation at 15 surrounding stations are shown in the following table.

(a) Determine the consistency of the record at station X. (b) In what year is a change in regime indicated? (c) Compute the mean annual precipitation for station X for the entire 30 year period

without adjustment. (d) Repeat (c) for station X at its 1979 site with the data adjusted for the change in

regime. Yean Sta. X 15 Sta. Avg Year Sta. X 15 Sta. Avg 1950 47 29 1965 36 34 1951 24 21 1966 35 28 1952 42 36 1967 28 23 1953 27 26 1968 29 33 1954 25 23 1969 32 33 1955 35 30 1970 39 35 1956 29 26 1971 25 26 1957 36 26 1972 30 29 1958 37 26 1973 23 28 1959 35 28 1974 37 34 1960 58 40 1975 34 33 1961 41 26 1976 30 35 1962 34 24 1977 28 26 1963 20 22 1978 27 25 1964 26 25 1979 34 35 * * A rain gage recorded the following accumulated rainfall during the storm. Draw the

mass rainfall curve and the hyetograph. Time (AM) 8:00 8:05 8:10 8:15 8:20 8:25 8:30 Accumulated rainfall (mm)

0 1 2 6 13 18 19

* * 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: Time (hr) 0 1 2 3 4 5 6 Accumulated Rainfall (cm)

0 0.05 1.65 3.55 5.65 6.80 7.75

Calculate the index ( constant loss rate ) for the storm.

5

** A 10 hour storm occurred over 18 sq.km basin . The hourly values of rainfall were as follows 1.8,4.2,10.4,5.8,16.4,7.7,15.2,9.6,5.4, 1.2 cm. If the surface runoff was observed to be 705 6 ha-m, determine the infiltration index

Time from start (hour)

1 2 3 4 5 6 7 8 9 10

Incremental rainfall (cm)

1.8 4.2 10.4 5.8 16.4 7.7 15.2 9.6 5.4 1.2

Chapter 3 * A class A pan set up adjacent to a a late. the depth of water in the pan at beginning of

a certain week was 195 mm . In that week , there was a rainfall of 45 mm and 15 mm of water removed from the pan to keep the water level within the specified depth range. If the depth of the depth of the water in the pan at the end of the week was 190 mm, estimate the lake evaporation in that week.

* A reservoir had an average surface area of 20 km2 during June 1992 . In that month , the

mean rate of inflow is 10m3/s , out flow is 15 m3/s, monthly rainfall is 10 cm and change in storage is 16 Mm3 Assuming the seepage losses to be 1.8 cm, estimate the evaporation in that month .

* * The average annual discharge at the outlet of a catchment is 0.5 m3/s . The catchment is

situated in desert area (no vegetation) and the size is 800 Mm2 .The average annual precipitation is 200 mm / year (a) Compute the average annual evaporation from the catchment in mm / year.

In the catchment area an irrigation project covering 10 Mm2 is developed. After some years the average discharge at the outlet of the catchment appears to be 0.175 m3/s.

(b) Compute the evapotranspiration from the irrigated area in mm/ year, assuming no change in the evaporation from the rest of the catchment.

* Determine the monthly evaporation (mm) from a free water surface using the Penmans

method for a given weather station

locality Yangon N16 07' Month March Temperature C 36.2(max) and 19.8 (min) Relative humidity (%) 64 (max)and 48 (min) Mean wind speed 200 Km /day Mean daily sunshine hours 9.6 Mean daily possible sunshine hours 12

6

Reflection coefficient (albedo) 0.05 Psychrometer constant 0.49 * At a reservoir in a certain location, the following climatic month of June by Penmans

method, assuming that the lake evaporation is the same as P.E.T. Latitude 28N Elevation 230m above MSL Mean monthly temperature 33.5 C Mean relative humidity 52 % Mean observed sunshine hour 9 hr wind speed at 2m height 10 Km /hr * For an area (latitude 12 N) the mean monthly temperature are given Month June July Aug Sept Oct Temp(C) 31.5 31.0 30.0 29.0 28.0 Calculate the seasonal consumptive use of water for the rice crop in the season (June to

October) by using the Blaney- Criddle method . Monthly daytime hour percentage, P N lat June July Aug Sept Oct 12 8.68 8.94 8.76 8.26 8.31

Chapter 4 * The following data were collected during a stream gaging operation in a river. Compute the discharge.

Distance from bank (m)

Velocity (m/s)

Depth

at 0.2d at 0.8 d 0.0 0.0 0.0 0.0 1.5 1.3 0.6 0.4 3.0 2.5 0.9 0.6 4.5 1.7 0.7 0.5 6.0 1.0 0.6 0.4 7.5 0.4 0.4 0.3 9.0 0.0 0 0

7

*** Given below are data for a station rating curve Extend the relations and estimate the

flow at a stage of 14.5 ft by A D method and logarithmic method.

Stage (ft) Area (ft2) Depth (ft) Discharge (ft2/s) 1.72 263 1.5 1070 2.50 674 1.8 2700 3.47 1200 2.1 4900 4.02 1570 2.8 6600 4.26 1790 3.2 7700 5.08 2150 3.9 9450 5.61 2380 4.6 10700 5.98 2910 4.9 13100 6.70 3280 5.2 15100 6.83 3420 5.4 16100 7.80 3960 5.7 19000 8.75 4820 6.0 24100 9.21 5000 6.1 25000 9.90 5250 6.5 27300

14.50 8200 9.0

* * The following data were collected at a gauging station on a stream. Compute the discharge by (a) the mid-section method (b) the mean-section method. Distance from one bank (m)

0 3 6 9 12 15 18 21 24 27

Water depth (m) 0 1.5 3.2 5.0 9.0 5.5 4.0 1.6 1.4 0 Mean velocity (m/s) 0 0.12 0.24 0.25 0.26 0.24 0.23 0.16 0.14 0 * Calculate the discharge of river from the following measurements made with a flow meter. Distance from one bank (m)

0.0 15 30 45 60 75 90 105

depth of water (m) 0.0 0.8 1.2 1.5 1.8 1.5 0.9 0.0 average velocity (m/s) 0.0 0.15 0.24 0.30 0.36 0.33 0.24 0.0 Chapter 5 * * The data given below are the annual rainfall, X and annual runoff, Y for a certain river

catchment for 16 years. It has been decided to develop a linear relation between these two variables so as to estimate runoff for those years where rainfall data only are available.

8

Year X, cm Y, cm Year X, cm Y,cm

1 2 3 4 5 6 7 8

150 141 184 205 131 222 181 133

124 123 134 178 127 158 147 106

9 10 11 12 13 14 15 16

135 184 119 150 192 179 156 182

116 151 104 113 164 133 140 162

Find the equation of regression line. Is the linear relationship appropriate for the above data? * * The following table gives the mean monthly flows in a river during a year. Calculate

the minimum storage required to maintain a demand rate of 90m3/s.

Month Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Flow (m3/s)

80 60 40 30 25 60 200 300 200 150 100 90

* * The average annual discharge of a river for 11 years is as follows:

Year 1960 1961 1962 1963 1964 1965 1966 1967 1968

1969 1970

Discharge (cumecs)

1750 2650 3010 2240 2630 3200 1000 950 1200 4150 3500

Determine the storage capacity required to meet a demand of 2000 cumecs throughout

the year. * * * The runoff from a catchment area during successive months in a year is given below.

Determine the maximum capacity of the reservoir required if the entire volume of water is to be drawn off at a uniform rate, without any loss of water over the spillway.

Month Jan Feb March Apri May June July Aug Sept Oct Nov DecRunoff(Mm3) 1.3 2.0 2.7 8.5 12.0 12.0 19.0 22.0 2.5 2.2 1.9 1.7 * * * The average monthly runoff that flowed down a river during a critical year is given

below

9

Month Jan Feb March Apri May June July Aug Sept Oct Nov Dec Runoff (hect-m)

500 350 650 600 300 650 7500 6000 3500 2500 600 700

(a) If the monthly demands are as under, determine the required storage capacity. Assume

that the reservoir is full on Jan 1.

Month Jan Feb March Apri May June July Aug Sept Oct Nov Dec Demand (Cumecs)

5 6 7 5 8 10 5 6 4 8 10 12

(b) If there is a uniform demand of 6 m3/s, determine the required storage.

Chapter 6

* What is a hydrograph? What are its different segments? * Explain various methods for the separation of base flow a hydrograph. Why the

separation of flow is required? * Explain the procedure for the derivation of a unit hydrograph from an isolated storm

hydrograph. * What is S-hydrograph? How would you derive a S-hydrograph? Discuss the procedure of

derivation of the unit hydrograph from a S-hydrograph. * How would you obtain a storm hydrograph from a unit hydrograph? * The ordinates of 3 hour unit hydrograph of a basin at 6 hour interval are below

0,3,5,9,11,7,5,4,2,1,0 Cumecs. Derive the storm hydrograph due to a 3 hour storm with a total rainfall of 15 cm. Assume an initial loss of 0.5 cm and - index of 1 cm/hr. Take base flow = 4 cumecs.

* A 3 hour duration unit hydrograph has the following ordinates:

Time(hour) 0 3 6 9 12 15 18 21 24 27 30 Q(cumec) 0 3.08 4.94 8.64 9.88 7.41 4.94 3.70 2.47 1.23 0

Develop a unit hydrograph of 6 hour duration.

* Find out the ordinates of storm hydrograph resulting from a 9 hour storm with rainfall of 2.0, 5.75 and 2.75 cm during subsequent 3 hour intervals. The ordinates of 3 hour U.H at 3 hour intervals are as follows:

0,100,355,510,380,300,200,225,165,120,85,55,30,22,10,0 (cumecs) Assume an initial loss of 0.5 cm, an infiltration index of 0.25 cm/hr and a base flow of 10 cumecs.

10

* Given below are observed flows from a storm of 6 hour duration on a stream with a catchment area of 500 km2.

Time(hr) 0 6 12 18 24 30 36 42 48 54 60 66 72 Flow(m3/s) 20 120 270 220 170 120 90 70 55 45 35 25 20 Assuming a constant base flow of 20 m3/s, derive the ordinates of a 6 hour unit hydrograph.

* Given below is the 4 hour UH for a basin. Compute the S-curve ordinate and find the

6 hour UH.

Hour 0 2 4 6 8 10 12 14 16 18 20 22 4 hr UH

0 150 500 610 450 320 220 140 80 40 10 0

* Calculate the streamflow hydrograph for a storm of 6 inches excess rainfall, with 2

inches in the first half-hour, 3 inches in the second half-hour and 1 inch I the third half-hour. Use the half-hour unit hydrograph and assume the base is constant at 500 cfs throughout the flood.

Check that the depth of direct runoff is equal to the total excess precipitation (watershed area = 7.03 sq.mile). The ordinates of half hour unit hydrograph are given below.

Time(hour) 0 1 1 2 2 3 3 4 4 5 Q(cumec) 0 404 1979 2343 2506 1460 453 381 274 173 0

* * * A catchment of 5 km2 has rainfall of 5.0, 7.5 and 5.0 cm in three consecutive days.

The average - index is 2.5 cm/day. The surface runoff extends over 7 days for each rainfall of 1 day duration. Distribution graph percentage for each day are 5,15,35,25,10,6,4. Determine the ordinates of the storm hydrograph. Neglect base flow.

Chapter 7 * The annual rainfall for 10 years are as follows: 40, 35, 55, 65, 70, 25, 45, 30, 50 and 42

cm. Determine the rainfall which has a recurrence interval of 12 years. * The maximum values of 24 hr rainfall at a place from 1960 to 1980 are as follows:

11

12.7 13.2 12.8 11.6 16.9 17.2 14.0 14.2 17.8 18.8 11.7 13.3 13.6 13.9 16.4 14.7 8.4 12.5 11.2 20.7 19.7 19.7 18.9 17.4 15.8 14.9 18.3 17.7 18.6 19.2

Estimate the maximum rainfall having a recurrence interval of 10 years and 50 years. ** The maximum annual observed floods for 20 years from 1950 to 1969 for a catchment

are given below. Determine the maximum flood with a recurrence interval of 30 years by the following methods:

(a) Probability plotting, using a log-log paper (b) Gumble's method

Year 1950 1951 1952 1953 1954 1955 1956 1957 Discharge

(Lakh cumecs)

1.38

1.25

1.92

1.45

1.65

1.43

1.84

1.74 Year

Discharge (Lakh cumecs)

1958

1.32

1959

1.86

1960

1.20

1961

1.82

1962

1.70

1963

1.95

1964

1.60

1965

1.32 Year

Discharge (Lakh cumecs)

1966

1.41

1967

1.78

1968

1.80

1969

1.50

** The maximum annual floods for 23 years are given below, arranged in the descending

order

Year Flood

discharge(m3/s)

1960

720

1952

710

1970

705

1954

665

1972

570

1971

490

1968

450

1964

440

Year Flood

discharge(m3/s)

1966

425

1973

410

1956

405

1957

400

1951

395

1965

390

1951

385

1961

375

Year Flood

discharge(m3/s)

1955

360

1963

345

1958

340

1962

330

1969

320

1959

310

1967

300

Find the magnitude of 100-Year flood, using Gumbel's method.

12

* A well of diameter 30 cm fully penetrates a confined aquifer of thickness 15 m. When pumped at a steady rate of 30 lps, the draw downs observed in wells at radial distances of 10 m and 40 m, are 1.5 and 1.0 m respectively. Compute the radius of influence, the permeability, the transmissibility and the draw down at the well.

* A 0.4 m diameter well fully penetrates an unconfined aquifer whose bottom is 80 m

below the undisturbed ground water table. When pumped at a steady rate of 1.5 m3/min, the draw downs observed in two observation wells at radial distances of 5 m and 15 m are, respectively, 4 m and 2 m. Determine the drawn down in the well.

* A well penetrates in the centre of an unconfined aquifer bounded externally by a circle

of radius 600m along which the height of water table is 8m. If at a distance of 10m from the centre of well, the height of the water table is 7.5m when steady conditions are established, determine the discharge of the well. Take k = 10-4 m/s.

* * A well fully penetrating a confined aquifer was pumped at a constant rate of 0.03

cusecs. During the pumping period, the draw down S in an observation well measured at different instants of time are given below. If the distance of the observation well from the pump well was 50m, determine the formation constants S and T by (a) Theis' method (b) Cooper Jacob's method.

Time(t)minutes 0 1 2 3 4 5 6 8 10 12

Drawdown 0.0 0.4 0.32 0.38 0.43 0.49 0.52 0.57 0.61 0.64 14 18 22 26 30 40 50 60 80 067 0.71 0.75 0.78 0.81 0.85 0.89 0.94 0.97 100 140 180 240 1.02 1.07 1.12 1.15

Chapter 9 *** Tabulated below are the elevation storage and elevation discharge data for a small

reservoir.

Elevation(ft) 0 5 10 15 20 25 30 35 Storage(sfd) 0 30 50 80 110 138 160 190

Discharge(cfs) 0 5 10 20 25 30 80 130 From the inflow hydrograph shown below, Compute the maximum outflow discharge

and pool level to be expected. Assume initial outflow = 20 cfs

13

* The following inflow and outflow hydrographs were observed in a river reach. Estimate the values of k and x applicable to this reach for use in the Muskingum equation.

Time (hr) 0 6 12 18 24 30 36 42 48 54 60 66

Inflow (m3/s) 5 20 50 50 32 22 15 10 7 5 5 5 Outflow (m3/s) 5 6 12 29 38 35 29 23 17 13 9 7

* The inflow hydrograph for a stream channel reach is tabulated below. Compute the

outflow hydrograph using Muskingum method of routing with k = 36 hr and x = 0.25. Assume initial outflow as 30 cumecs.

Date hr Inflow (cumec) 1 6 AM 30 Noon 50 6 PM 86 MN 124 2 6 AM 155 Noon 140 6 PM 127 MN 103 3 6 AM 95 Noon 76 6 PM 65 MN 54 4 6 AM 40 Noon 30 6 PM 24 MN 20

MINISTRY OF SCIENCE AND TECHNOLOGY

DEPARTMENT OF TECHNICAL AND VOCATIONAL EDUCATION

CE-04026 ENGINEERING HYDROLOGY

Worked Out Examples

B.Tech. (Second Year)

Civil Engineering

1

12550 600

NX PA PB PC M NA NB NC

800 98 80 110 3 1008 842 1080

CE04026 Engineering Hydrology

1.(2-7)* The isohyets for annual rainfall over a catchment were drawn and the area enclosed by the isohyets are given below. Determine the average depth of annual rainfall over the catchment. Isohyet (cm) 40 35 30 25 20 15 10 Area enclosed (km2) - 20 70 150 320 450 600 Solution

Isohyet (cm)

Area enclosed (km2)

Net Area (km2)

Average depth (cm)

ppt. volume

40 - - - - 35 20 20 37.5 750 30 70 50 32.5 1625 25 150 80 27.5 2200 20 320 170 22.5 3825 15 450 130 17.5 2275 10 600 150 12.5 1875

12550 Average depth of annual rainfall over the catchment =

= 20.92 cm 2.(2-7)* Precipitation station X was inoperative for part of a month during which a storm occured. The respective storm totals at three surrounding stations A, B and C were 98, 80 and 110 mm. The normal annual precipitation amounts at station X, A, B and C are, respectively, 800, 1008, 842 and 1080 mm. Estimate the storm precipitation for station X. Solution PA = 98 mm, PB = 80 mm, PC = 110 mm, PX = ? NA = 1008 mm, NB = 842 mm, NC = 1080 mm, NX = 800 mm

PX = + +

PX = + +

PX = 78.42 mm

2

infiltration loss 4.25 te 6

infiltration loss 4.2 te 5

3.(2-7)** 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. Time (hr) 0 1 2 3 4 5 6 Accumulated Rainfall (cm) 0 0.05 1.65 3.55 5.65 6.80 7.75

Calculate the index (constant loss rate) for the storm. Solution

Time from start (hr) 1 2 3 4 5 6 Incremental rainfall (cm) 0.05 1.6 1.95 2.1 1.15 0.95

Total rainfall = 7.75 cm direct runoff = 3.5 cm Total infiltration = 7.75 3.5 = 4.25 cm 1st trial Assume te = 6 hr 1 = = = 0.708 cm/hr

1 is not effective the 1st hr

2nd trial Total infiltration = 4.25 0.05 = 4.20 cm Assume te = 5 hr 2 = = 0.84 cm/hr infiltration index = 0.84 cm/hr 4.(3-7)* A class A pan set up adjacent to a lake. The depth of water in the pan at beginning of a certain week was 195 mm. In that week, there was a rainfall of 45mm and 15mm of water removed from the pan to keep the water level within the specified depth range. If the depth of the water in the pan at the end of the week was 190 mm, estimate the lake evaporation in that week. Solution pan evaporation = 195 + 45 15 190 = 35 mm pan coeff. for class A pan = 0.7

lake evaporation = pan evaporation x pan coefficient = 35 x 0.7 = 25.5 mm

3

10 m3/s 20 x 106m2

15 m3/s 20 x 106m2

16 x 106 m3 20 x 106

5.(3-7)* A reservoir had an average surface area of 20 km2 during June 1992. In that month, the mean rate of inflow is 10m3/s, outflow is 15m3/s, monthly rainfall is 10cm and change in storage is 16 Mm3. Assuming the seepage losses to be 1.8 cm, estimate the evaporation in that month. Solution Surface area = 20 km2 = 20 x (103) = 20 x 106 m2 Inflow for June = x 30 x 24 x 3600 x 100 = 129.6 cm

outflow for June = x 30 x 24 x 3600 x 100 = 194.4 cm storage change = 16 Mm3 = = 0.8 m x 100 = 80 cm seepage losses = 1.8 cm ( assume ) rainfall (monthly) = 10 cm Evaporation for June = S + I + P O Os ( Water balance method ) = 80 + 129.6 + 10 194.4 1.8 = 23.4 cm

6(4-7)* The following data were collected during a stream gaging operation in a river. Compute the discharge.

Distance from bank Depth Velocity (m/s) (m) at 0.2 d at 0.8 d 0.0 1.5 3.0 4.5 6.0 7.5 9.0

0.0 1.3 2.5 1.7 1.0 0.4 0.0

0.0 0.6 0.9 0.7 0.6 0.4 0.0

0.0 0.4 0.6 0.5 0.4 0.3 0.0

Solution

Distance Width Depth Meter depth

Velocity (m/s) Area Discharge

(m) (m) (m) (m) at point mean velo.

(m2) (m3/s)

0 1.5

3.0

0 1.5

1.5

0 1.3

2.5

0 0.3 1.0

0.5 2.0

0 0.6 0.4

0.9 0.6

0

0.5

0.75

0

1.95

3.75

0

0.975

2.8125

4

N (XY) (X) (Y) N (X2) (X)2

16 (368896) 2644 x 2180 16 (450264) (2644)2

4.5

6.0

7.5

9.0

1.5

1.5

1.5

0.75

1.7

1.0

0.4 0

0.34 1.36

0.2 0.8

0.1 0.3

0

0.7 0.5

0.6 0.4

0.4 0.3

0

0.60

0.50

0.35

2.55

1.5

0.6 0

1.53

0.75

0.21 0

6.2775

7.(5-7)** The data given below are the annual rainfall, X and annual runoff, Y for a certain river catchment for 16 years. It has been decided to develop a linear relation between these two variables so as to estimate runoff for those years where rainfall data only are available. Year X,cm Y,cm Year X,cm Y,cm Year X,cm Y,cm Year X,cm Y,cm 1 150 124 5 131 127 9 135 116 13 192 164 2 141 123 6 222 158 10 184 151 14 179 133 3 184 134 7 181 147 11 119 104 15 156 140 4 205 178 8 133 106 12 150 113 16 182 162 Find the equation of regression line. Is the linear relationship appropriate the above data? Solution

Year X, cm Y, cm X2 Y2 XY 1 150 124 22500 15376 18600 2 141 123 19881 15129 17343 3 184 134 33856 17956 24656 4 205 178 42025 31864 36490 5 131 127 17161 16129 16637 6 222 158 49284 24964 35076 7 181 147 32761 21609 26607 8 133 106 17689 11236 14098 9 135 116 18225 13456 15660

10 184 151 33856 22801 27784 11 119 104 14161 10816 12376 12 150 113 22500 12769 16950 13 192 164 36864 26896 31488 14 179 133 32041 17689 23807 15 156 140 24336 19600 21840 16 182 162 33124 26244 29484 2644 2180 450264 304354 368896

Y = a + bX

b = = = 0.648

5

Y - bX N

2180 0.648 x 2644 16

N (XY) - (X) (Y) [NX2 (X)2 ] [NY2 (Y)2]

N (XY) - (X) (Y) [NX2 (X)2 ] [NY2 (Y)2]

16 (368896) - 2644 x 2180

[16 x 450264 (2644)2] [16 x 304354 (2180)2 ]

a = = = 29.10 Y = 29.10 + 0.648 X Regression line Correlation coefficient r = r = r = 0.875 > 0.6 good correlation Linear relationship is appropriate for above data. 8.(6-8)* The ordinates of a 3hr unit hydrograph of a basin at 6 hr interval are given below. 0, 3 , 5 , 9 , 11 , 7 , 5 , 4 , 2 , 1 , 0 cumecs. Derive the storm hydrograph due to a 3 hr storm with a total rainfall of 15 cm. Assume an initial loss of 0.5 cm and a index of 1 cm/ hr. Take base flow = 4 cumecs. Solution Effective rainfall depth R = 15 0.5 1 x 3 = 11.5 cm

Time (hours) Unit hydrograph ordinates (cumecs)

Direct runoff ordinates (cumecs)

Base flow

Ordinate of storm hydrograph (cumecs)

0 6 12 18 24 30 36 42 48 54 60

0 3 5 9 11 7 5 4 2 1 0

0 34.5 57.5 103.5 115.0 80.5 57.5 46.0 23.0 11.5

0

4 4 4 4 4 4 4 4 4 4 4

4 38.5 61.5 107.5 119.0 84.5 61.5 50.0 27.0 15.5 4.0

6

2 bk (Z2 Z1) Log (r1 / r2)

2 x 15 x k (1.5 1.0) Log (40/10)

2 bk (Zw 1.0) Log (40/0.15)

2 x 15 x 8.8 x 10-4 (Zw 1.0) 5.586

9.(6-8)* A 3 hr duration unit hydrograph has the following ordinates: Time (hr) 0 3 6 9 12 15 18 21 24 27 30 Q (cumec) 0 3.08 4.94 8.64 9.88 7.41 4.94 3.70 2.47 1.23 0 Develop a unit hydrograph of 6 hour duration Solution

Time (hr)

Ordinate of 3 hr unit

hydrograph

3 hr U.H lagged 3hr

Combined hydrograph

6 hr UH

0 0 0 0 3 3.08 0 3.08 1.54 6 4.94 3.08 8.02 4.01 9 8.64 4.94 13.58 6.79

12 9.88 8.64 18.52 9.26 15 7.41 9.88 17.29 8.65 18 4.94 7.41 12.35 6.18 21 3.70 4.94 8.64 4.32 24 2.47 3.70 6.17 3.09 27 1.23 2.47 3.70 1.85 30 0 1.23 1.23 0.62 33 0 0 0

10.(8-8)* A well of diameter 30 cm fully penetrates a confined aquifer of thickness 15m. When pumped at a steady rate of 30 lps, the drawdowns observed in wells at radial distances of 10m and 40m, are 1.5 and 1.0 m respectively. Compute the radius of influence, the permeability, the transmissibility and the drawdown at the well. Solution Q =

30 x 10-3 = k = 8.8 x 10-4 m/s T = bk = 15 x 8.8 x 10-4 = 1.32 x 10-2 m2 /s Let Zw be the drawdown at the well face Q =

30 x 10-3 =

7

2 bk Zw Log (R/rw)

2 x 15 x 8.8 x 10-4 x 3.02 Log (R/0.15)

k (h 21 - h 22 ) Log (r1 /r2)

1.5 60

k [ (80 2)2 (80-4)2] Log 15/5

k (h 22 h 2w ) Loge (r2 /rw)

1.5 60

x 2.84 x 10-5 (782 h 2w ) Loge (15/0.2)

Zw = 3.02 m

Let R be the radius of influence ( ie drawdown Z = 0 ) Q =

30 x 10-3 = R = 634.0 m 11.(8-8)* A 0.4 m diameter well fully penetrates an unconfined aquifer whose bottom is 80 m below the undisturbed ground water table. When pumped at a steady rate of 1.5 m3/min, the drawdowns observed in two observation wells at radial distance of 5m and 15m are, respectively, 4m and 2m. Determine the drawdown in the well. Solution Q =

= k = 2.84 x 10-5 m/s Let hw = the depth of water in the well Q =

= hw = 69.82 m Zw = 80 69.82 = 10.18 m

8

2s t

12(9-8)*** Tabulated below are the elevation-storage and elevation-discharge data for a small reservoir.

Elevation (ft) Storage (sfd)

Discharge (cfs)

0 0 0

5 30 5

10 50 10

15 80 20

20 110 25

25 138 30

30 160 80

35 190 130

From the inflow hydrograph shown below, compute the maximum outflow discharge and pool level to be expected. Assume initial outflow = 20 cfs. Data 1 2 3 4 5 Hour Inflow, cfs

MN 20

NOON 50

MN 100

NOON 120

MN 80

NOON 40

MN 20

NOON 10

Solution t = 0.5 day

Elevation Discharge (cfs)

Storage (sfd)

+ Q , cfs

0 5 10 15 20 25 30 35

0 5 10 20 25 30 80 130

0 30 50 80 110 138 160 190

0 125 210 340 465 582 720 890

Date Hour Inflow (cfs)

(2s/t) - Q (2s/t) + Q outflow Q , cfs

1 2 3 4 5

MN NOON

MN NOON

MN NOON

MN NOON

20 50 100 120 80 40 20 10

300 328 426 544 572 560 534

340 370 478 646 744 692 620 564

20 21 26 51 86 66 43 29

Maximum outflow discharge = 86 cfs

at pool level = 30.5 ft