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Hydrology & Irrigation Engineering Formulas for Civil Engineering Exam - Notes | Study Engineering Hydrology - Civil Engineering (CE)

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 Page 1


Short Notes on Engineering Hydrology 
 
 
Precipitation & General aspects of Hydrology 
Index of Wetness 
• index of wetness = 
 
 
• % Rain deficiency = 100 - % index of wetness 
 
Aridity index 
 
 
Where, A.I = Aridity index 
 
PET = Potential Evapo- transpiration 
AET = Actual Evapotranspiration 
a. AI = 0 ? Nonarid 
b. 1 = A.I = 25 ? Mild Arid 
c. 26 = A.I = 50 ? Moderate arid 
d. A.I > 50 ? Severe Arid 
 
Optimum Number of rain Gauge: (N) 
 
   
     
where, Cv = Coefficient of variation, 
Page 2


Short Notes on Engineering Hydrology 
 
 
Precipitation & General aspects of Hydrology 
Index of Wetness 
• index of wetness = 
 
 
• % Rain deficiency = 100 - % index of wetness 
 
Aridity index 
 
 
Where, A.I = Aridity index 
 
PET = Potential Evapo- transpiration 
AET = Actual Evapotranspiration 
a. AI = 0 ? Nonarid 
b. 1 = A.I = 25 ? Mild Arid 
c. 26 = A.I = 50 ? Moderate arid 
d. A.I > 50 ? Severe Arid 
 
Optimum Number of rain Gauge: (N) 
 
   
     
where, Cv = Coefficient of variation, 
? = Allowable % Error, 
 
s Standard deviation of the data, n = Number of stations, 
 
mean of rainfall value 
 
Estimation of missing rainfall data 
 
 
where, N1,N2 ,… Nx..Nn are normal annual percipitation of 1,2,…x…n respectively. 
 
P1,P2 …Pn are rainfall at station 1,2,…. N respectively. 
 
And Px is the rainfall of station x. 
 
Case: A minimum number of three stations closed to station ‘x’ 
 
 
 
If any of N1, N2, N3… 
Nn > 10% of Nx 
Mean rainfall Data 
To convert the point rainfall values at various into an average value over a 
catchment the following three methods ar in use 
 
(i) Arithmetic Avg Method: when the rainfall measured at various stations in a 
catchment area is taken as the arithmetic mean of the station values. 
 
 
Where, P1,P2 …Pn are rainfall values 
 
Of stations 1,2…n respectively. 
 
In practice this method is used very rerely. 
Page 3


Short Notes on Engineering Hydrology 
 
 
Precipitation & General aspects of Hydrology 
Index of Wetness 
• index of wetness = 
 
 
• % Rain deficiency = 100 - % index of wetness 
 
Aridity index 
 
 
Where, A.I = Aridity index 
 
PET = Potential Evapo- transpiration 
AET = Actual Evapotranspiration 
a. AI = 0 ? Nonarid 
b. 1 = A.I = 25 ? Mild Arid 
c. 26 = A.I = 50 ? Moderate arid 
d. A.I > 50 ? Severe Arid 
 
Optimum Number of rain Gauge: (N) 
 
   
     
where, Cv = Coefficient of variation, 
? = Allowable % Error, 
 
s Standard deviation of the data, n = Number of stations, 
 
mean of rainfall value 
 
Estimation of missing rainfall data 
 
 
where, N1,N2 ,… Nx..Nn are normal annual percipitation of 1,2,…x…n respectively. 
 
P1,P2 …Pn are rainfall at station 1,2,…. N respectively. 
 
And Px is the rainfall of station x. 
 
Case: A minimum number of three stations closed to station ‘x’ 
 
 
 
If any of N1, N2, N3… 
Nn > 10% of Nx 
Mean rainfall Data 
To convert the point rainfall values at various into an average value over a 
catchment the following three methods ar in use 
 
(i) Arithmetic Avg Method: when the rainfall measured at various stations in a 
catchment area is taken as the arithmetic mean of the station values. 
 
 
Where, P1,P2 …Pn are rainfall values 
 
Of stations 1,2…n respectively. 
 
In practice this method is used very rerely. 
(ii) Thiessen Polygon Method: In this method, the rainfall recorded at each 
station is given a weightage on the basis of an area closest to the station. 
 
 
Where, P1,P2 …Pn are the rainfall data of areas A1,A2…An. The thiessen-polygon 
method of calculating the average percipitation over an area is superior to the 
arithmetic average method. 
 
(iii) Isohyetal Method: An isohyet is a line joining points of equal rainfall 
magnitude. The recorded values for which areal average P is to be detarmined are 
then maked on the plot at appropirate stations.Neighbouring stations outside the 
catchment are also considered. 
 
 
 
 
 
 
 
Page 4


Short Notes on Engineering Hydrology 
 
 
Precipitation & General aspects of Hydrology 
Index of Wetness 
• index of wetness = 
 
 
• % Rain deficiency = 100 - % index of wetness 
 
Aridity index 
 
 
Where, A.I = Aridity index 
 
PET = Potential Evapo- transpiration 
AET = Actual Evapotranspiration 
a. AI = 0 ? Nonarid 
b. 1 = A.I = 25 ? Mild Arid 
c. 26 = A.I = 50 ? Moderate arid 
d. A.I > 50 ? Severe Arid 
 
Optimum Number of rain Gauge: (N) 
 
   
     
where, Cv = Coefficient of variation, 
? = Allowable % Error, 
 
s Standard deviation of the data, n = Number of stations, 
 
mean of rainfall value 
 
Estimation of missing rainfall data 
 
 
where, N1,N2 ,… Nx..Nn are normal annual percipitation of 1,2,…x…n respectively. 
 
P1,P2 …Pn are rainfall at station 1,2,…. N respectively. 
 
And Px is the rainfall of station x. 
 
Case: A minimum number of three stations closed to station ‘x’ 
 
 
 
If any of N1, N2, N3… 
Nn > 10% of Nx 
Mean rainfall Data 
To convert the point rainfall values at various into an average value over a 
catchment the following three methods ar in use 
 
(i) Arithmetic Avg Method: when the rainfall measured at various stations in a 
catchment area is taken as the arithmetic mean of the station values. 
 
 
Where, P1,P2 …Pn are rainfall values 
 
Of stations 1,2…n respectively. 
 
In practice this method is used very rerely. 
(ii) Thiessen Polygon Method: In this method, the rainfall recorded at each 
station is given a weightage on the basis of an area closest to the station. 
 
 
Where, P1,P2 …Pn are the rainfall data of areas A1,A2…An. The thiessen-polygon 
method of calculating the average percipitation over an area is superior to the 
arithmetic average method. 
 
(iii) Isohyetal Method: An isohyet is a line joining points of equal rainfall 
magnitude. The recorded values for which areal average P is to be detarmined are 
then maked on the plot at appropirate stations.Neighbouring stations outside the 
catchment are also considered. 
 
 
 
 
 
 
 
Infiltration, Run off and Hydrographs 
 
Infiltration 
 
Infiltration is the flow of water into the ground through the soil surface. 
 
• Horton’s Equation: Horton expressed the decay of infiltration capacity with 
time as an exponential decay given by 
 
 
Where, 
 
 
fct = infiltration capacity at any time t from start of the rainfall 
fco = initial infiltration capacity at t = 0 
fct = final steady state value 
td = Duration of rainfall 
kh = constant depending on soil. 
 
Infiltration indices 
 
In hydrological calculations involving floods it is found convenient to use a constant 
value of filtration rate for the duration of the storm. The defined average infiltration 
rate is called infiltration index and two types of indices are in common use 
Page 5


Short Notes on Engineering Hydrology 
 
 
Precipitation & General aspects of Hydrology 
Index of Wetness 
• index of wetness = 
 
 
• % Rain deficiency = 100 - % index of wetness 
 
Aridity index 
 
 
Where, A.I = Aridity index 
 
PET = Potential Evapo- transpiration 
AET = Actual Evapotranspiration 
a. AI = 0 ? Nonarid 
b. 1 = A.I = 25 ? Mild Arid 
c. 26 = A.I = 50 ? Moderate arid 
d. A.I > 50 ? Severe Arid 
 
Optimum Number of rain Gauge: (N) 
 
   
     
where, Cv = Coefficient of variation, 
? = Allowable % Error, 
 
s Standard deviation of the data, n = Number of stations, 
 
mean of rainfall value 
 
Estimation of missing rainfall data 
 
 
where, N1,N2 ,… Nx..Nn are normal annual percipitation of 1,2,…x…n respectively. 
 
P1,P2 …Pn are rainfall at station 1,2,…. N respectively. 
 
And Px is the rainfall of station x. 
 
Case: A minimum number of three stations closed to station ‘x’ 
 
 
 
If any of N1, N2, N3… 
Nn > 10% of Nx 
Mean rainfall Data 
To convert the point rainfall values at various into an average value over a 
catchment the following three methods ar in use 
 
(i) Arithmetic Avg Method: when the rainfall measured at various stations in a 
catchment area is taken as the arithmetic mean of the station values. 
 
 
Where, P1,P2 …Pn are rainfall values 
 
Of stations 1,2…n respectively. 
 
In practice this method is used very rerely. 
(ii) Thiessen Polygon Method: In this method, the rainfall recorded at each 
station is given a weightage on the basis of an area closest to the station. 
 
 
Where, P1,P2 …Pn are the rainfall data of areas A1,A2…An. The thiessen-polygon 
method of calculating the average percipitation over an area is superior to the 
arithmetic average method. 
 
(iii) Isohyetal Method: An isohyet is a line joining points of equal rainfall 
magnitude. The recorded values for which areal average P is to be detarmined are 
then maked on the plot at appropirate stations.Neighbouring stations outside the 
catchment are also considered. 
 
 
 
 
 
 
 
Infiltration, Run off and Hydrographs 
 
Infiltration 
 
Infiltration is the flow of water into the ground through the soil surface. 
 
• Horton’s Equation: Horton expressed the decay of infiltration capacity with 
time as an exponential decay given by 
 
 
Where, 
 
 
fct = infiltration capacity at any time t from start of the rainfall 
fco = initial infiltration capacity at t = 0 
fct = final steady state value 
td = Duration of rainfall 
kh = constant depending on soil. 
 
Infiltration indices 
 
In hydrological calculations involving floods it is found convenient to use a constant 
value of filtration rate for the duration of the storm. The defined average infiltration 
rate is called infiltration index and two types of indices are in common use 
 
 
(i) W-index: In an attempt to refine the f-index the initial losses are separated 
from the total abstractions and an average value of infiltration rate, called W-index, 
is defined as 
 
 
Where, P = Total storm precipitation (cm) 
R = Total storm runoff (cm) 
Ia = initial losses (cm) 
 
te = Duration of rainfall excess 
 
W-index = Avg. rate of infiltration (cm/hr) 
 
(ii) f-index: The f index is the average rainfall above which the rainfall volumes is 
equal to the runoff volume. The f index is derived from the rainfall hyetograph with 
the edge of the resulting run- off volume. 
 
? - ?nd?x =
I - R
24
 
 
 
Where, R = Runoff in cm from a 24- h rainfall of intensity I cm/day 
 
Runoff 
 
Runoff means the draining or flowing off of precipitation from a catchment area 
through a surface channel. It thus represents the output from the catchment in a 
given unit of time. 
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