Short Notes: Infiltration, Run off and Hydrographs | Short Notes for Civil Engineering - Civil Engineering (CE) PDF Download

 Page 1


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 
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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. 
 
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. 
Page 3


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. 
 
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. 
Direct Runoff: it is that part of the runoff which enters the stream immediately 
after the rainfall. It includes surface runoff, prompt interflow and rainfall on the 
surface of the stream. In the case of snow-melt, the resulting flow entering the 
stream is also a direct runoff, sometimes terms such as direct storm runoff are used 
to designate direct runoff. 
Base Flow: The delayed flow that reaches a stream essentially as groundwater flow 
is called base flow. 
(i) Direct runoff = surface runoff + Prompt interflow 
(ii) Direct runoff = Total runoff- Base flow 
(iii) Form Factor  where, A = Area of the catchment l Axial length of basin. 
(iv) Compactness coefficient  
re = Radius of equivalent circle whose Area is equal to area of catchment (A) 
(v) Elevation of the water shed, (z) 
 
Where, A1, A2 … Area between successive contours. 
Z1, z2 … mean elevation between two successive contours. 
Method to compute Runoff 
(i) By Runoff coefficient 
Q = KP where, p = precipitation 
K = Runoff coefficient 
Q = Runoff 
(ii) By infiltration Capacity Curve 
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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. 
 
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. 
Direct Runoff: it is that part of the runoff which enters the stream immediately 
after the rainfall. It includes surface runoff, prompt interflow and rainfall on the 
surface of the stream. In the case of snow-melt, the resulting flow entering the 
stream is also a direct runoff, sometimes terms such as direct storm runoff are used 
to designate direct runoff. 
Base Flow: The delayed flow that reaches a stream essentially as groundwater flow 
is called base flow. 
(i) Direct runoff = surface runoff + Prompt interflow 
(ii) Direct runoff = Total runoff- Base flow 
(iii) Form Factor  where, A = Area of the catchment l Axial length of basin. 
(iv) Compactness coefficient  
re = Radius of equivalent circle whose Area is equal to area of catchment (A) 
(v) Elevation of the water shed, (z) 
 
Where, A1, A2 … Area between successive contours. 
Z1, z2 … mean elevation between two successive contours. 
Method to compute Runoff 
(i) By Runoff coefficient 
Q = KP where, p = precipitation 
K = Runoff coefficient 
Q = Runoff 
(ii) By infiltration Capacity Curve 
 
(iii) By Rational Formula 
 
Where, k = Runoff coefficient 
PC = Critical design rainfall intensity in cm/hr 
A = Area of catchment in hectare 
Qp = Peak discharge in m
3
/sec. 
(iv) Direction runoff depath  
Where, 
A = Area in KM
2
 
T = Time in hour 
Oi = ordinate of i
th
 element i.e. discharge in m
3
/sec. 
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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. 
 
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. 
Direct Runoff: it is that part of the runoff which enters the stream immediately 
after the rainfall. It includes surface runoff, prompt interflow and rainfall on the 
surface of the stream. In the case of snow-melt, the resulting flow entering the 
stream is also a direct runoff, sometimes terms such as direct storm runoff are used 
to designate direct runoff. 
Base Flow: The delayed flow that reaches a stream essentially as groundwater flow 
is called base flow. 
(i) Direct runoff = surface runoff + Prompt interflow 
(ii) Direct runoff = Total runoff- Base flow 
(iii) Form Factor  where, A = Area of the catchment l Axial length of basin. 
(iv) Compactness coefficient  
re = Radius of equivalent circle whose Area is equal to area of catchment (A) 
(v) Elevation of the water shed, (z) 
 
Where, A1, A2 … Area between successive contours. 
Z1, z2 … mean elevation between two successive contours. 
Method to compute Runoff 
(i) By Runoff coefficient 
Q = KP where, p = precipitation 
K = Runoff coefficient 
Q = Runoff 
(ii) By infiltration Capacity Curve 
 
(iii) By Rational Formula 
 
Where, k = Runoff coefficient 
PC = Critical design rainfall intensity in cm/hr 
A = Area of catchment in hectare 
Qp = Peak discharge in m
3
/sec. 
(iv) Direction runoff depath  
Where, 
A = Area in KM
2
 
T = Time in hour 
Oi = ordinate of i
th
 element i.e. discharge in m
3
/sec. 
 
Hydrograph 
A plot of the discharge in a stream plotted against time chronologically is called a 
hydrograph. 
Unit Hydrograph 
This method was first suggested by Sherman in 1932 and has undergone many 
refinements since then. 
A unit hydrograph is defined as they hydrograph of direct runoff resulting from one 
unit depath (1 cm) of rainfall excess occurring uniformly over the basin and at a 
uniform rate for a specified duration (D hours). 
Time invariance: The first basic assumption is that the direct-runoff response to a 
given effective rainfall in a catchment is time invariant. This implies that the DRH for 
a given ER in a catchment is always the same irrespective of when it occurs. 
Linear Response: The direct-runoff response to the rainfall excess is assumed to 
be linear. This is the most important assumptions of the unit-hydrograph theory. 
Linear response means that if an input X1(t) cause an output y1(t) an output x2(t) 
causes an output y2(t) then an input x1(t) + x2(t) gives an output y1(t) + y2(t). 
Consequently if x2(t) = rx1(t), then y2(t) = r1y1(t) thus, if the rainfall excess in a 
duration D is r times the unit depth, the resulting DRH will have ordinates bearing 
ratio r to those of the corresponding D-h unit hydrograph. 
 
Where,  Base period of T hr U.H 
tB = Base period of D hr U.H 
Also, T>D 
T = n.D where ‘n’ is an integer.